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Publications | The Federmann Center for the Study of Rationality

Publications

2001
Goren, Harel . Effect Of Out-Group Competition On Individual Behavior And Out-Group Perception In The Intergroup Prisoner's Dilemma (Ipd) Game, The. Discussion Papers 2001. Web. Publisher's VersionAbstract
Hebrew University of Jerusalem students participated in two experiments of repeated play of the Intergroup Prisoners' Dilemma (IPD) game, which involves conflict of interests between two groups and, simultaneously, within each group. The experiments manipulated the level of competition exhibited by the out-group members (i.e., their level of contribution to their group's effort in the conflict). Consistent with the hypothesis that participants use strategies of reciprocal cooperation between groups, higher levels of out-group competition caused participants to increase their contribution and lower levels caused them to decrease it. In addition, participants had accurate recall of the contribution levels of out-group members, and they attributed motivations to out-group members in a manner that reflected their level of contribution. The nature of reciprocation with the out-group is discussed in light of both behavioral and cognitive data.
Haimanko, Pradeep Dubey, and Ori, B. Envy And The Optimality Of Tournaments. Discussion Papers 2001. Web. Publisher's VersionAbstract
We show that tournaments tend to outperform piece-rate contracts when there is sufficient envy among the agents.
Bracht, Hidehiko Ichimura, and Juergen. Estimation Of Learning Models On Experimental Game Data. Discussion Papers 2001. Web. Publisher's VersionAbstract
The objective of this paper is both to examine the performance and to show properties of statistical techniques used to estimate learning models on experimental game data. We consider a game with unique mixed strategy equilibrium. We discuss identification of a general learning model and its special cases, reinforcement and belief learning, and propose a paramaterization of the model. We conduct Monte Carlo simulations to evaluate the finite sample performance of two kinds of estimators of a learning model's parameters. Maximum likelihood estimators of period to period transitions and mean squared deviation estimators of the entire path of play. In addition, we investigate the performance of a log score estimator of the entire path of play and a mean squared deviation estimator of period to period transitions. Finally, we evaluate a mean squared estimator of the entire path of play with observed actions averaged over blocks, instead of behavioral strategies. We propose to estimate the learning model by maximum likelihood estimation as this method performs well on the sample size used in practice if enough cross sectional variation is observed.
Itzhak Venezia, Dan Galai, and Zur Shapira. Exclusive Vs. Independent Agents: A Separating Equilibrium Approach. Discussion Papers 2001. Web. Publisher's VersionAbstract
We provide a separating equilibrium explanation for the existence of the independent insurance agent system despite the potentially higher costs of this system compared to those of the exclusive agents system (or direct underwriting). A model is developed assuming asymmetric information between insurers and insureds; the formers do not know the riskiness of the latter. We also assume that the claims service provided by the independent agent system to its clients is superior to that offered by direct underwriting system, that is, insureds using the independent agent system are more likely to receive reimbursement of their claims. Competition compels the insurers to provide within their own system the best contract to the insured. It is shown that in equilibrium the safer insureds choose direct underwriting, whereas the riskier ones choose independent agents. The predictions of the model agree with previous research demonstrating that the independent agent system is costlier than direct underwriting. The present model suggests that this does not result from inefficiency but rather from self-selection. The empirical implication of this analysis is that, ceteris paribus, the incidence of claims made by clients of the independent agents system is higher than that of clients of direct underwriting. Implications for the co-existence of different distribution systems due to unbundling of services in other industries such as brokerage houses and the health care industry are discussed.
Klaus Abbink, Ron Darziv, Zohar Gilula Harel Goren Bernd Irlenbusch Arnon Keren Bettina Rockenbach Abdolkarim Sadrieh Reinhard Selten, and Shmuel Zamir. Fisherman's Problem: Exploring The Tension Between Cooperative And Non-Cooperative Concepts In A Simple Game, The. Discussion Papers 2001. Web. Publisher's VersionAbstract
We introduce and experiment the Fisherman s Game in which the application of economic theory leads to four different benchmarks. Non-cooperative sequential rationality predicts one extreme outcome while the core (which coincides with the competitive market equilibrium) predicts the other extreme. Intermediate, disjoint outcomes are predicted by fairness utility models and the Shapley value. Non of the four benchmarks fully explains the observed behavior. However, since elements of both cooperative and non-cooperative game theory are crucial for organizing our data, we conclude that effort towards bridging the gap between the various concepts is a promising approach for future economic research.
