Discussion Papers » Full Abstract List

1. Sergiu Hart & Andreu Mas-Colell, Egalitarian Solutions of Large Games: I. The Asymptotic Approach (January 1992) Mathematics of Operations Research 20 (1995), 959-1002

This is the first of two papers concerned with the theory of egalitarian solutions for games in coalitional form with non-transferable utility (NTU) and a large number of players. This paper is devoted to the construction of egalitarian solutions for the limit situation with a continuum of players. We build on the concept of the Potential introduced in an earlier paper (Hart-Mas-Colell, 1989) and exploit partial differential equations techniques. In particular,we associate to the egalitarian solutions a variational problem which may be viewed as a generalization to the non-transferable utility context of the diagonal principle discovered by Aumann-Shapley (1974) in the transferable utility setting.

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2. Sergiu Hart & Andreu Mas-Colell, Egalitarian Solutions of Large Games: II. The Asymptotic Approach (January 1992) Mathematics of Operations Research 20 (1995), 1003-1022

This is the second of two papers developing the theory of Egalitarian solutions for games in coalitional form with non-transferable utility (NTU) and a large number of players. This paper is devoted to the study of the egalitarian solutions of finite games as the number of players increases. We show that these converge to the egalitarian solution of the limit game with a continuum of players as defined in our previous paper. The same convergence holds for the underlying potential functions.

 

3. Sergiu Hart & Andreu Mas-Colell, A Non-Cooperative Interpretation of Value and Potential (January 1992) In R. Selten (ed.) Rational Interaction (1992) Springer-Verlag 83-93

Given a (TU or NTU) game in characteristic form an auxiliary two-person zero sum game is presented whose maximin = minimax value is precisely the potential of the game. In the auxiliary game one of the players tries to buy off the members of the original game by choosing the order in which to approach them, while the other player sets the price of those members so as to make the expense incurred as high as possible.

 

4. Oscar Volij, Epistemic Conditions for Equilibrium in Beliefs without Independence (January 1992) Journal of Economic Theory 70 (1996), 391-406

Aumann and Brandenburger (1991) describe sufficient conditions on the knowledge of the players in a game for a Nash equilibrium to exist. They assumed, among other things, mutual knowledge of rationality. By rationality of a player, they mean that the action chosen by him maximizes his expected utility, given his beliefs. There is, however, no need to restrict the notion of rationality to expected utility maximization. This paper shows that their result can be generalized to the case where the players preferences over uncertain outcomes can be represented by a continuous function, not necessarily linear in the probabilities.

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5. Jose-Luis Ferreira, Itzhak Gilboa & Michael Maschler, Credible Equilibria in Games with Utilities Changing during the Play (February 1992) Games and Economic Behavior 10 (1995), 284-317

Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflict. In this paper we propose an extensive-form game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games.

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6. Nathan Linial, Games Computers Play: Game-Theoretic Aspects of Computing (February 1992) Handbook of Game Theory, Vol. II, R. J. Aumann & S. Hart (eds.), North-Holland (1994), 1340-1395

This is a survey of some connections between game theory and theoretical computer science. The main emphasis is on theories of fault-tolerant computing. The paper is largely self-contained.

 

7. Eyal Winter, Mechanism Robustness in Multilateral Bargaining (March 1992) Theory and Decision 40 (1996), 131-147

We describe a non-cooperative bargaining model for games in coalition form without transferable utility. In this model random moves determine the order by which the players take their actions. the specific assignment of probability distributions to these chance moves is called the mechanics of the bargaining. Within this framework we examine the relation between the property of mechanism robustness, and coalition stability of the bargaining outcome, by showing that these two properties boil down to be the same.

 

8. Sergiu Hart, On Prize Games (May 1992) Essays in Game Theory, N. Megiddo (ed.), Springer-Verlag (1994), 111-121

We consider the class of hyperplane coalition games (H-games): the feasible set of each coalition is a half-space, with a slope that may vary from one coalition to another. H-games have turned out in various approaches to the value of general non-transferable utility (NTU) games. In this paper we introduce a simple model -- prize games -- that generates the hyperplane games. next, we provide an axiomatization for the Maschler & Owen (1989) consistent value of H-games.

 

9. Ezra Einy & Bezalel Peleg, Coalition-Proof Communication Equilibria (July 1992) Social Choice Welfare and Ethics, W.A. Barnet, H. Moulin, M. Salles & N.J. Schofield (eds.), Cambridge University Press (1995), 289-300

We offer a definition of coalition-proof communication equilibria. The use of games of incomplete information is essential to our approach. Deviations of coalition are introduced after their players are informed of the actions they should follow. therefore, improvements by coalition on a given correlated strategy should always be made when their players have private information. Coalition-proof communication equilibria of two-person games are characterized by "information efficiency". Several examples are analyzed, including the Voting Paradox.

 

10. Sergiu Hart & Andreu Mas-Colell, A Model of n-Person Non-Cooperative Bargaining (July 1992) Pubslied as "Bargaining and Value" in Econometrica 64 (1996), 357-380

We present and analyze a model of non-cooperative bargaining among n participants, applied to games in cooperative form. This leads to a unified theory that has as special cases the Shapley value solution in the transferable utility case; the Nash bargaining solution in the pure bargaining case; and finally, the recently introduced Maschler-Owen consistent value solution in the general (non-transferable utility) case.

 

11. Avi Shmida & Bezalel Peleg, Strict and Symmetric Correlated Equilibria Are the Distributions of the ESS's of Biological Conflicts with Asymmetric Roles (August 1992) In W. Albers, W. Guth, P. Hammerstein, B. Moldovanu & E. van Damme (eds.), Understanding Strategic Interaction, Essays in Honor of R. Selten, (1997) Springer-Verlag 149-170

We investigate the ESS's of payoff-irrelevant asymmetric animal conflicts in Selten's (1980) model. We show that these are determined by the symmetric and strict correlated equilibria of the underlying (symmetric) two-person game. More precisely, the set of distributions (on the strategy space) of ESS's coincides with the set of strict and symmetric correlated equilibria (described as distributions). Our result enables us to predict all possible stable payoffs in payoff-irrelevant asymmetric animal conflicts using Aumann's correlated equilibria. Italso enables us to interpret correlated equilibria as solutions to biological conflicts: Nature supplies the correlation device as a phenotypic conditional behavior.

 

12. Yaacov Z. Bergman, Bayesian Non-Cooperative Foundations for Axiomatic Bargaining Theories (September 1992) 

In the first part, Rubinstein's two-person, complete information, alternating-offers bargaining model is extended to that of a fairly general contested pie which accommodates non-stationary preferences and physical joint payoffs with non-stationary constraints and outside options. The generalization in discrete-time and its continuous-time limit as bargaining rounds shorten are designed to bring the non-cooperative alternating-offers bargaining model to a form whose predictions can be compared and contrasted with those of the various axiomatic bargaining theories. This is done in the second part, where a bayesian approach is developed, which is used to optimally predict bargaining outcomes in game situations where full information about the bargaining procedure is lacking. This methodology gives rise to bayesian bargaining solution-functions, that generalize axiomatic bargaining solution-functions, thus setting the axiomatic theories on non-cooperative foundations.

 

13. David Budescu & Maya Bar-Hillel, To Guess or Not to Guess (September 1992) Journal of Educational Measurement 30 (1993), 277-291

Multiple choice tests that are scored by formula scoring typically include instructions that discourage guessing. In this paper we look at test taking from the normative and descriptive perspectives of judgment and decision theory. We show that for a rational test taker, whose goal is the maximization of expected score, answering is either superior or equivalent to omitting -- a fact which follows from the scoring formula. For test takers who are not fully rational, or have goals other than the maximization of expected score, it is very hard to give adequate formula scoring instructions, and the recommen-dation to answer under partial knowledge is problematic (though generally beneficial). Our analysis derives from a critical look at standard assumptions about the epistemic states, response strategies, and strategic motivations of test takers. In conclusion, we endorse the "number right" scoring rule, which discourages omissions, and is robust against variability in respondent motivations, limitations in judgments of uncertainty, and item vagaries.

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14. James W. Friedman & Avi Shmida, Pollination, Gathering Nectar, and the Distribution of Flower Species (October 1992) Journal of Theoretical Biology 175 (1995), 127-138

We present here a model of pollination having one species of bees and several species of flowers. Each flower species is distinguished by its rate of nectar production and the resources it devotes to display. The flowers and bees are assumed to have identical lifetimes that comprise a number of days within a single year. At the start of the year the bees in their naive phase are attracted to flowers according to the relative sizes of the flowers' displays; however, the bees soon become experienced and continually monitor the amounts of the nectar standing crops of each species, altering their visiting habits over time so that they always tend to visit most frequently the flower species having the largest nectar standing crop. This, in turn, tends equalize the nectar standing crop across species. From one year to the next the relative abundance of the flower species can change in accordance with the reproductive success of each species. This, in turn, depends upon the number of visits by bees to the flowers of each species, the amount of energy devoted to reproduction, and the relative abundance of each species in the preceding year. The model described below has been programmed so that it is possible to run simulations. We make no attempt to model the absolute number of bees or of flowers, but do assume the ratio of bees to flowers is the same from one season to the next. Within this model systematic deviations by the bees from apparently optimal foraging policies can be seen, due to monitoring by the bees, and also the ability to survive of large display flowers that produce no nectar ("cheaters") can be explained.

