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Publications | The Federmann Center for the Study of Rationality

Publications

2002
Bruno Bassan, Yosef Rinott, and Yehuda Vardi. On Stochastic Comparisons Of Excess Times. Discussion Papers 2002. Web. Publisher's VersionAbstract
A stationary renewal process based on iid random variables Xi is observed at a given time. The excess time, that is, the residual time until the next renewal event, is of course smaller than the total current X which consists of the residual time plus the current age. Nevertheless in certain types of data the distribution of the excess times is stochastically larger than that of Xi's. We find necessary and sufficient conditions that explain this phenomenon, and related results on stochastic orderings arising from observations on renewal processes.
Zamir, Philip J. Reny, and Shmuel. On The Existence Of Pure Strategy Monotone Equilibria In Asymmetric First-Price Auctions. Discussion Papers 2002. Web. Publisher's VersionAbstract
We establish the existence of pure strategy equilibria in monotone bidding functions in first-price auctions with asymmetric bidders, interdependent values and affiliated one-dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second-price auctions.
Yaakov Kareev, Sharon Arnon, and Reut Horwitz-Zeliger. On The Misperception Of Variability. Discussion Papers 2002. Web. Publisher's VersionAbstract
Ever since the days of Francis Bacon it has been claimed that people perceive the world as less variable and more regular than it actually is. Such misperception, if shown to exist, could explain a host of perplexing behaviors. However, the only evidence supporting the claim is indirect, and there is no explanation of its cause. As a possible cause, we suggest the use of sample variability as an estimate of population variability. This is so since the sampling distribution of sample variance is downward attenuated, the attenuation being substantial for sample sizes that people are likely to consider. The results of five experiments show that people use sample variability, uncorrected for sample size, in tasks in which a correction is normatively called for, and indeed perceive variability as smaller than it actually is.
Weinberger, Shmuel . On The Topological Social Choice Problem. Discussion Papers 2002. Web. Publisher's VersionAbstract
Extending earlier work of Chichilnisky and Heal, we show that any connected space of the homotopy type of a finite complex admitting a continuous symmetric choice function respeting unanimity is contractible for any fixed finite number (>1) of agents. On the other hand, removing the finiteness condition on the homotopy type, we show that there are a number of non-contractible spaces that do admit such choice functions, for any number of agents, and, characterize precisely those spaces.
Motro, Osnat Yaniv, and Uzi. Parental Investment Conflict In Continuous Time: St. Peter S Fish As An Example, The. Discussion Papers 2002. Web. Publisher's VersionAbstract
The parental investment conflict considers the question of how much each sex should invest in each brood, thereby characterizing different animal groups. Each such group usually adopts a certain parental care pattern: female-care only, male-care only, biparental care, or even no parental care at all. The differences in care patterns are usually explained by the different costs and benefits arising from caring for the offspring in each animal group. This paper proposes a game-theoretical model to the parental investment conflict based on the parental behavior in Cichlid fish. Cichlid fish exhibit different parental care patterns, allowing the examination of the factors which determine the particular behavior in each mating. We present a continuous time, two-stage, asymmetric game, with two types of players: male and female. According to the model s results, three parental care patterns: male-only care, female-only care and biparental care, are possible Evolutionarily Stable Strategies. Fixation depends on the investment costs and benefits, and on the initial conditions of the game. These results may explain the different parental care patterns observed in di erent animal groups as well as in Cichlid fish.
Bruno Bassan, Olivier Gossner, Marco Scarsini, and Shmuel Zamir. Positive Value Of Information In Games. Discussion Papers 2002. Web. Publisher's VersionAbstract
We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments   la Blackwell.More specifically, we consider pairs consisting of a game with incomplete information G and an information structure S such that the extended game “(G,S) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of “(G,S), and that for any information structure that is coarser than S, all Nash payoff profiles of “(G,T) are dominated by u. We then prove that our condition is also necessary in the following sense: Given any convex compact polyhedron of payoff profiles, whose Pareto frontier is not a singleton, there exists an extended game “(G,S) with that polyhedron as the convex hull of feasible payoffs, an information structure T coarser than S and a player i who strictly prefers a Nash equilibrium in “(G,T) to any Nash equilibrium in “(G,S).