Simon, Robert Samuel . Games Of Incomplete Information, Ergodic Theory, And The Measurability Of Bayesian Equilibria. Discussion Papers 2001. Web. Publisher's VersionAbstract
This paper discusses the difference between Harsanyi and Bayesian equilibria for games of incomplete information played onuncountable belief spaces. A conjecture belonging to ergodic theory is presented. If the conjecture were valid then there would exist a game played on an uncountable belief space with a common prior for which there are Bayesian equilibria but no Harsanyi equilibrium.
Yigal Attali, Maya Bar-Hillel . Guess Where: The Position Of Correct Answers In Multiple-Choice Test Items As A Psychometric Variable. Discussion Papers 2001. Web. Publisher's VersionAbstract
In this paper, we show that test makers and test takers have a strong and systematic tendency for hiding correct answers – or, respectively, for seeking them – in middle positions. In single, isolated questions, both prefer middle positions over extreme ones in a ratio of up to 3 or 4 to 1. Because test makers routinely, deliberately and excessively balance the answer key of operational tests, middle bias almost, though not quite, disappears in those keys. Examinees taking real tests also produce answer sequences that are more balanced than their single question tendencies, but to a lesser extent than the correct key. In a typical 4-choice test, about 55% of erroneous answers (which are the only answers whose position is determined by the test taker, not the test maker) are in the two central positions. We show that this bias is large enough to have real psychometric consequences, as questions with middle correct answers are easier and – what's more important – less discriminating than questions with extreme correct answers, a fact some of whose implications we explore.
Heifetz, Robert J. Aumann, and Aviad. Incomplete Information. Discussion Papers 2001. Web. Publisher's VersionAbstract
In interactive contexts such as games and economies, it is important to take account not only of what the players believe about substantive matters (such as payoffs), but also of what they believe about the beliefs of other players. Two different but equivalent ways of dealing with this matter, the semantic and the syntactic, are set forth. Canonical and universal semantic systems are then defined and constructed, and the concepts of common knowledge and common priors formulated and characterized. The last two sections discuss relations with Bayesian games of incomplete information and their applications, and with interactive epistemology - the theory of multi-agent knowledge and belief as formulated in mathematical logic.
Bornstein, Gary . Intergroup Prisoner's Dilemma Game As A Model Of Intergroup Conflict, The. Discussion Papers 2001. Web. Publisher's VersionAbstract
Intergroup conflicts are characterized by conflicts of interests within the competing groups as well. The intragroup conflict stems from a basic fact: while all group members are better off if they all cooperate in competing against the outgroup, each individual group member is better off defecting. The Intergroup Prisoner's Dilemma (IPD) game is proposed as a theoretical framework for combining the intragroup and intergroup levels of conflict. This framework is used to examine major issues concerning individual and group behavior in intergroup conflict. These include: the effect of real intergroup conflict on intragroup cooperation; the motivational basis of cooperation; the distinction between non-cooperative groups, unitary groups, and individuals; and alternative routes to conflict resolution.
Kalai, Gil . Learnability And Rationality Of Choice. Discussion Papers 2001. Web. Publisher's VersionAbstract
The purpose of this paper is to examine the extent to which the concepts of individual and collective choice unsed in economic theory desribe "predictable" or "learnable" behavior. Given a set X of N alternatives, a choice function c is a mapping which assigns to nonempty subsets S of X an element c(S) of S. A rational choice function is one for which there is a linear ordering on the alternatives such that c(S) is the maximal element of S according to that ordering. Using the basic concept of PAC-learnability from statistical learning theory we define a class of choice functions on a ground set of N elements as learnable if it is possible to predict, with small amount of error, the chosen element from a set A after viewing a "few examples." Here, "few" means a polynomial number in N. Learnability is quite a strict condition on a class of choice functions. The main point we discuss in this regard are: The class of rational choice function can be learned quickly and efficiently. Various natural classes of choice functions, which represent indidivual choices and strategic choices of several interacting agents, are learnable. The class of rational choice functions has superior learnability properties in comparison to other classes. We make the conjecture that classes of choice functions that represent a genuine aggregation of individual choices in a large society are never learnable. We also ask to what extent learnability can replace or reinforce the rationality hypothesis in some economic situations.