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15. Igal Milchtaich, Congestion Games with Player-Specific Payoffs (October 1992) Games and Economic Behavior 13 (1996), 111-124

A class of non-cooperative games in which the players share a common set of strategies is described. The payoff a player receives for playing a particular strategy depends only on the total number of playing the same strategy and decreases monotonously with that number in a manner which is specific to the particular player. It is shown that each game in this class possesses at least one Nash equilibrium in pure strategies.

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16. Nir Dagan & Oscar Volij, The Bankruptcy Problem: A Cooperative Bargaining Approach (November 1992) Mathematical Social Sciences 26 (1993), 287-297

We associate each bankruptcy problem with a bargaining problem and derive old and new allocation rules for the former by applying well known bargaining solutions to the latter.

 

17. Maya Bar-Hillel & Menahem Yaari, Judgments of Distributive Justice (September 1992) Psychological Perspectives on Justice. B. Mellers & J. Baron (eds.) Cambridge University Press (1993) Ch. 4, 55-84

The basic rule of distributive justice is the proportionality rule, which states that "Distributive justice involves a relationship between ... two persons, P1 and P2 one of whom can be assessed as higher than, or lower than, the other; and their two shares, or ... rewards, R1 and R2. The condition of distributive justice is satisfied when ... : P1/P2=R1/R2". (Homans, 1961). We studied this rule, in survey style, using cases such as the following: "suppose you have 12 grapefruit which you divide between Jones and Smith in as just a manner as possible. How should this be done ?". in our problems, either one or two goods were to be allocated between two recipients who differed on at most one dimension, either needs (e.g, Smith requires more grapefruit than Jones), beliefs (e.g, Smith believes that grapefruit are less nutritious than Jones believes them to be), or tastes (e.g, Smith enjoys grapefruit more than Jones). the results show that it is very hard to be more specific than the general formulation above without being ad hoc. For example, most people wish to allocate proportionately to need, only a minority wish to allocate proportionately to beliefs, and insofar as people wish to take tastes into consideration, they do so in a non-compensatory fashion. In other words, with regard to needs, less efficient extractors are awarded larger shares, but with regard to pleasure, more efficient extractors are awarded larger shares. Since real world distribution problems don't come neatly labelled as needs, tastes, etc., it is hard to predict or theorize what would be "just" in them.

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18. Uzi Motro & Avi Shmida, Near-Far Search: An Evolutionarily Stable Foraging Strategy (October 1992) Journal of Theoretical Biology 173 (1995), 15-22

This study addresses the momentary rules of foraging behavior on carpet inflorescences. It has long been suggested that patchiness in the distribution of nectar can give an advantage to near-far type of foraging strategies, that is, to foragers which search "near" (in the neighborhood of the last visited flower) as long as the nectar yield is high enough, and go "far" otherwise. Here we show that under certain conditions, such a strategy can be evolutionary stable. Furthermore, prior patchiness in the nectar distribution is not a necessary condition for the evolutionary stability of a near-far search. It turns out that during near-far foraging, some patchiness is created by the foraging process itself, which the near-far forager can exploit later on. To show the evolutionary stability of near-far search, various foraging strategies were compared, according to two, slightly different optimality criteria : the number of flowers emptied during a fixed length bout, and the number of flowers visited until total extraction of the entire inflorescence. We find that long enough bouts (in the case of a single forager) or a substantial probability of revisits to the same inflorescence (in the case of multipleforagers) are necessary for near-far to be an ESS.

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19. Bezalel Peleg & Stef Tijs, The Consistency Principle for Games in Strategic Form (November 1992) International Journal of Game Theory 25 (1996), 13-34

We start with giving an axiomatic characterization of the Nash equilibrium (NE) correspondence in terms of consistency, converse consistency, and one-person rationality. Then axiomatizations are given of the strong NE correspondence, the coalition proof NE correspondence and the semi-strong NE. In all these characterizations consistency and suitable variants of converse consistency play a role. Finally, the dominant NE correspondence is characterized. We also indicate how to generalize our results to Bayesian and extensive games.

 

20. Maya Bar-Hillel & Efrat Neter, How Alike Is It Versus How Likely Is It: A Disjunction Fallacy in Probability Judgments (November 1992) Journal of Personality and Social Psychology 65 (1993), 1119-1132

Formally, a conjunction fallacy and a disjunction fallacy cannot be distinguished. Both consist of a violation of the rule that an event cannot be more probable than another event which includes it. Hitherto, only a special kind of violation of this rule has been demonstrated, namely, that people sometimes judge the probability of A & B to be higher than the probability of A (Tversky & Kahneman, 1983). This study demonstrates a violation of the rule in a context that justifies the label disjunction fallacy. Subjects received brief case descriptions, and ordered seven categories according to one of four criteria for including the case as a member of the category : 1. probability of membership ; 2. willingness to bet on membership ; 3. inclination to predict membership ; 4. suitability for membership. The category list included nested pairs of categories, such as Brazil and South American country, or Physics and A Natural Science. The more inclusive category was a union of basic level sets like the smaller category. From a normative standpoint, the first two criteria are equivalent, and either ranking a category as more probable than its superordinate, or betting on it rather than on its superordinate, is fallacious. On the other hand, inclination to predict may be guided by the desire to be maximize informativeness rather than merely likelihood of being correct, and suitability needs to conform to no formal rule. Hence, with respect to these two criteria, such a ranking pattern is not fallacious. In spite of this crucial difference, subjects in all four groups rendered highly similar judgments, and the ranking of categories higher than their superodinates was not lower when it amounted to a fallacy than when it did not. The results support the representativeness thesis against some alternative interpretations.

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21. Motty Perry & Philip J. Reny, A Noncooperative View of Coalition Formation and the Core (November 1992) Econometrica 62 (1994), 795-818

Much of the core's appeal stems from the intuitive and natural story behind it, the story that first motivated F.Y Edgeworth in 1881. Thus the primary motivation for the core is noncooperative in nature. Nonetheless, the core is not a noncooperative solution concept. This is because, in particular, the possibilities for forming coalitions, and making offers and counteroffers, are not explicitly modeled. In this work, we provide a noncooperative implementation of the core. However, we do not merely implement the core. The nature of the game form employed is designed to reflect the motivating story as accurately as possible. The present results thus provide formal content to the usual intuitive justification for the core. In our view, the core would lose much of its appeal were it not possible to provide such a noncooperative foundation.

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22. Eyal Winter, Bargaining in Committees (December 1992) Published as "Negotiations in Multi-issue Committees", Journal of Public Economics 65 (1997), 323-342

We propose a non-cooperative treatment to the problem of collective decision making within committees, by modelling this process as a sequential bargaining game. We show that stationary subgame perfect equilibria of this bargaining game fully implements the core of the corresponding committee problem. We also discuss the inefficiency of non-stationary (subgame perfect) equilibria, and shortly refer to the problem of manipulability. Based on these results we then consider multi-issue committees, and address the problem of constructing agendas. In particular we will argue in favor of agendas where the important issues are discussed first.

 

23. Benny Moldovanu & Eyal Winter, Core Implementation and Increasing Returns to Scale for Cooperation (December 1992) Journal of Mathematical Economics 23 (1994), 533-548

In this paper we analyze a simple non-cooperative bargaining model for coalition formation and payoff distribution in games with coalition form. We show that under our bargaining regime a cooperative game is core implementable if and only if it possesses the property of increasing returns to scale for cooperation. Namely, the game is convex. This offers a characterization of a purely cooperative notion by means of its non-cooperative foundations.

 

24. Oscar Volij, Rationality without the Reduction Axiom (January 1993) 

Two results concerning the relation between rationality and equilibrium concepts in normal form games are generalized for the case where players do not satisfy the reduction of compound lotteries axiom. The crucial axiom of expected utility theory is the independence axiom which itself is a combination of two axioms: the compound independence axiom and the reduction of compound lotteries axiom. This paper is an effort to extend game theory to non-expected utility preferences. It generalizes the results of Aumann (1987) and Aumann and Brandenburger (1991) to games with players who do not satisfy the reduction of compound lotteries axiom. We show that the results of the above authors do not depend on the specific definition of rationality applied by them.

 

25. Sergiu Hart & Andreu Mas-Colell, Harsanyi Values of Large Economies: Non-Equivalence to Competitive Equilibria (February 1993) Games and Economic Behavior 13 (1996), 74-99

We consider the relations between the competitive equilibria in economies with many agents and the value allocations of the resulting coalition games. In particular, we provide a (smooth and robust) example where the "value principle" does not hold for the Harsanyi NTU-value: there is a unique competitive equilibrium, which however does not belong to the (non-empty) set of Harsanyi value allocations.