Gary Bornstein, Tamar Kugler, and Reinhard Selten. Repeated Price Competition Between Individuals And Between Teams. Discussion Papers 2002. Web. Publisher's VersionAbstract
We conducted an experimental study of price competition in a duopolistic market. The market was operationalized as a repeated game between two teams  with one, two, or three players in each team. Each player simultaneously demanded a price, and the team whose total asking price was smaller won the competition and was paid its asked price. The losing team was paid nothing. In case of a tie, the teams split the asking price. For teams with multiple players we manipulated the way in which the team s profit was divided between the team members. In one treatment each team member was paid his or her asking price if the team won, and half that if the game was tied, while in the other treatment the team s profit for winning or tying the game was divided equally among its members. We found that asking (and winning) prices were significantly higher in competition between individuals than in competition between two- or three-person teams. There were no general effects of team size, but prices were sustained at a higher level when each team member was paid his or her own asked price than when the team s profits were divided equally.
Aumann, Robert J. . Risk Aversion In The Talmud. Discussion Papers 2002. Web. Publisher's VersionAbstract
Evidence is adduced that the sages of the ancient Babylonian Talmud, as well as some of the medieval commentators thereon, were well aware of sophisticated concepts of modern theories of risk-bearing.
Neyman, Abraham . Stochastic Games: Existence Of The Minmax. Discussion Papers 2002. Web. Publisher's Version
Gershon Ben-Shakhar, 5a Bar-Hillel, Mordechai Kremnitzer . Trial By Polygraph: Reconsidering The Use Of The Guilty Knowledge Technique In Court. Discussion Papers 2002. Web. Publisher's VersionAbstract
Polygraph test results are by and large ruled inadmissible evidence in criminal courts in the US, Canada and Israel. This is well-conceived with regard to the dominant technique of polygraph interrogation, known as the Control Question Technique (CQT), because it indeed does not meet the required standards for admissible scientific evidence. However, a lesser known and rarely practiced technique, known as the Guilty Knowledge Test (GKT), is capable, if carefully administered, of meeting the recently set Daubert criteria. This article describes the technique, and argues for considering its admissibility as evidence in criminal courts.
Ullmann-Margalit, Edna . Trust Out Of Distrust. Discussion Papers 2002. Web. Publisher's VersionAbstract
The paper aims to establish the possibility of trust from within a Hobbesian framework. It shows that distrust situations can be structured in two ways, the first referred to as Hard and the second as Soft, both of which are compatible with Hobbes s stark assumptions about human nature. In Hard distrust situations (which are prisoner s-dilemma structured) the distrust strategy is dominant; in the Soft variety (which are stag-hunt structured) trust is an equilibrium choice. In order to establish the possibility of trust there is no need to claim that the state of nature is Soft rather than Hard, nor even that Soft is likelier. Game theoretical considerations show that all that is needed to give trust a chance is the ambiguity or uncertainty on the part of the players as to which of the two basic situations of distrust in fact obtains: which game was picked by Nature for them to play.
David Assaf, Larry Goldstein, and Ester Samuel-Cahn. Two Choice Optimal Stopping. Discussion Papers 2002. Web. Publisher's VersionAbstract
Let Xn, . . . ,X1 be i.i.d. random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X s using stopping rules. The statistician s goal is to stop at a value of X as small as possible. Let V2n equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We obtain the asymptotic behavior of the sequence V2n for a large class of F s belonging to the domain of attraction (for the minimum) D(G'$\pm$), where G'$\pm$(x) = [1 'ˆ’ exp('ˆ’x'$\pm$)] I(x'¥0). The results are compared with those for the asymptotic behavior of the classical one choice value sequence V1n ,as well as with the 'prophet value  sequence E(minXn, . . . ,X1).
Mas-Colell, Sergiu Hart, and Andreu. Uncoupled Dynamics Cannot Lead To Nash Equilibrium. Discussion Papers 2002. Web. Publisher's VersionAbstract
We call a dynamical system uncoupled if the dynamic for each player does not depend on the payoffs of the other players. We show that there are no uncoupled dynamics that are guaranteed to converge to Nash equilibrium, even when the Nash equilibrium is unique.
