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Publications | The Federmann Center for the Study of Rationality

Publications

2004
Harel, Ehud Guttel, and Alon. Probability Matching And The Law: A Behavioral Challenge To Law & Economics. Discussion Papers 2004. Web. Publisher's VersionAbstract
Contrary to the conventional assumption that individuals maximize payoffs, robust experimental studies show that individuals who face repeated choices involving probabilistic costs and benefits often make sub-optimal decisions by applying the strategy of "probability matching." The following study, by integrating this literature with the traditional models of law and economics, and through experimental illustration, presents the possible effects of probability matching in the legal context. The paper also explores how probability matching can guide policy making.
Maya Bar-Hillel, David Budescu, and Yigal Attali. Scoring And Keying Multiple Choice Tests: A Case Study In Irrationality. Discussion Papers 2004. Web. Publisher's VersionAbstract
We offer a case-study in irrationality, showing that even in a high stakes, deliberate context, highly intelligent professionals may adopt dominated practices. Multiple-choice tests (MCTs) enjoy many advantages that made them popular tools in educational and psychological measurement. But they suffer from the so-called guessing problem: test-makers cannot distinguish lucky guesses from answers based on knowledge. One way professional test-makers have dealt with this problem is by attempting to lower the incentive to guess, through penalizing errors (called formula scoring). Another is to rid tests of various cues (e.g., a preponderance of correct answers in middle positions) that might help testwise test-takers guess at better than chance odds. Key balancing is the strategy test-takers adopted for ridding tests of positional biases. We show that formula scoring and key balancing, though widespread and intuitively appealing, are in fact "irrational" practices. They do not dispose of the guessing problem and are fraught with problems of their own. Yet they persist, even in the presence of more rational alternatives: Number right scoring is superior to formula scoring, and key randomization is superior to key balancing.
Kalai, Gil . Social Indeterminacy. Discussion Papers 2004. Web. Publisher's VersionAbstract
An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict-preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to arbitrary neutral monotone social welfare functions which can be described by a strong simple game G if the voting power of each individual, measured by the it Shapley-Shubik power index, is sufficiently small. Our proof is based on an extension to another classic result concerning the majority rule. Condorcet studied an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is p > 1/2. Condorcet's Jury Theorem asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. We prove that this assertion extends to a sequence of arbitrary monotone strong simple games if and only if the maximum voting power for all individuals tends to zero.
Mas-Colell, Sergiu Hart, and Andreu. Stochastic Uncoupled Dynamics And Nash Equilibrium. Discussion Papers 2004. Web. Publisher's VersionAbstract
In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it suffices to recall the last two periods of play.
Toxvaerd, Flavio . Strategic Merger Waves: A Theory Of Musical Chairs. Discussion Papers 2004. Web. Publisher's VersionAbstract
This paper proposes an explanation of merger waves based on the interaction between competitive pressure and irreversibility of mergers in an uncertain environment. A set of acquirers compete over time for scarce targets. At each point in time, an acquirer can either postpone a takeover attempt, or raid immediately. By postponing the takeover attempt, an acquirer may gain from more favorable future market conditions, but runs the risk of being preempted by rivals. First, a complete information model is considered, and it is shown that the above tradeoff leads to a continuum of subgame perfect equilibria in monotone strategies that are strictly Pareto ranked. All these equilibria share the feature that all acquirers rush simultaneously in merger waves. The model is then extended to a dynamic global game by introducing slightly noisy private information about merger profitability. This game is shown to have a unique Markov perfect Bayesian equilibrium in monotone strategies, and the timing of the merger wave can thus be predicted. Last, the comparative dynamics predictions of the model are related to stylized facts.
Toxvaerd, Flavio . Time Of The Essence. Discussion Papers 2004. Web. Publisher's VersionAbstract
In most industries, ranging from information systems development to construction, an overwhelming proportion of projects are delayed beyond estimated completion time. This fact constitutes somewhat of a puzzle for existing theory. The present paper studies project delays and optimal contracts under moral hazard in a setting with time to build. Within this setup, project delays are found to be most likelyto happen at early stages of development, and intimately connected to the degree ofcommitment of the procurer and the class of contracts that can be enforced. The firstbest,optimal spot contracting and optimal long-term contract scenarios are analyzed, aswell as commonly encountered additional constraints on the long-term contract.