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26. Michael Landsberger & Shmuel Zamir, Loan Contracts with Collateral and Credit Rationing: A Signaling Approach (June 1993) 

Loan contracts with collateral are a common instrument to allocate credit to entrepreneurs who invest in risky projects. Collateral provides lenders with partial insurance against bad outcomes. Since typically, credit is provided under incomplete information about the nature of the project to be undertaken, we investigate in this paper whether collateral can be used as an instrument to identify projects which the bank may consider to be 'bad'. We prove that the ability of collateral to serve as a screening device depends on whether the entrepreneurs and the bank have similar ranking of project quality. If they do not, collateral is less effective as a signal. Within each regime, we identify conditions under which separating and pooling equilibria take place and we characterize the properties of these equilibria. When credit is scarce, we derive equilibria in which credit is rationed. A rationing regime eliminates pooling equilibria and generates more surplus to the bank on every project for which a loan was granted.

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27. Gary Bornstein & Roger Hurwitz, Team Games as Models of Intergroup Conflicts (June 1993) 

The internal problem of collective action that arises when groups, as opposed to individuals, are in conflict cannot be studied in the context of two-person games that treat the competing groups as unitary players. Traditional N-person games are also too restrictive for this purpose, since they ignore the conflict of interests between the groups. Because the intergroup conflict motivates the need for intragroup collective action, and the groups' respective success in mobilizing collective action determines the outcome of the intergroup competition, the intergroup and intragroup levels should be considered simultaneously. This paper: (a) proposes to model intergroup conflicts as team games (Palfrey & Rosenthal, 1983); (b) offers an initial taxonomy for this class of games; and (c) illustrates some applications for strategic analyses of intergroup conflict and political interactions.

 

28. Alon Harel, Efficiency and Fairness in Criminal Law: The Case for a Criminal Law Doctrine of Comparative Fault (June 1993) California Law Review 82 (1994), 1181-1222

Criminal law is traditionally described as directing its injunctions exclusively to actual or potential criminals. This article will argue that the traditional view is normatively unjustified both on efficiency and fairness grounds. To disregard the victim's conduct in determining the sanctions of criminals is both inefficient and unfair. It is inefficient because dismissing the behavior of the victim as irrelevant to the concerns of the criminal justice system does not provide optimal incentives for victims to take precautions against crime. It is unfair to disregard the victim's conduct because given the greater likelihood that careless potential victims (relative to cautious ones) will become actual victims of crime, the expected costs of protecting careless victims are higher than the expected costs of protecting cautious ones. Hence, under the current system, cautious victims are exploited for the sake of protecting careless ones. Both efficiency and fairness considerations suggest that criminal law should adopt a criminal law doctrine of comparative fault, under which criminals who act against careless victims would be exculpated or their punishment mitigated.

 

29. Maya Bar-Hillel & David Budescu, The Elusive Wishful Thinking Effect (July 1993) Thinking and Reasoning 1 (1995), 71-104

We define a desirability effect as the inflation of the judged probability of desirable events and the diminution of the judged probability of undesirable events. A series of studies designed to detect this effect is reported. In the first four experiments, subjects were presented with visual stimuli (a grid matrix in two colors, or a jar containing beads in two colors), and asked to estimate the probability of drawing at random one of the colors. The estimated probabilities for a defined draw were not higher when the draw entailed a gain than when it entailed a loss. In the fifth and sixth experiment, subjects read short stories each describing two contestants competing for some desirable outcome (e.g., firms competing for a contract). Some judged the probability that A would win, others judged the desirability that A would win. Story elements which enhanced a contestant's desirability without having normative bearing on its winning probability did not cause the favored contestant to be judged more likely to win. Only when a contestant's desirability was enhanced by promising the subject a monetary prize contingent on that contestant's win was there some slight evidence for a desirability effect: contestants were judged more likely to win when the subject expected a prize if they won than when the subject expected a prize if the other contestant won. In the last experiment, subjects estimated the probability of an over-20 point weekly change in the Dow Jones average, and were promised monetary prizes contingent on such a change either occurring, or failing to occur. They were also given a monetary incentive for accuracy. Subjects who desired a large change did not judge it more likely to occur than subjects who desired a small change. We discuss the difficulty of obtaining a desirability effect on probabilities, and argue that apparently wishful thinking-- in the form of optimistic cognitions -- can occur without affecting the evaluation of evidence.

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30. Frank Thuijsman, Bezalel Peleg, Mor Amitai & Avi Shmida, Automata, Matching and Foraging Behavior of Bees (August 1993) Journal of Theoretical Biology 175 (1995), 305-316

In this paper we discuss two types of foraging strategies for bees. Each of these explicit strategies explains that in the environment of a monomorphic bee community the bees will distribute themselves over the available homogeneous nectar sources according to the Ideal Free Distribution. At the same time these strategies explain that in single-bee experimental settings a bee will match, by its number of visits, the nectar supply from the available sources (the Matching Law). Moreover, both strategies explain that in certain situations the bees may behave as if they are risk averse, i.e spend more time on the flower type with the lower variance in nectar supply.

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31. Cristina Bicchieri & Gian Aldo Antonelli, Game-Theoretic Axioms for Local Rationality and Bounded Knowledge (September 1993) Journal of Logic, Language and Information 4 (1995), 1-23

We present an axiomatic approach for a class of finite, extensive form games of perfect iformation that makes use of notions like "rationality at a node" and "knowledge at a node". We show that, in general, a theory that is sufficient to infer an equilibrium must be modular: for each subgame G' of a game G the theory of game G must contain just enough information about the subgame G' to infer an equilibrium for G'. This means, in general, that the level of knowledge relative to any subgame of G must not be the same as the level of knowledge relative to the original game G. We show that whenever the theory of the game is the same at each node, a deviation from equilibrium play forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not cause any revision of the theory of the game.

 

32. Cristina Bicchieri, Counterfactuals, Belief Changes, and Equilibrium Refinements (September 1993) Philosophical Topics 21 (1993), 21-52

The literature on Nash equilibrium refinements provides several ways to check the stability of a Nash equilibrium against deviations from equilibrium play. Stability, however, is a function of how a deviation is being interpreted. An equilibrium that is stable under one interpretation may cease to be stable under another, but the refinement literature provides no general criterion to judge the plausibility of different interpretations of off-equilibrium play. This paper specifies a model of belief revision that minimizes the loss of useful information. When several interpretations are compatible with off-equilibrium play, the one that requires the least costly belief revision (in terms of informational value) will be chosen by the players. This model of belief revision generates a plausibility ranking of interpretations of deviations, hence it also provides a ranking of Nash equilibrium refinements.

 

33. Philip J. Reny, Eyal Winter & Myrna Holtz Wooders, The Partnered Core of a Game with Side Payments (September 1993) 

We introduce the notion of the partnered core of a game. A payoff is partnered if there are no asymmetric dependencies between any two players. A payoff is in the partnered core of a game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partner core satisfies additional properties.

 

34. Rudolf Avenhaus & Shmuel Zamir, Game-Theoretical Analysis of Material Accountancy (September 1993) 

Game theoretical models and analysis are provided for the sequential material accountancy problem. We model the n-period problem as a general sequential game played between the Operator and the Inspector. The game is analyzed through the solution concept of (Nash) equilibrium. We study several versions of the game corresponding to various assumption on the payoffs and the strategy sets. The first model solved is what we refer to as the static game. This is a game in which detection time is unimportant and the operator has to decide about his diversion plan at the beginning of the game (and he cannot deviate from it in a later stage). The solution of this game is obtained by its decomposition into two simpler game: a zero-sum game which determines the diversion plan and the statistical test (which turned out to be the CUMUFtest) and a second, non zero-sum game which determines the diversion probability and the false alarm probability. Next we return to the sequential game and prove that under the assumptions underlying the statistical analysis, the CUMUFtest emerges as part of the solution of the game i. e., as the inspector's strategy in equilibrium. Then we consider a `really sequential' game in which early detection is important and in which the operator can retreat (in view of high observed intermediate MUF) from completing a diversion plan that he have started. We find the structure of the equilibrium and the equilibrium equations of this game. These equations turn out to be too complex to be solved analytically, hence we provide numerical solutions which give interesting insight into the problem.

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35. Yaacov Z. Bergman, Option Pricing with Differential Interest Rates: Arbitrage-Bands Beget Arbitrage-Ovals (September 1993) Review of Financial Studies 8 (1995), 475-500

The classic Option Pricing Model is generalized to a more realistic, imperfect, dynamically incomplete capital market with different interest-rates for borrowing and for lending and a return differential between long and short positions in stock. It is found that in the absence of arbitrage opportunities, the equilibrium price of any contingent claim, or of a portfolio of such claims, must lie within an arbitrage-band. The boundaries of an arbitrage-band are computed as solutions to a quasi-linear partial-differential-equation, and, in general, each end-point of such a band depends on both interest-rates for borrowing and for lending. This, in turn, implies that the vector of concurrent equilibrium prices of different contingent-claims - even claims that are written on different underlying assets - must lie within a computable oval in the price space.