2001
Yaari, Menahem E. . A Credit Market A La David Hume. Discussion Papers 2001. Web. Publisher's VersionAbstract
In Book III of his Treatise of Human Nature, David Hume considers the following simple interaction: "I suppose a person to have lent me a sum of money, on condition that it be restor'd in a few days, and also suppose, that after the expiration of the term agreed on, he demands the sum" and Hume asks: "What reason or motive have I to restore the money?" [1740, p. 479] The answer, he concludes, must be "that the sense of justice and injustice [which is the motive for repaying the loan] is not deriv'd from nature, but arises artificially, tho' necessarily, from education and human conventions." [p. 483] It is my purpose in this essay to offer formal (and modern) underpinnings for Hume's argument. I shall do so in the context of Hume's own example, cited above, where the interaction being considered is one between lender and borrower.
Peleg, Peter Sudholter, and Bezalel. A Note On An Axiomatization Of The Core Of Market Games. Discussion Papers 2001. Web. Publisher's VersionAbstract
As shown by Peleg, the core of market games is characterized by nonemptiness, individual rationality, superadditivity, the weak reduced game property, the converse reduced game property, and weak symmetry. It was not known whether weak symmetry was logically independent. With the help of a certain transitive 4-person TU game it is shown that weak symmetry is redundant in this result. Hence the core on market games is axiomatized by the remaining five properties, if the universe of players contains at least four members.
Neyman, Jean-Francois Mertens, and Abraham. A Value On 'An. Discussion Papers 2001. Web. Publisher's VersionAbstract
We prove here the existence of a value (of norm 1) on the spaces 'NA and even 'AN, the closure in the variation distance of the linear space spanned by all games f o mu, where mu is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0, 1] which satisfies a much weakened continuity at zero and one.
Jacob, Alon Harel, and Assaf. An Economic Rationale For The Legal Treatment Of Omissions In Tort Law. Discussion Papers 2001. Web. Publisher's VersionAbstract
This paper provides an economic justification for the exemption from liability for omissions and for the exceptions to this exemption. It interprets the differential treatment of acts and omissions in tort law as a proxy for a more fundamental distinction between harms caused by multiple injurers each of whom can single-handedly prevent the harm (either by acting or failing to act) and harms caused by a single injurer (either by acting or failing to act). Since the overall cost to which a group of injurers is exposed is constant, attributing liability to many injurers reduces the part each has to pay and consequently reduces one's incentives to take precautions. The broad exemption from liability for omissions is a way of carving a simple, practical rule to distinguish between the typical cases in which an agent can be easily selected and provided with sufficient incentives (typically, cases of acts) and cases in which there is a serious problem of dilution of liability (typically, cases of omissions). The exceptions to the rule exempting from responsibility for omissions are also explained in terms of efficiency. The imposition of liability for omissions depends on the ability to identify a salient agent, i.e., to single out one or few legally responsible agents and differentiate their role from that of others. Tort law designs three types of "salience rules." It either creates salience directly (by attributing liability to a single agent), or it can exploit salience created "naturally", or it can induce injurers to create salience voluntarily.
Winter, Bezalel Peleg, and Eyal. Constitutional Implementation. Discussion Papers 2001. Web. Publisher's VersionAbstract
We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of H, E^H, is a sub-correspondence of E. We found necessary and efficient conditions for a game form Gamma to implement H (in Nash equilibria) and to satisfy, at the same time, that E^Gamma, the effectivity function of Gamma, is a sub-correspondence of E^H (which guarantees that Gamma is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of E^Gamma and E^H, and for E^Gamma=E^H. All our results are sharp as is shown by suitable examples.
Pradeep Dubey, John Geanakoplos, and Martin Shubik. Default And Punishment In General Equilibrium. Discussion Papers 2001. Web. Publisher's VersionAbstract
We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of moral hazard, adverse-selection, and signalling phenomena (including the Akerloflemons model and Rothschild-Stiglitz insurance model) in a general equilibrium framework. We impose a condition on the expected delivery rates for untraded assets that is similar to the trembling hand refinements used in game theory. Despite earlier claims about the nonexistence of equilibrium with adverse selection, we show that equilibrium always exists, even with exclusivity constraints on asset sales, and transactions-liquidity costs or information-evaluation costs for asset trade. We show that more lenient punishment which encourages default may be Pareto improving because it allows for better risk spreading. We also show that default opens the door to a theory of endogenous assets.
Sudholter, Bezalel Peleg, and Peter. Dummy Paradox Of The Bargaining Set, The. Discussion Papers 2001. Web. Publisher's VersionAbstract
By means of an example of a superadditive 0-normalled game, we show that the maximum payoff to a dummy in the bargaining set may decrease when the marginal contribution of the dummy to the grand coalition becomes positive.