Samuel-Cahn, Ruma Falk, and Ester. Lewis Carroll's Obtuse Problem. Discussion Papers 2001. Web. Publisher's VersionAbstract
Carroll's apparently impeccable solution to one of his probability problems is shown to answer another problem that is based on reasonable assumptions. His original assumptions, however, are self-contradictory, hence entailing paradoxical results.
Simon, Robert Samuel . Locally Finite Knowledge Structures. Discussion Papers 2001. Web. Publisher's VersionAbstract
With respect to the S5 multi-agent epistemic logic, we define a cell to be a minimal subset of knowledge structures known in common semantically by all the agents. A cell has finite fanout if at every knowledge strcuture every agent considers only a finite number of other knowledge structures to be possible. A set of formulas in common knowledge is finitely generated if the common knowledge of some finite subset implies the common knowledge of the whole set. For every finitely generated set of formulas held in common knowledge at some knowledge structure either this set determines uniquely a finite cell or there are uncountable many cells of finite fanout (and also uncountably many cells of uncountable size) at which exactly this set of formulas is known in common. The situation is very different, however, for sets of formulas held in common knolwedge that are not finitely generated - if there are uncountably many corresponding cells then either none of these cells or all of them could have finite fanout.
Vulkan, Zvika Neeman, and Nir. Markets Versus Negotiations: The Emergence Of Centralized Markets. Discussion Papers 2001. Web. Publisher's VersionAbstract
We study the incentives of privately informed traders who have access to two forms of trade: direct negotiations with a small number of buyers and sellers (or decentralized trade), and centralized markets with a relatively large number of buyers and sellers. We show that "weak" trader types (that is, buyers with a high willingness to pay and sellers with low costs) will prefer to trade through centralized markets. This leads to a complete unraveling of direct negotiations, so that ultimately, all "serious" buyers and sellers opt for trading through the centralized market. Once this happens, no trader can pro''¯tably trade through direct negotiations.
Bezalel Peleg, Hans Peters, and Ton Storcken. Nash Consistent Representation Of Constitutions: A Reaction To The Gibbard Paradox. Discussion Papers 2001. Web. Publisher's VersionAbstract
The concept of an effectivity function is adopted as a formal model of a constitution. A game form models the actions available and permissible to individuals in a society. As a representation of the constitution such a game form should endow each group in society with the same power as it has under the constitution. Another desirable property is Nash consistency of the game form: Whatever the individual preferences, the resulting game should be minimally stable in the sense of possessing a Nash equilibrium. A first main result of the paper is a characterization of all effectivity functions that have a Nash consistent representation for the case without special structure on the sent of alternatives (social states). Next, a similar result is derived for the case where the set of alternatives is a compact metric space and the effectivity function is topological. As a sepcial case, veto functions are considered. Further results concern Pareto optimality of Nash equilibrium outcomes.
Simon, Robert Samuel . On The Unique Extensibility And Surjectivity Of Knowledge Structures. Discussion Papers 2001. Web. Publisher's VersionAbstract
With the S5 multi-agent epistemic logic we consider the canonical maps from Krpke structures to knowledge structures. We define a cell to be a minimal subset of knowledge structures known in common semantically by the agents. A cell has finite fanout if at every point every agent considers only a finite number of other points to be possible. We define a cell to be surjective if every Kripke structure that maps to it does so surjectively. All cells with finite fanout are surjective, but the converse does not hold. To construct a counter-example we need topological insights concerning the relationship between the logic and its semantic models. The difference between syntactic and semantic common knowledge is central to this construction.
Judith Avrahami, Werner Guth, and Yaakov Kareev. Parasite Game: Exploiting The Abundance Of Nature In The Face Of Competition, The. Discussion Papers 2001. Web. Publisher's VersionAbstract
A situation in which the regularity in nature can be utilized while competition is to be avoided is modeled by the Parasite game. In this game regular behavior could enhance guessing nature but strategic randomization is required to avoid being outguessed. In an experiment, 60 pairs of participants (partner design) played many rounds of the Parasite game. The treatements differed in nature's probabilities and whether or not these probabilities were announced in advance or oculd only be experienced over time. Before playing, the working memory (WM) of participants was measured. Data analyses test the correspondence of participants' behavior to game-theoretic benchmarks and the effect of participants' WM on their behavior.