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36. Sergiu Hart, Aviad Heifetz & Dov Samet, 'Knowing Whether', 'Knowing That,' and the Cardinality of State Spaces (October 1993) Journal of Economic Theory 70 (1996), 249-256

We introduce a new operator on information structures which we call `Knowing whether' as opposed to the standard knowledge operator which may be called `Knowing that'. The difference between these operators is simple. Saying that an agent knows that a certain event occurred implies that this event indeed occurred, while saying that the agent knows whether an event occurred does not imply that the event occurred. (Formally, knowing whether X means that either it is known that X occurred or it is known that X did not occur). We show that iterating `Knowing whether' operators of different agents has a remarkable property that iterations of `knowing that' do not have. When we generate a sequence of events, starting with a given event and then applying `Knowing that' or `not knowing that' to the previous event, then the events in this sequence may be, somewhat surprisingly, contradictory. In contrast, any sequence of this type, generated with `knowing whether' and `not knowing whether' is never contradictory. We use this property of the `knowing whether' operator to construct a simple and natural state space and information structures for two agents, such that: (1) any two states are distinct relative to some interactive knowledge of a fixed event, (2) the space has the cardinality of the continuum. This result - originally proved in a complicated manner by Aumann (1989) - demonstrates the usefulness of the `knowing whether' operator.

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37. Nir Dagan, Roberto Serrano & Oscar Volij, A Noncooperative View of Consistent Bankruptcy Rules (December 1993) Games and Economic Behavior 18 (1997), 55-72

We introduce a game form that captures a non-cooperative dimension of the consistency property of bankruptcy rules. Any consistent and monotone rule is fully characterized by a bilateral principle and consistency. Like the consistency axiom, our game form, together with a bilateral principle, yields the respective consistent bankruptcy rule as a result of a unique outcome of subgame perfect equilibria. The result holds for a large class of consistent and monotone rules, including the Constrained Equal Award, the Proportional and many other well-known rules. Moreover, for a large class of rules, all the subgame perfect equilibria are coalition-proof.

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38. Murali Agastya, An Evolutionary Bargaining Model (December 1993) (revised in DP #61)

Varying quantities of a single good can be produced using at least two and at most n factors of production. The problem of allocating the surplus is studied in a dynamic model with adaptive behavior. Representatives for the factors (referred to as players) make wage demands based on precedent and ignorant of each others utilities for this good. Necessary and sufficient conditions are provided under which the long-run equilibria coincide with the core allocations. Moreover, allowing for the possibility of mistakes by the players, it is shown that the unique limiting stochastically stable outcome maximizes the product of the players' utilities subject to being in the core of the technology.

 

39. Yossi Feinberg, Evolutionary Selection of an Equilibrium (January 1994) 

We analyze the long-run behavior of a population engaged in a 2x2 evolutionary game undergoing mutation effects. We assume that the rates of mutation are exogenously and randomly determined. It is shown that if high mutation rates are possible but highly improbable, then the population evolves towards the risk dominant equilibrium (Harsanyi and Selten, 1988).

 

40. Avishai Margalit & Menahem E. Yaari, Rationality and Comprehension (February 1994) In K. J. Arrow, E. Colombatto, M. Perlman & C. Schmidt (eds.), The Rational Foundations of Economic Behavior, (1996) Macmillan, Basingstoke and London, 89-100

Devising a theory of knowledge for interacting agents has been on many people's minds recently. A near consensus has emerged, that the appropriate framework is a multi-agent version of C.I. Lewis's system S5 or one of S5's standard weakenings. In this essay, it is argued that such a framework cannot possibly be adequate, if it is to capture the intricacies of genuine inter-agent epistemics. Introducing a notion of "comprehension" -- knowledge which is non-sensory yet non-analytic -- may possibly be a remedy.

 

41. Avishai Margalit, The Ethics of Second-Order Beliefs (March 1994) 

The questions I address my paper are: Are people morally responsible for their beliefs? Are people's beliefs voluntary - can they be chosen and decided upon? What is the nature of the analogy between obligation of belief and the obligation of have certain emotions and not others? Can the skeptic suspend his belief? And finally, what is the sin of the heretic? I argue that it is right and proper for belief to be evaluated morally even if they are not voluntary and therefore not under our control. The key to my view is the fact that human beings possess second-order as well as first-order beliefs.

 

42. Itamar Pitowsky, On the Concept of the Proof in Modern Mathematics (March 1994) 

This paper deals with the attempts to characterize the set of all proofs in a given mathematical domain such as geometry or number theory. The characterization usually takes the form of a finite list of axiom schemata and inference rules, which is thought to be complete. A related effort, which originated with descartes, is to replace proofs - that is, reasoning about concepts and relations - by the solution of algebraic equations which are shown to be equivalent to the proofs. These formalist tendencies have always been opposed by intuitionists. I trace the dispute from descartes and Leibnitz through Kant all the way to its climax in the fifty years between the demonstration of the relative consistency of hyperbolic geometry and the discovery of Godel's theorems. My purpose is both historical and philosophical. On the historical level, I argue that Hilbert's program was not only a foundationalist effort to secure the consistency of mathematics. It was, in addition, an internal mathematical program in the aforementioned cartesian tradition of replacing proofs by computations. The demise of Hilbert's philosophical pretensions brought considerable and unexpected success to the mathematical program: Godel's theorem, which shows how to replace proofs by computations in very extensive domains of mathematics, and, ultimately, the Davis-Robinson-Putnam-Matijacevic theorem, which demonstrates, roughly, that every proof in those domains is equivalent to a solution of an algebraic (i.e. polynomial) equation. The fact that the notion of proof in number theory is indefinitely extensible (by Godel's theorem) depends on a complete characterization of the concept of `computation' (the Church-Turing thesis). On the philosophical level, I argue that this dependence undermines some contemporary intuitionist claims (by Weyl and Dummett) which are based on Godel's results.

 

43. Nir Dagan, Consistency, Decentralization and the Walrasian Allocations Correspondence (January 1994) 

In this paper we study finite-agent exchange economies. We extend the classical model by adding an imports-exports vector, which defines the markets clearing conditions of the economy. Equipped with this new definition, self-consistency properties are naturally defined. We show that the Core correspondence and the Walrasian allocations correspondence are self-consistent. In addition, we present an axiomatic characterization of the Walrasian allocations correspondence for a class of convex and smooth economies. All the axioms presented in the characterization are satisfied by the Core, except for a converse-consistency property, which can be interpreted as a requirement of decentralization.

 

44. Nir Dagan, New Characterizations of Old Bankruptcy Rules (January 1994) Social Choice and Welfare 13 (1996), 51-59

This paper presents axiomatic characterizations of two bankruptcy rules discussed in Jewish legal literature: the Constrained Equal Awards rule and the Contested Garment principle (the latter is defined only for two-creditor problems). A major property in these characterizations is independence of irrelevant claims, which requires that if an individual claim exceeds the total to be allocated it should be considered irrelevant.

 

45. Daniel Granot, Michael Maschler, Guillermo Owen & Weiping R. Zhu, The Kernel/Nucleolus of a Standard Tree Game (March 1994) International Journal of Game Theory 25 (1996), 219-244

In this paper we characterize the nucleolus (which coincides with the kernel) of a tree enterprise. We also provide a new algorithm to compute it, which sheds light on its structure. We show that in particular cases, including a chain enterprise one can compute the nucleolus in O(n) operations, where n is the number of vertices in the tree.

 

46. Gary Bornstein, Ido Erev & Harel Goren, The Effect of Repeated Play in the IPG and IPD Team Games (March 1994) Journal of Conflict Resolution 38 (1994), 690-707

Repeated interaction in intergroup conflict was studied in the context of two team games: The Intergroup Public Goods (IPG) game and the Intergroup Prisoner's Dilemma (IPD) game. The results reveal (a) a main effect for game type; subjects were twice as likely to contribute towards their group effort in the IPG game than in the IPD game, and (b) a game-type X time interaction; subjects contributed less over time in the IPD game while continuing to contribute at about the same rate in the IPG game. The second finding supports the hypothesis that subjects learn the structure of the game and adapt their behavior accordingly, and is compatible with a simple learning model (Roth & Erev, 1993) which assumes that choices that have led to good outcomes in the past are more likely to be repeated in the future. A reciprocal cooperation hypothesis which assumes that players make their choices contingent on the earlier choices of the other players received little support.

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47. Pradeep Dubey & Abraham Neyman, An Equivalence Principle for Perfectly Competitive Economies (May 1994) Journal of Economic Theory 75 (1997), 314-344

It is a striking fact that different solutions become equivalent in the setting of perfectly competitive economies. We provide an axiomatic approach to this equivalence phenomenon. A solution is viewed as a correspondence which maps each economy to a subset of its individually rational and Pareto-optimal allocations. Four axioms are placed on the correspondence: anonymity, equity, consistency and restricted continuity. It is shown that the axioms categorically determine the Walrasian correspondence. The equivalence of other solutions, such as the core or value allocations, now follows by checkingthat they too satisfy the axioms.

