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Publications | The Federmann Center for the Study of Rationality

Publications

2003
Sheshinski, Eytan . Optimum And Risk-Class Pricing Of Annuities. Discussion Papers 2003. Web. Publisher's VersionAbstract
When information on longevity (survival functions) is unknown early in life, individuals have an interest to insure themselves against future 'risk-class' classification. Accordingly, the First-Best typically involves transfers across states of nature. Competitive equilibrium cannot provide such transfers if insurance firms are unable to precommit their customers. On the other hand, public insurance plans that do not distinguish between 'risk-class' realizations are also inefficient. It is impossible, a-priori, to rank these alternatives from a welfare point of view.
Sheshinski, Eytan . Optimum Delayed Retirement Credit. Discussion Papers 2003. Web. Publisher's VersionAbstract
A central question for pension design is how benefits should vary with the age of retirement beyond early eligibility age. It is often argued that in order to be neutral with respect to individual retirement decisions benefits should be actuarially fair, that is, the present value of additional contributions and benefits ('Delayed Retirement Credit' - DRC) due to postponed retirement should be equal. We show that in a self-selection, asymmetric information model, because individual decisions are suboptimal, the socially optimal benefit structure should be less than actuarially fair.
Maimaran, Michal . Reducing The Reluctance To Exchange Gambles. Discussion Papers 2003. Web. Publisher's VersionAbstract
Bar-Hillel and Neter (1996) found that although people are willing to trade identical objects, they are reluctant to trade identical lottery tickets. Is this simply due to the fact that these are gambles? It was found that if the value of the tickets is guaranteed to be ex-post, not just ex ante, identical, people are more willing to exchange them. Indeed, just the possibility of ex-post difference between the lottery tickets induces as much reluctance to exchange them as when ex-post difference is guaranteed. In addition, this study examines how the vividness of lottery tickets influences the willingness to trade them. Specifically, it examines whether people are equally reluctant to exchange lottery tickets (when given a bonus for doing so) when they cannot even distinguish between them (e.g., when the tickets are concealed in envelopes). When one cannot see the ticket, it is less vivid and it is harder to imagine it winning. Indeed, it was found that people are more willing to exchange when they cannot distinguish between the tickets than when they can.In 2011, a revised version of this paper was published under the title To trade or not to trade:  The moderating role of vividness when exchanging gambles in Judgment and Decision Making, 6, 147-155.  In the link todp341, it follows the original manuscript. 
Mas-Colell, Sergiu Hart, and Andreu. Regret-Based Continuous-Time Dynamics. Discussion Papers 2003. Web. Publisher's VersionAbstract
Regret-based dynamics have been introduced and studied in the context of discrete-time repeated play. Here we carry out the corresponding analysis in continuous time. We observe that, in contrast to (smooth) fictitious play or to evolutionary models, the appropriate state space for this analysis is the space of distributions on the product of the players' pure action spaces (rather than the product of their mixed action spaces). We obtain relatively simple proofs for some results known in the discrete case (related to "no-regret" and correlated equilibria), and also a new result on two-person potential games (for this result we also provide a discrete-time proof).
Ariane Lambert Mogiliansky, Shmuel Zamir, and Herv\copyright Zwirn. Type Indeterminacy: A Model Of The Kt(Kahneman-Tversky)-Man. Discussion Papers 2003. Web. Publisher's VersionAbstract
In this note we propose to use the mathematical formalism of Quantum Mechanics to capture the idea that agents preferences, in addition to being typically uncertain, can also be indeterminate. They are determined (realized, and not merely revealed) only when the action takes place. An agent is described by a state which is asuperposition of potential types (or preferences or behaviors). This superposed state is projected (or collapses ) onto one of the possible behaviors at the time of the interaction. In addition to the main goal of modelling uncertainty of preferences which is not due to lack of information, this formalism, seems to be adequate to describe widely observed phenomena like framing and instances of noncommutativityin patterns of behavior. We propose two experiments to test the theory.
Tom Baker, Alon Harel, and Tamar Kugler. Virtues Of Uncertainty In Law: An Experimental Approach, The. Discussion Papers 2003. Web. Publisher's VersionAbstract
Predictability in civil and criminal sanctions is generally understood as desirable. Conversely, unpredictability is condemned as a violation of the rule of law. This paper explores predictability in sanctioning from the point of view of efficiency. It is argued that, given a constant expected sanction, deterrence is increased when either the size of the sanction or the probability that it will be imposed is uncertain. This conclusion follows from earlier findings in behavioral decision research and the results of an experiment conducted specifically to examine this hypothesis. The findings suggest that, within an efficiency framework, there are virtues to uncertainty that may cast doubt on the premise that law should always strive to be as predictable as possible.