Zultan, Carsten Schmidt, and Ro ˜i. Unilateral Face-To-Face Communication In Ultimatum Bargaining "A Video Experiment. Discussion Papers 2004. Web. Publisher's VersionAbstract
It is commonly accepted that face-to-face communication induces cooperation. The experiment disentangles communication and social effect (replication of Roth, 1995) and examines the components of the social effect with the help of unilateral communication. Results suggest that separate processes, both of a strategic and of an affective-social nature may induce cooperative outcomes in ultimatum bargaining with pre-play communication, depending on the communication protocol. Unilateral communication is found to have weaker effects than bilateral communication, and affects especially the recipient of the communication.
The Ethics of Memory
Avishai, Margalit . The Ethics Of Memory. 2004. Print.

Much of the intense current interest in collective memory concerns the politics of memory. In a book that asks, "Is there an ethics of memory?" Avishai Margalit addresses a separate, perhaps more pressing, set of concerns. The idea he pursues is that the past, connecting people to each other, makes possible the kinds of "thick" relations we can call truly ethical. Thick relations, he argues, are those that we have with family and friends, lovers and neighbors, our tribe and our nation--and they are all dependent on shared memories. But we also have "thin" relations with total strangers, people with whom we have nothing in common except our common humanity. A central idea of the ethics of memory is that when radical evil attacks our shared humanity, we ought as human beings to remember the victims. Margalit's work offers a philosophy for our time, when, in the wake of overwhelming atrocities, memory can seem more crippling than liberating, a force more for revenge than for reconciliation. Morally powerful, deeply learned, and elegantly written, The Ethics of Memory draws on the resources of millennia of Western philosophy and religion to provide us with healing ideas that will engage all of us who care about the nature of our relations to others.

2003
Hart, Sergiu . A Comparison Of Non-Transferable Utility Values. Discussion Papers 2003. Web. Publisher's VersionAbstract
Three values for non-transferable utility games – the Harsanyi NTU-value, the Shapley NTU-value, and the Maschler-Owen consistent NTU-value – are compared in a simple example.
Hart, Sergiu . An Axiomatization Of The Consistent Non-Transferable Utility Value. Discussion Papers 2003: n. pag. Print.Abstract
The Maschler-Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom.
Shapira, Elizabeth Boyle, and Zur. Aspiration And Survival In Jeopardy! . Discussion Papers 2003. Web. Publisher's VersionAbstract
Behavior in dynamic competitive situations requires decision makers to evaluate their own as well as their competitors positions. This paper uses data from a realistic competitive risk taking setting, Jeopardy s Tournament of Champions, to test whether individual players choose the strategic best response in making their betting decisions. The analyses show that the percentage of players choosing the strategic best response is very low, a rather surprising finding because the Tournament of Champions is contested by the very best and most experienced players of the Jeopardy game. We conjecture that performance aspiration and survival targets guide risk-taking behavior in competitive situations. Furthermore, in situations where decisions are made under pressure, contestants tend to focus on one target while ignoring alternative targets and the choices that are available to their competitors. This may lead them to select inferior competitive strategies.
Smorodinsky, Abraham Neyman, and Rann. Asymptotic Values Of Vector Measure Games. Discussion Papers 2003. Web. Publisher's VersionAbstract
The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of ¼(S) where ¼ is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games where a two-house weighted majority game is a game in which a coalition is winning if and only if it is winning in two given weighted majority games. All weighted majority games have an asymptotic value. However, not all two-house weighted majority games have an asymptotic value. In this paper we prove that the existence of infinitely many atoms with sufficient variety suffice for the existence of the asymptotic value in a general class of nonsmooth vector measure games that includes in particular two-house weighted majority games.
Barry O'Neill, Dov Samet, Zvi Wiener, and Eyal Winter. Bargaining With An Agenda. Discussion Papers 2003. Web. Publisher's VersionAbstract
Gradual bargaining is represented by an agenda: a family of increasing sets of joint utilities, parameterized by time. A solution for gradual bargaining specifies an agreement at each time. We axiomatize an ordinal solution, i.e., one that is covariant with order-preserving transformations of utility. It can be viewed as the limit of a step-by-step bargaining in which the agreement of the last negotiation becomes the disagreement point for the next. The stepwise agreements may follow the Nash solution, the Kalai-Smorodinsky solution or many others.