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48. Dieter Balkenborg & Eyal Winter, A Necessary and Sufficient Epistemic Condition for Playing Backward Induction (June 1994) Journal of Mathematical Economics 27 (1997), 325-345

In an epistemic framework due to Aumann we characterize the minimal condition on the rationality of the players that implies backward induction in perfect information games in agent form. This condition requires each player to know that the players are rational at later, but not at previous decision nodes.

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49. Eyal Winter, Voting and Vetoing (June 1994) American Political Science Review 90 (1996), 813-823

The consequences of veto power in committees is analyzed using the approach of non-cooperative bargaining theory. It is first shown that in equilibrium non-veto players do not share in the benefits gained by the decision making of the committee, i.e, in every equilibrium outcome of the bargaining game non-veto players earn zero. Some measures for reducing the excessive power of veto members in committees are analyzed. Specifically, we study the effects of imposing a deadline on negotiations and of expanding the committee by increasing the number of non-veto players.

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50. Nir Dagan, On the Least Sacrifice Principle in Taxation (June 1994) 

Utilitarian philosophers and economists recommended that when applying taxation programs, government should minimize the sum total of sacrifice made by individuals. This paper presents a model and an axiom system of taxation policies, in which the Least Sacrifice Principle is derived. A key axiom in our characterization is self-consistency. Other relations between self-consistency and welfare maximization in our model and in other models are also discussed.

 

51. Nir Dagan & Oscar Volij, Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems (June 1994) International Journal of Game Theory 26 (1997), 11-26

We analyze the problem of extending a given bilateral principle of justice to a consistent n-creditor bankruptcy rule. Based on the bilateral principle, we build a family of binary relations on the set of creditors in order to make bilateral comparisons between them. We find that the possibility of extending a specific bilateral principle of justice in a consistent way is closely related to the quasi-transitivity of the binary relations mentioned above.

 

52. Dieter Balkenborg, Strictness and Evolutionary Stability (July 1994) 

The notion of a strict equilibrium set is introduced as a natural extension of the notion of a strict equilibrium point. The evolutionary stable sets of a truly asymmetric contest are shown to be behaviorally equivalentto the strict equilibrium sets of an "agent representation" of the contest. Using variants of the replicator dynamic we provide dynamic characterizations of strict equilibrium sets. We do this both for truly asymmetric contests and for arbitrary normal form games modelling conflicts between several distinct species.

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53. Sergiu Hart & Dov Monderer, Potentials and Weighted Values of Non-Atomic Games (August 1994) Mathematics of Operations Research 22 (1997), 619-630

The "potential approach" to value theory for finite games was introduced by Hart and Mas-Colell (1989). Here this approach is extended to non-atomic games. On appropriate spaces of differentiable games there is a unique potential operator, that generates the Aumann and Shapley (1974) value. As a corollary we obtain the uniqueness of the Aumann - Shapley value on certain subspaces of games. Next, the potential approach is applied to the weighted case, leading to "weighted non-atomic values". It is further shown that the asymptotic weighted value is well-defined, and that it coincides with the weighted value generated by the potential.

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54. Jinpeng Ma, Infinitely Repeated Rental Model with Incomplete Information (June 1994) Economics Letters 49 (1995), 261-266.

In an infinitely repeated rental model with two types of buyer and no discounting, the set of all Nash equilibrium payoffs for the seller and the buyer is characterized.

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55. Jinpeng Ma, Stable Matchings and Rematching-Proof Equilibria in a Two-Sided Matching Market (June 1994) Journal of Economic Theory 66 (1995), 352-369

In this paper we introduce the notion of a rematching-proof equilibrium for a two-sided matching market to resolve Roth's open question: What kind of equilibria of the game induced by any stable mechanism with respect to misreported profiles produce matchings that are stable with respect to the true profile. We show that the outcome of a rematching-proof equilibrium is stable with respect to the true profile even though the equilibrium profile may contain misreported preferences. We show that a rematching-proof equilibrium exists. Moreover, we extend these two results to the strong equilibria. Furthermore, the Nash equilibria in Roth [11] are shown to be rematching-proof equilibria. The relation between the rematching-proof equilibria and the strong equilibria is discussed as well.

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56. Vijay Krishna & John Morgan, An Analysis of the War of Attrition and the All-Pay Auction (August 1994) 

We study the war of attrition and the all-pay auction when players' signals are affiliated and symmetrically distributed. We (a) find sufficient conditions for the existence of symmetric monotonic equilibrium biddingstrategies; and (b) examine the performance of these auction forms in terms of the expected revenue accruing to the seller. Under our conditions the war of attrition raises greater expected revenue than all other known sealed did auction forms.

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57. Robert J. Aumann & Adam Brandenburger, Epistemic Conditions for Nash Equilibrium (October 1994) Econometrica 63 (1995), 1161-1180

Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe - about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the part of other players, as to what a player will do. Common knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures implies that the conjectures form a Nash equilibrium. When n % 3 and there is a common prior, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures, imply that the conjectures form a Nash equilibrium. Examples show the results to be tight.

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58. Ezra Einy, Ron Holzman & Benyamin Shitovitz, Core and Stable Sets of Large Games Arising in Economics (November 1994) Journal of Economic Theory 68 (1996), 200-211

It is shown that the core of a non-atomic glove-market game which is defined as the minimum of finitely many non-atomic probability measures is a von-Neumann Morgenstern stable set. This result is used to characterize some stable set of large games which have a decreasing returns to scale property. We also study exact non-atomic glove-market games. In particular we show that in a glove-market game which consists of the minimum of finitely many mutually singular non-atomic measures, the core is a von-Neumann Morgenstern stable set if the game is exact. We also discuss the intuitive appeal of the equivalence of the core and stable set. We do this by employing the theory of social situations [5] and highlighting the negotiation processes that underlie these two notions.

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59. Robert J. Aumann, Backward Induction and Common Knowledge of Rationality (December 1994) Games and Economic Behavior 8 (1995), 6-19

We formulate precisely and prove the proposition that if common knowledge of rationality obtains in a game of perfect information, then the backward induction outcome is reached.

 

60. Gonni Orshan, Non-Symmetric Prekernels (December 1994) 

A "symmetry" property, either in the version of "equal treatment" or in the version of "anonymity", is one of the standard intuitively acceptable properties satisfied by most well known solution concepts in game theory. However,there are many instances where symmetry is counterintuitive. This paper analyzes non-symmetric prekenels: solution concepts that satisfy Peleg's axioms for the prekernel [1986, 1987], with equal treatment replaced by the requirement that the solution of each 2-person game consists of a unique point. It is shown that non-symmetric prekernels do exits and then a full characterization is provided.

 

61. Murali Agastya, An Evolutionary Bargaining Model (revision of Discussion Paper #38) (December 1994) 

A non-negative function f defined on the class of subsets of a finite set of factors of production describes the production possibilities at each date. The problem of allocating the surplus among the factors is studied in a dynamic learning model. Representatives for the factors (called players) make wage demands naively based on precedent and ignorant of each others' utilities for this good. A global convergence result shows that players learn to reach some (and only a) core allocation in the long run. If players make mistakes however, only a strict subset of the core allocations are likely, i.e., stochastically stable. The main result shows that in the limit, these stable allocations for a particular set of players, converge to the allocation that maximizes the product of all the players' utilities over core allocations.

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62. Murali Agastya, Ordinality of the Shapley Value (December 1994) 

In Roth (1977) it is argued that the Shapley value is the cardinal utility of playing a game and it inherits properties used to define the underlying game itself. Implicit in this statement is the assumption that the TU game is generated by allowing for lotteries over an underlying set of alternatives.However, often there is a single numeraire good that can generate a game. In such instances, it is unclear why the utility of playing a game is cardinal when the preferences for the underlying good are ordinal. This paper presents a framework in which the Shapley value emerges as the representation of a preference ordering over a set of games. This representation is unique only up to a positive monotone transformations thereby establishing the ordinality of the value.

 

63. Murali Agastya, Perseverance, Information and Stochastically Stable Outcomes (December 1994) 

One bargainer from a finite population X, is matched at random with a bargainer from another finite population Y. They simultaneously precommit to "minimal" shares of a unit surplus. Populations differ in their degree of perseverance, parameterized by c E (0,1). If the players precommit to x and y such that x + y % 1, then player i gets his demand xi as well as a fraction % i of the unbargained surplus (1 - x - y). If x + y % 1, they get nothing.When players play adaptively and sometimes make errors as in Young (1993b), in the long run, a single division of surplus is observed most often. This is close to the asymmetric Nash bargaining solution with the weights (1 - % x) and (1 - %y). The surprise here is that the population that seemingly does well in the one shot encounters loses in the long run.

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64. Jacob Glazer & Motty Perry, Virtual Implementation in Backwards Induction (December 1994) Games and Economic Behavior 15 (1996), 27-32

We examine a sequential mechanism which is a simple modification of the normal form mechanism introduced by Abreu and Matsushima (1992). We show that almost any social choice function can be virtually implemented via a finite sequential game of perfect information. The solution concept assumed is Subgame Perfect Equilibrium or Iterative Elimination of Strictly Dominated Strategies. In particular, any social choice function that is virtually implementable via the Abreu-Matsushima's mechanism is also virtually implementable by a sequential mechanism.