Venezia, Zur Shapira, and Itzhak. Patterns Of Behavior Of Professionally Managed And Independent Investors. Discussion Papers 2001. Web. Publisher's VersionAbstract
In this paper, we analyze the investment patterns of a large number of clients of a major Israeli brokerage house during 1994. We compare the behavior of clients making independent investment decisions to that of investors whose accounts were managed by brokerage professionals. Our main objective is to investigate whether the disposition effect (i.e., the tendency to sell winners quicker than losers), demonstrated in the US only for individual investors, also holds for professional investors. This analysis is important, as accepted financial theory predicts that prices are determined mainly by decisions made by professionals. We show that both professional and independent investors exhibit the disposition effect, although the effect is stronger for independent investors. The second objective of our study is the comparison of trade frequency, volume and profitability between independent and professionally managed accounts. We believe that these comparisons not only provide insights of their own, but also help to put the differences in the disposition effect in a wider perspective. We demonstrate that professionally managed accounts were more diversified and that round trips were both less correlated with the market and slightly more profitable than those of independent accounts.
Gooni Orshan, Peter Sudholter . Positive Core Of A Cooperative Game, The. Discussion Papers 2001. Web. Publisher's VersionAbstract
The positive core is a nonempty extension of the core of transferable utility games. If the core is nonempty, then it coincides with the core. It shares many properties with the core. Six well-known axioms which are employed in some axiomatizations of the core, the prenucleolus, or the positive prekernel, and one new intuitive axiom, characterize the positive core on any infinite universe of players. This new axiom requires that the solution of a game, whenever it is nonempty, contains an element which is invariant under any symmetry of the game.
Albert Blarer, Tamar Keasar, and Avi Shmida. Possible Mechanisms For The Formation Of Flower Size Preferences By Foraging Bumblebees. Discussion Papers 2001. Web. Publisher's VersionAbstract
Large flowers often contain larger nectar rewards, and receive more pollinator visits, than small flowers. We studied possible behavioral mechanisms underlying the formation of flower size preferences in bumblebees, using a two-phase laboratory experiment. Experimentally naive Bombus terrestris (L.) foraged on artificial flowers that bore either a big (3.8cm diameter) or a small (2.7cm diameter) display of a uniform color. Only flowers of one display size contained nectar rewards. We changed the display color and the locations of big and small flowers in the second experiment phase. We recorded the bees' choices in both phases. Almost one half of the bees (41) made their first visit to a small flower. The bees learned to associate display size with food reward, and chose rewarding flowers with >85 accuracy by the end of each experimental phase. Some learning occurred within the bees' first three flower visits. Learning of the size-reward association was equally good for big and small displays in the first experimental phase, but better for small displays in the second phase. Formation of size-reward associations followed a similar course in both phases. This suggests that the bees did not apply their experience from the first learning phase to the new situation of the second phase. Rather, they treated each phase of the experiment as an independent learning task. Our results suggest that associative learning is involved in the formation of preferences for large displays by bees. Moreover, bees that had learned to prefer large displays in one foraging situation may not transfer this preference to a novel situation that is sufficiently different. We propose that this feature of the bees' behavior can select for honest advertising in flowers.
Cass R. Sunstein, Daniel Kahneman, David Schkade, and Ilana Ritov. Predictably Incoherent Judgements. Discussion Papers 2001. Web. Publisher's VersionAbstract
When people make moral or legal judgments in isolation, they produce a pattern of outcomes that they would themselves reject, if only they could see that pattern as a whole. A major reason is that human thinking is category-bound. When people see a case in isolation, they spontaneously compare it to other cases that are mainly drawn from the same category of harms. When people are required to compare cases that involve different kinds of harms, judgments that appear sensible when the problems are considered separately often appear incoherent and arbitrary in the broader context. Another major source of incoherence is what we call the translation problem: The translation of moral judgments into the relevant metrics of dollars and years is not grounded in either principle or intuition, and produces large differences among people.. The incoherence produced by category-bound thinking is illustrated by an experimental study of punitive damages and contingent valuation. We also show how category-bound thinking and the translation problem combine to produce anomalies in administrative penalties. The underlying phenomena have large implications for many topics in law, including jury behavior, the valuation of public goods, punitive damages, criminal sentencing, and civil fines. We consider institutional reforms that might overcome the problem of predictably incoherent judgments. Connections are also drawn to several issues in legal theory, including valuation of life, incommensurability, and the aspiration to global coherence in adjudication.