Sheshinski, Eytan . Bounded Rationality And Socially Optimal Limits On Choice In A Self-Selection Model. Discussion Papers 2003. Web. Publisher's VersionAbstract
When individuals choose from whatever alternatives available to them the one that maximizes their utility then it is always desirable that the government provide them with as many alternatives as possible. Individuals, however, do not always choose what is best for them and their mistakes may be exacerbated by the availability of options. We analyze self-selection models, when individuals know more about themselves than it is possible for governments to know, and show that it may be socially optimal to limit and sometimes to eliminate individual choice. As an example, we apply Luce s (1959) model of random choice to a work-retirement decision model and show that the optimal provision of choice is positively related to the degree of heterogeneity in the population and that even with very small degrees of non-rationality it may be optimal not to provide individuals any choice.
Warglien, Yaakov Kareev, and Massimo. Cognitive Overload And The Evaluation Of Risky Alternatives: The Effects Of Sample Size, Information Format And Attitude To Risk. Discussion Papers 2003. Web. Publisher's VersionAbstract
When the amount of information to be dealt with exceeds people s short-term memory capacity, they must resort to the sampling of information. In the present study we show that, under conditions of cognitive overload (which could result from decision-making under stress, time constraints or information abundance), individuals exhibit systematic differences in estimating variance. Moreover, these differences critically depend on the format of the evidence presented: Variance is downward attenuated when information is presented analogically, but amplified when it is presented numerically. These distortions in the perception of variance affect individuals pricing of risky alternatives. We suggest that these results may help to explain economic anomalies, such as excess trading in financial markets. We also point out possibilities for manipulating the perception of variability and normative implications concerning the presentation of information on the variance of phenomena.
Pradeep Dubey, Ezra Einy, and Ori Haimanko. Compound Voting And The Banzhaf Power Index. Discussion Papers 2003. Web. Publisher's VersionAbstract
We present three axioms for a power index defined on the domain of simple (voting) games. Positivity requires that no voter has negative power, and at least one has positive power. Transfer requires that, when winning coalitions are enhanced in a game, the change in voting power depends only on the change in the game, i.e., on the set of new winning coalitions. The most crucial axiom is composition: the value of a player in a compound voting game is the product of his power in the relevant first-tier game and the power of his delegate in the second-tier game. We prove that these three axioms categorically determine the Banzhaf index.
Peters, Bezalel Peleg, and Hans. Consistent Voting Systems With A Continuum Of Voters. Discussion Papers 2003. Web. Publisher's VersionAbstract
Voting problems with a continuum of voters and finitely many alternatives are considered. The classical Arrow and Gibbard-Satterthwaite theorems are shown to persist in this model, not for single voters but for coalitions of positive size. The emphasis of the study is on strategic considerations, relaxing the nonmanipulability requirement: are there social choice functions such that for every profile of preferences there exists a strong Nash equilibrium resulting in the alternative assigned by the social choice function? Such social choice functions are called exactly and strongly consistent. The study offers an extension of the work of Peleg (1978a) and others. Specifically, a class of anonymous social choice functions with the required property is characterized through blocking coefficients of alternatives, and associated effectivity functions are studied. Finally, representation of effectivity functions by game forms having a strong Nash Equilibrium is studied.
Peleg, Bezalel, and Ton Storcken. Constitutional Implementation Of Social Choice Correspondences. Discussion Papers 2003. Web. Publisher's VersionAbstract
A game form constitutionally implements a social choice correspondence if it implements it in Nash equilibrium and, moreover, the associated effectivity functions coincide. This paper presents necessary and sufficient conditions for a unanimous social choice correspondence to be constitutionally implementable, and sufficient and almost necessary conditions for an arbitrary (but surjective) social choice correspondence to be constitutionally implementable. It is shown that the results apply to interesting classes of scoring and veto rules.
Jean-Marc Tallon, Jean-Christophe Vergnaud, Shmuel Zamir . Contradicting Beliefs And Communication. Discussion Papers 2003. Web. Publisher's VersionAbstract
We address the issue of the representation as well as the evolution of (possibly) mistaken beliefs. We develop a formal setup (a mutual belief space) in which agents might have a mistaken view of what the model is. We then model a communication process, by which agents communicate their beliefs to one another. We define a revision rule that can be applied even when agents have contradictory beliefs. We study its properties and, in particular, show that, when mistaken, agents do not necessarily eventually agree after communicating their beliefs. We finally address the dynamics of revision and show that when beliefs are mistaken, the order of communication may affect the resulting belief structure.
Weiss, Sergiu Hart, and Benjamin, Nathans. Decay And Growth For A Nonlinear Parabolic Equation. Discussion Papers 2003. Web. Publisher's VersionAbstract
We prove a difference equation analogue for the decay-of-mass result for the nonlinear parabolic equation ut = ”u + ¼ |ˆ‡u| when ¼ 0.