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65. Abraham Neyman, Cooperation in the Repeated Prisoners' Dilemma when the Number of Stages Is Not Commonly Known (January 1995) (revised in DP #162)

It has often been observed that cooperative behavior emerges in actual play of the repeated prisoners' dilemma. This observation seems to be in conflict with the fact that, in any finite repetition of the prisoners' dilemma, all Nash equilibria (and even all correlated equilibria) lead to the non-cooperative outcome in each stage. In this paper we show that a very small departure from the common knowledge assumption on the number, T, of repetitions already enables cooperation. More generally, with such a departure, any feasible individually-rational outcome of any one-shot game can be approximated by a Nash equilibrium of a finitely-repeated version of that game. The sense in which the departure from common knowledge is "small" is as follows: (i) With probability one, the players know T with precision +- 1. (ii) With probability 1 - %, the players know T precisely; moreover, this knowledge is mutual to degree %T. (iii) the deviation of T from its expectation is extremely small.

 

66. Sergiu Hart & Andreu Mas-Colell, Bargaining and Value (January 1995) Econometrica 64 (1996), 357-380

We present and analyze a model of non-cooperative bargaining among n participants, applied to situations describable as games in coalitional form. This leads to a unified theory that has as special cases the Shapley value in the transferable utility case, the Nash bargaining solution in the pure bargaining case, and the recently introduced Maschler-Owen consistent value solution in the general (non-transferable utility) case.

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67. Robert J. Aumann, Interactive Epistemology (February 1995) International Journal of Game Theory 28 (1999), 263-314

Formal Interactive Epistemology deals with the logic of knowledge and belief when there is more than one agent or "player". One is interested not only in each person's knowledge about substantive matters, but also in his knowledge about the others' knowledge. These notes examine two parallel approaches to the subject. The first is the semantic approach, in which knowledge is represented by a space % of states of the world, together with partitions %i of % for each player i; the atom of %i containing a given state % of the world represents the set of those states that i cannot distinguish from %. The second is the syntactic approach, in which knowledge is represented by abstract formulas constructed according to certain syntactic rules. These notes examine the relation between the two approaches, and show that they are in a sense equivalent. In game theory and economics, the semantic approach has heretofore been most prevalent. A question that often arises in this connection is whether, in what sense, and why the space % and the partitions %i can be taken as given and commonly known by the players. An answer to this question is provided by the syntactic approach. Other topics that are taken up include various formalizations of "common knowledge", and the "Agreement Theorem" of J. Cave and M. Bacharach. The notes end with an application of these ideas to the context of probabilistic beliefs.

 

68. Rudolf Avenhaus, Bernhard von Stengel & Shmuel Zamir, Inspection Games (February 1995) In R. J. Aumann & S. Hart (eds.), Handbook of Game Theory, Vol. III, (2002) North-Holland

Starting with the analysis of arms control and disarmament problems in the sixties, inspection games have evolved into a special area of game theory with specific theoretical aspects, and, equally important, practical applications in various fields of human activities where inspection is mandatory. In this contribution, a survey of applications is given first. Then, the general problem of inspection is presented in a game theoretic framework as an extension of a statistical hypothesis presented in a testing problem. Using this framework, two important models are solved: material accountancy and dataverification. A second important aspect of inspection games are limited inspection resources that have to be used strategically. This is presented in the context of sequential inspection games, where many mathematically challenging models have been studies. Finally, the important concept of leadership, where the inspector becomes a leader by announcing and committing himself to his strategy, is shown to apply naturally to inspection games.

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69. Abraham Neyman, Finitely Repeated Games with Finite Automata (June 1995) (revised in DP #161)

The paper studies the implication of bounding the complexity of the strategies players may select on the set of equilibrium payoffs in repeated games. The complexity of a strategy is measured by the size of the minimal automaton that can implement it. A finite automaton is an automated machine that implements a strategy; it has a finite number of states and an initial state. It prescribes the action to be taken as a function of the current state and a transition function changing the states of the automaton as a function of its current state and the present actions of the other players. The size of an automaton is its number of states. The Main results imply in particular that in two person repeated games, the equilibrium payoffs of a sequence of such games, G(n), n = 1,2,..., converges as n goes to infinity to the individual rational and feasible payoffs of the one shot game, whenever the bound on one of the two automata sizes is polynomial or subexponential in n and the length of the game and the bounds of the automata sizes are at least n. A special case of such result justifies cooperation in the finitely repeated prisoner's dilemma, without departure from strict utility maximization or complete information, but under the assumption that there are bounds (possibly very large) to the complexity of the strategies that the players may use.

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70. Jean-Francois Mertens & Shmuel Zamir, Incomplete Information Games and the Normal Distribution (February 1995) 

We consider a repeated two-person zero-sum game in which the payoffs in the stage game are given by a 2 % 2 matrix. This is chosen (once) by chance, at the beginning of the game, to be either G1 or G², with probabilities p and 1 - p respectively. The maximizer is informed of the actual payoff matrix chosen but the minimizer is not. Denote by vn(p) the value of the n -times repeated game (with the payoff function defined as the average payoff per stage), and by v%(p) the value of the infinitely repeated game. It is proved that vn(p)=v%(p) + %(p)%(p)/%n + %%1/%n% , where %(p) is on appropriately scaled normal distributiondensity function evaluated at its p-quantile, and the coefficient K(p) is either 0 or the absolute value of a linear function in p.

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71. Maya Bar-Hillel & Efrat Neter, Why Are People Reluctant to Exchange Lottery Tickets? (March 1995) Journal of Personality and Social Psychology 70 (1996), 17-27

In a series of experiments, we demonstrate that people are reluctant to exchange lottery tickets. In other words, when given a small incentive to exchange a lottery ticket with which they had just been endowed for a different one, with the same probability of winning the same prize, only about 50% choose to do so. In contrast, when given the same incentive to exchange a pen with which they had just been endowed for another pen just like it, over 90% choose to do so. We discuss -- and rule out -- a series of possible explanations for this effect, including: distorted subjective probabilities; fear of finding out that you gave up a wining ticket; lack of sufficient incentive (i.e.,transaction cost); general confusion or "paranoia"; etc. We conclude that people will not exchange ex ante identical tokens of the same type unless the two tokens will be identical ex post as well. A lottery ticket with which one has been endowed becomes at once the status quo, or reference point, with respect to which changes are evaluated for possible gains and losses. Since losses loom larger than gains, two lottery tickets which are symmetrical before they pass into one's possession are no longer symmetrical once one of them becomes one's own.

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72. James A. Sundali, Amnon Rapoport & Darryl A. Seale, Coordination in Market Entry Games with Symmetric Players (March 1995) Organizational Behavior and Human Decision Processes 64 (1995), 203-218

We report the results of two experiments designed to study tacit coordination in a class of market entry games with linear payoff functions, binary decisions, and zero entry costs, in which each of n = 20 players must decide on each trial whether or not to enter a market whose capacity is public knowledge. The results show that although the subjects differ considerably from one another in their decision policies, tacit coordination emerges quickly on the aggregate level and is accounted for most successfully by the Nash equilibrium solution for noncooperative n-person games.

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73. Amnon Rapoport, Darryl A. Seale & James A. Sundali, Equilibrium play in large group market entry games (March 1995) Management Science 44 (1998), 119-141

Coordination behavior is studies experimentally in a class of market entry games featuring symmetric players, complete information, zero entry costs, and several randomly presented values of the market capacity. Once the market capacity, c, becomes common knowledge, each player must decide privately whether to enter the market and receive a payoff which increases in the difference between c and the number of entrants, m, or stay out. Payoffs forstaying out are either positive, giving rise to the domain of gains, or negative, giving rise to the domain of losses. The major findings are substantial individual differences in decision policies, which do not diminish with practice, and aggregate group behavior which is organized extremely well in both the domains of gains and loses by the Nash equilibrium solution.

 

74. Daniel Rothenstein, A Two-Period Pollution Safeguards Game with n Operators (March 1995) 

The environmental need to control the quality of the air is represented by a multi-players sequential game. One model is a two period game with n + 1 players, of which n are operators and one is an inspector. The game is analyzed via the solution concept of the strategies equilibrium (Nash equilibrium). The second model assumes that all operators are identical,i.e. the payoffs are the same to all operators. The equations that describe the Nash equilibrium, are solved analytically under this assumption, and enable us to compare games with a different number of operators (n). Numerical solutions are included. A discussion of the advantages and disadvantages of individual punishment vs. collective punishment appears in the last section. The model includes a parameter which varies from full individual punishment when the inspector raises an alarm (i.e. only the operators that acted illegally are fined), to full collective punishment (i.e. all operators are fined regardless their actions). Numerical results are added.

 

75. Vijay Krishna & Robert W. Rosenthal, Simultaneous Auctions with Synergies (March 1995) 

Motivated by recent auctions of licenses for the radio-frequency spectrum, we consider situations where multiple objects are auctioned simultaneously by means of a second-price, sealed-bid auction. For some buyers, called global bidders, the value of multiple objects exceeds the sum of objects' values separately. Others, called local bidders, are interested in only one object. In a simple independent private values setting, we (a) characterize an equilibrium that is symmetric among the global bidders; (b) show that the addition of bidders often leads to less aggressive bidding; and (c) compare the revenues obtained from the simultaneous auction to those from its sequential counterpart.

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76. Robert J. Aumann, Rationality and Bounded Rationality (May 1995) In S. Hart & A. Mas-Colell (eds.) Cooperation: Game Theoretic Approaches. Berlin: Springer (1997) 219-232; also in Frontiers of Research in Economic Theory, The Nancy L. Schwartz Memorial Lectures, 1983-1997

A survey of bounded rationality models and ideas in Game Theory. Topics covered include: The evolutionary approach to optimization -- and specifically to game theory -- and its implications for the idea of bounded rationality; evolutionary dynamics; "rule rationality" as opposed to "act rationality"; "trembles" and refinements in general; "crazy" perturbations; failure of common knowledge of rationality; limiting average payoff in infinitelyrepeated games; epsilon equilibria; players modeled as computers, finite state automata, or Turing machines; paradoxes (such as Ellsberg or Allais); laboratory experiments; and finally, an open problem.

 

77. Yaacov Z. Bergman, Bruce D. Grundy & Zvi Wiener, General Properties of Option Prices (May 1995) Journal of Finance 51 (1996), 1573-1610

This article establishes that, in a one-dimensional diffusion world, any contingent claim's delta is bounded by its delta at maturity and, if its payoff is convex, its current value is convex in the underlying's value. A decline in the present value of the exercise price can be associated with a decline in a call's price. Bounds on call prices and deltas are derived for the case when the underlying's volatility is bounded. If the underlying follows a multi-dimensional diffusion (a stochastic volatility world), or a discontinuous or non-Markovian process, call prices can be decreasing, concave function of the underlying's value.

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78. Robert J. Aumann, Reply to Margalit and Yaari (June 1995) In K. J. Arrow, E. Colombatto, M. Perlman & C. Schmidt (eds.), The Rational Foundations of Economic Behavior (1996), Macmillan, Basingstoke and London 106-107

A reply to Margalit and Yaari's paper "Rationality and Comprehension", in which they comment on my papers "Agreeing to disagree" [1] and "Notes on Interactive Epistemology" [2]. Inter alia, we point out that contrary to Margalit and Yaari's claim, in [1] the agents need not condition on the same events; and in [2], the state space is not assumed as analytic knowledge, but is derived. In addition, a simple resolution of the "hangman's paradox" is offered.

 

79. Mathias Risse, A Syntactic Model of Forgetting: A Partially Solved Problem (June 1995) 

We look at a set % of states of the world which are defined as maximal consistent lists of formulae formed in a language which contains a knowledge operator ki for each agent i. The states of the world induce an information partition for each agent i such that all those % % % are included in the same information cell which contain the same range of knowledge for this agent (this range of knowledge we will call the agent's ken). We can then ask what it means that some agent i forgets which one of a variety of kens he has. This question can be answered easily if we use states of the world as primitives: then the answer is just to take a union over information cells. This does not make sense any more when states of the world are lists of formulae. We find a solution to this question for the case of one agent and show why the same solution cannot be used for the case of more than one agent. In an appendix, we apply results obtained before to analyze the j-operator (the knowing-whether operator). The larger context in which our question arose was to prove the Bachrach-Cave Agreement-Theorem in a model where states of the world are not primitives.

 

80. Abraham Neyman, Correlated Equilibrium and Potential Games (July 1995) International Journal of Game Theory 26 (1997), 223-227

Any correlated equilibrium of a strategic game with bounded payoffs and convex strategy sets which has a smooth concave potential, is a mixture of pure strategy Nash equilibrium. If moreover, the strategy sets are compact and the potential is strictly concave, then the game has a unique correlated equilibrium.

 

81. Daniel Granot & Michael Maschler, The Reactive Bargaining Set: Structure, Dynamics and Extension to NTU Games (August 1995) International Journal of Game Theory 26 (1997) 75-95.

The reactive bargaining set (Granot [1994]) is the set of outcomes for which no justified objection exists. Here, in a justified objection the objector first watches how the target tries to act (if he has such an option), and then reacts by making a profit and ruining the target's attempt to maintain his share. In this paper we explore properties of the reactive bargaining set, set up the system of inequalities that defines it, and construct a dynamic system in the sense of Stearn's transfer scheme that leads the players to this set. We also extend the definition of the reactive bargaining set to NTU games in a way that keeps it nonempty. To shed light on its nature and its relative ease of computation, we compute the reactive bargaining set for games that played important role in the game theory literature.

 

82. Abraham Neyman & Sylvain Sorin, Equilibria in Repeated Games of Incomplete Information: The Deterministic Symmetric Case (July 1995) In T. Parthasaraty et al. (eds.) Game-Theoretic Applications to Economics and Operations Research ( ) Kluwer Academic Press

Every two person game of incomplete information in which the information to both players is identical and deterministic has an equilibrium.

 

83. Yossi Feinberg, A Converse to the Agreement Theorem (November 1995) 

In Aumann (1976) - "Agreeing to Disagree" - it is shown that if there is a common prior then common knowledge of disagreement is impossible. This paper studies the converse proposition. The lack of a common prior is shown to yield common knowledge of disagreement in a variety of cases. However, an example demonstrates that this result cannot be generalized.

 

84. Eytan Sheshinski, On Atmosphere Externality and Corrective Taxes (October 1995) Journal of Public Economics 88 (2004), 727-734

It has been argued that in the presence of an `Atmosphere Externality' and competitive behavior by households, a uniform commodity tax on an externality - generating good attains the first best. It is demonstrated, however, that if income redistribution is desirable then personalized taxes are required for a second-best optimum. Each of these taxes is the sum of a uniform (across households) tax and a component, positive or negative, which depends on the household's income and demand elasticities. Second-best optimal indirect taxes and rules for investment in externality-reducing measures are also considered.

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85. Yossi Feinberg, An Incomplete Cooperation Structure for a Voting Game Can Be Stable (November 1995) Games and Economic Behavior 24 (1998), 2-9

Aumann and Myerson (1988) defined a linking game leading to the formation of cooperation structures. They asked whether it is possible for a simple game to have a stable structure in which no coalition forms, i.e., in which the cooperation graph is not internally complete. We answer this question affirmatively; specifically, we present a simple proper weighted majority game with a connected incomplete structure, and prove it to be stable.

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86. Abraham Neyman & Sylvain Sorin, Equilibria in Repeated Games of Incomplete Information: The General Symmetric Case (November 1995) International Journal of Game Theory 27 (1998), 201-210.

Every two person repeated game of symmetric incomplete information in which the signals sent at each stage to both players are identical and generated by a state and moves dependent probability distribution on a given finite alphabet has an equilibrium payoff.

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87. Igal Milchtaich, The Value of Nonatomic Games Arising from Certain Noncooperative Congestion Games (December 1995) Published as: "Social Optimality and Cooperation in Nonatomic Congestion games", Journal of Economic Theory 114 (2004), 56-87

For a class of nonatomic congestion games, two solution concepts, a noncooperative one and a cooperative one, are compared. Each player in the game chooses one of several common facilities. The player's payoff is the difference between the reward and the cost associated with choosing that facility. The rewards are fixed and player-specific. The costs are uniform, but variable: they strictly increase with the measure of the set of players using the facility. The noncooperative solution of the game is the (unique) Nash equilibrium outcome. The cooperative one is the Aumann-Shapley value of the cooperative game that results when players are willing to cooperate in order to minimize the total utility. Using a new result in the theory of values of nonatomic games, we derive a formula for the value. We show that there is exactly one case in which the Nash equilibrium outcome andthe value always coincide: this is the case in which the costs increase logarithmically with the measure of the set of users.

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88. Abraham Neyman, Cooperation, Repetition and Automata (November 1995) In S. Hart & A. Mas-Colell (eds.), Cooperation: Game-Theoretic Approaches, (1995) Springer-Verlag 233-255

This chapter studies the implications of bounding the complexity of players' strategies in long term interactions. The complexity of a strategy is measured by the size of the minimal automaton that can implement it. A finite automaton has a finite number of states and an initial state. It prescribes the action to be taken as a function of the current state and its next state is a function of its current state and the actions of the other players. The size of an automaton is its number of states. The results study the equilibrium payoffs per stage of the repeated games when players' strategies are restricted to those implementable by automata of bounded size.

 

89. Igal Milchtaich, Vector Measure Games Based on Measures with Values in an Infinite Dimensional Vector Space (December 1995) Games and Economic Behavior 24 (1998), 25-46

The following generalization of a theorem of Aumann and Shapley is proved: A vector measure game of the form f°%, where % is a nonatomic banach-space measure of bounded variation and f is a weakly continuously differentiable real-valued function defined on the closed convex hull of the range of % such that f(0)=0, is in pNA. If the game is monotonic, then the conclusion holds even if at 0 f is only continuous, and not differentiable. The value of the game is given by the diagonal formula. These results are used for giving a new, relatively short, proof to the result that, under certain conditions, a market game is in pNA.

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90. Mor Amitai, Cheap-Talk with Incomplete Information on Both Sides (January 1996) 

We provide a characterization of the set of equilibria of two-person cheap-talk games with incomplete information on both sides. Each equilibrium generates a martingale with certain properties and one can obtain an equilibrium from each such martingale. Moreover, the characterization depends on the number of possible messages. It is shown that for every natural number n, there exist equilibrium payoffs that can be obtained only when the number of possible messages is at least n.

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91. Mor Amitai, Cheap-Talk with Random Stopping (January 1996) 

Cheap-Talk with Random Stopping is a Cheap-Talk game in which after each period of communication, with probability 1- %, the talk ends and the players play the original game (i.e., choose actions and receive payoffs). In this paper the relations between Cheap-Talk games and Cheap-Talk with Random Stopping are analyzed.

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92. Theo S. H. Driessen, Tree Enterprises and Bankruptcy Ventures: A Game-Theoretic Similarity Due to a Graph-Theoretic Proof (January 1996) Discrete Applied Mathematics 79 (1997), 105-117

In a tree enterprise, users reside at the nodes of the tree and their aim is to connect themselves, directly or indirectly, to the root of the tree. The construction costs of arcs of the tree are given by means of the arc-cost-function associated with the tree. Face to face with this tree enterprise, the bankruptcy venture is described in terms of the estate of the bankrupt concern and the claims of the various creditors. The objective of the paper is to provide conditions (on the claims and the surplus of the claims in the bankruptcy venture) which are sufficient and necessary for the bankruptcy venture to agree with some tree enterprise. It is established that the bankruptcy venture agrees with some tree enterprise if and only if the surplus of claims in the bankruptcy venture is at most the size of the second smallest claim (in the weak sense). For that purpose, both the tree enterprise as well as the bankruptcy venture are modelled as a cooperative game with transferable utility. Within the framework of cooperative game theory, the proof of the equivalence theorem concerning the tree enterprise game and the bankruptcy game, under the given circumstances, is based on graph theoretic tools in a tree structure.

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93. Theo S. H. Driessen, An Alternative Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud: The Case of the Greedy Bankruptcy Game (January 1996) In: Game Theory IV, year 1998 (yearbook ''Theory of Games and Applications'') (Eds. L.A. Petrosjan and V.V. Mazalov) Nova Science Publishers Inc., New York, USA (1998), 45-61

The bankruptcy problem from the Talmud is modelled as a game (in coalitional form with transferable utility) which differs from the "standard bankruptcy game". A non-game theoretic solution to the bankruptcy problem is recovered by two different game theoretic approaches applied to the alternative game. The major game theoretic approach enables to interpret pairwise greedy or modest claims of creditors as largest or smallest core-allocations to creditors in the alternative game. A theory of consistency is elucidated with elementary game theoretic tools and proofs. As a separate topic, the indirect function of the "standard bankruptcy game" is determined and interpreted in an economic manner. The indirect function may be helpful to describe the game itself as well as its core (due to the duality between games and indirect functions).

 

94. Robert J. Aumann, Sergiu Hart & Motty Perry, The Absent-Minded Driver (January 1996) Games and Economic Behavior 20 (1997), 102-116

The example of the "absent-minded driver" was introduced by Piccione & Rubinstein [1995] in the context of games and decision problems with imperfect recall. They claim that a "paradox" or "inconsistency" arises when the decision reached at the "planning stage" -- before the game is played -- is compared with that at the "action stage" -- when the game is played. Though the example is provocative and worth having, their analysis is unsound. A careful analysis reveals that while the considerations at the planing and action stages do differ, there is no paradox or inconsistency. 94R. Robert J. Aumann, Sergiu Hart & Motty Perry, "The Absent-Minded Driver" (Revised, December 1996). The example of the "absent-minded driver" was introduced by Piccione & Rubinstein [1995] in the context of games and decision problems with imperfect recall. They claim that a "paradox" or "inconsistency" arises when the decision reached at the "planning stage" is compared with that at the "action stage". Though the example is provocative and worth having, their analysis is questionable. A careful analysis reveals that while the considerations at the planing and action stages do differ, there is no paradox or inconsistency.

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95. Gary Bornstein, Eyal Winter & Harel Goren, Experimental Study of Repeated Team-Games (January 1996) European Journal of Political Economy 12 (1996), 629-639

We report an experiment in which the Intergroup Prisoner's Dilemma (IPD) game was contrasted with a structurally identical (single-group) Prisoner's Dilemma (PD). The games were played repeatedly for 40 rounds. We found that subjects were initially more likely to cooperate in the IPD game than in the PD game. However, cooperation rates decreased as the game progressed and, as a result, the differences between the two games disappeared. This pattern is consistent with the hypothesis that subjects learn the structure of the game and adapt their behavior accordingly. Computer simulations based on a simple learning model by Roth & Erev (1995) support this interpretation.

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96. Gary Bornstein, David Budescu & Shmuel Zamir, Cooperation in Intergroup, n-Person and Two-Person Games of Chicken (January 1996) Journal of Conflict Resolution 41 (1997), 384-406

This paper introduces a new team game where players are engaged in simultaneous games of Chicken between and within teams. The intergroup Chicken game is proposed as a model of intergroup confrontations (e.g., military Conflicts, industrial disputes) involving bilateral threats where a failure on the part of either side to yield leads to an outcome (e.g., war, strike) that is disastrous to both sides. We report an experiment in which an intergroupChicken game with two players in each team was compared with a two-person Chicken and a (single-group) four-person Chicken. The games were played repeatedly and each round was preceded by a pre-game period in which players could signal their intention to cooperate or not. Our interest was in assessing the ability of the participants in the different games to cooperate, i.e., achieve the coordination necessary for the optimal realization of their mutual interests. We found that subjects were considerably less cooperative in the inter-group Chicken game than in either the two-person or the four-person game. Since the coordination problem in the intergroup game is of the same magnitude as that in the four-person game, we attribute most of the competitiveness observed in the intergroup conflict to the strategic properties of the game rather than the number of players involved.

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97. Igal Milchtaich, Generic Uniqueness of Equilibria in Nonatomic Congestion Games (January 1996) 

Generic uniqueness of pure-strategy Nash equilibrium, and uniqueness of the equilibrium outcome, are proved for a class of noncooperative nonatomic (large) games where a player's payoff depends on, and strictly decreases with, the measure of the set of players playing the same (pure) strategy he is playing. If the play of mixed strategies is allowed, then similar results still hold when the assumption of nonatomicity of the measure is removed. Generic uniqueness of the Cournot-Nash equilibrium distribution, corresponding to a description of a game in terms of distribution of player types, is also proved.

 

98. Dan S. Felsenthal & Moshe Machover, Ternary Voting Games (February 1996) International Journal of Game Theory 26 (1997), 335-351

We define ternary voting games (TVGs), a generalization of simple voting games (SVGs). In a play of an SVG each voter has just two options: voting `yes' or `no'. In a TVG a third option is added: abstention. Every SVG can be regarded as a (somewhat degenerate) TVG; but the converse is false. We define appropriate generalizations of the Shapley-Shubik and Banzhaf indices for TVGs. We define also the responsiveness (or degree of democratic participation) of a TVG and determine, for each n, the most responsive TVGs with n voters. We show that these maximally responsive TVGs are more responsive than the corresponding SVGs.

 

99. Mordecai Haimovich, The Simplex Algorithm Is Very Good!: On the Expected Number of Pivot Steps and Related Properties of Random Linear Programs (February 1996) 

In their paper How Good is the Simplex Algorithm?, Klee and Minty exhibited a sequence of linear programs for which the number of pivot steps in the simplex algorithm grows exponentially with the dimensions of the program. We present a probabilistic model in which the expected numberof steps for a variant of the simplex method grows linearly with the dimensions. For programs with parallel pair of inequalities (lower and upper bounds), we present a model in which the expected number of steps from minimum to maximum is d. We also present related results concerning the expected complexity of multi-objective linear programming.

 

100. Ran El-Yaniv & Richard M. Karp, Nearly Optimal Competitive Online Replacement Policies (March 1996) Mathematics of Operations Research 22 (1997), 814-839.

This Paper studies the following online replacement problem. There is a real function f(t), called the flow rate, defined over a finite time horizon [0,T]. It is known that m% f(t) % M for some reals 0 % m < M. At time 0 an online player starts to pay money at the rate of f(0). At each time 0 < t % T the player may changeover and continue paying money at the rate f(t). The complication is that each such changeover incures some fixed penalty. The player is called online as at each time t the player knows f only over the time interval [0,t]. The goal of the player is to minimize the total cost comprised of cumulative payment flow plus change over costs. This formulation of the replacement problem has various interesting applications among which are: equipment replacement, supplier replacement, the menu cost problem and mortgagere financing. With respect to the competitive ratio performance measure, this paper seeks to determine the best possible competitive ratio achievable by an online replacement policy. Our results include the following: a general lower bound on the performance of any deterministic policy, a policy that is optimal in several special cases and a simple policy that is approximately optimal.