Samuel-Cahn, David Assaf, and Ester. Why Is One Choice Different?. Discussion Papers 2003. Web. Publisher's VersionAbstract
Let Xi be nonnegative independent random variables with finite expectations and Xn* = max X1,..., Xn. The value Xn* is what can be obtained by a "prophet". A "mortal" onthe other hand, may use k '¥ 1 stopping rules t1,...,tk yielding a return E[max i = 1,...,k X ti]. For n '¥ k the optimal return is Vkn (X1,...,Xn) = sup E[max i = 1,...,k X ti] where the supremum is over all stopping rules which stop by time n. The well known "prophet inequality" states that for all such Xi's and one choice EXn* < 2 V1n (X1,...,Xn) and the constant "2" cannot be improved on for any n '¥ 2. In contrast we show that for k=2 the best constant d satisfying EXn* < d V2n (X1,...,Xn) for all such Xi's depends on n. On the way we obtain constants ck such that EXk+1* < ck Vkk+1 (X1,...,Xk+1).
2002
Zamir, Todd R. Kaplan, and Shmuel. A Note On Revenue Effects Of Asymmetry In Private-Value Auctions. Discussion Papers 2002. Web. Publisher's VersionAbstract
We formulate a way to study whether the asymmetry of buyers (in the sense of having different prior probability distributions of valuations) is helpful to the seller in private-value auctions (asked first by Cantillon [2001]). In our proposed formulation, this question corresponds to two important questions previously asked: Does a first-price auction have higher revenue than a second-price auction when buyers have asymmetric distributions (asked by Maskin and Riley[2000])? And does a seller enhance revenue by releasing information (asked by Milgrom and Weber[1982])? This is shown by constructing two Harsanyi games of incomplete information each having the same ex-ante distribution of valuations but in one beliefs are symmetric while in the other beliefs are sometimes asymmetric. Our main result is that answers to all three questions coincide when values are independent and are related when values are affiliated.
Rinott, Larry Goldstein, and Yosef. A Permutation Test For Matching. Discussion Papers 2002. Web. Publisher's VersionAbstract
We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a hypothesis where there is no distinguished pairing of the observations, a normal approximation, with explicit bounds and rates, is presented for determining approximate critical test levels.
Neeman, Alon Klement, and Zvika. Against Compromise: A Mechanism Design Approach. Discussion Papers 2002. Web. Publisher's VersionAbstract
We consider the following situation. A risk-neutral plaintiff sues a risk-neutral defendant for damages that are normalized to one. The defendant knows whether she is liable or not, but the plaintiff does not. We ask what are the settlement procedure and fee-shifting rule (which, together, we call a mechanism) that minimize the rate of litigation subject to maintaining deterrence. Two main results are presented. The first is a characterization of an upper bound on the rate of settlement that is consistent with maintaining deterrence. This upper bound is shown to be independent of the litigants' litigation cost. It is further shown that any mechanism that attains this upper bound must employ the English fee-shifting rule according to which all litigation costs are shifted to the loser in trial. The second result describes a simple practicable mechanism that attains this upper bound. We discuss our results in the context of recent legal reforms in the U.S. and U.K.
Pitowsky, Itamar . Betting On The Outcomes Of Measurements: A Bayesian Theory Of Quantum Probability. Discussion Papers 2002. Web. Publisher's VersionAbstract
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the others is returned to the agent. If the rules of rationality are followed one obtains the peculiarities of quantum probability, the uncertainty relations and the EPR paradox among others. The consequences of this approach for hidden variables and quantum logic are analyzed.
Peleg, Bezalel . Complete Characterization Of Acceptable Game Forms By Effectivity Functions. Discussion Papers 2002. Web. Publisher's VersionAbstract
Acceptable game forms were introduced in Hurwicz and Schmeidler (1978). Dutta (1984) considered effectivity functions of acceptable game forms. This paper unifies and extends the foregoing two papers. We obtain the following characterization of the effectivity functions of acceptable game forms: An effectivity function belongs to some acceptable game form if (i) it belongs to some Nash consistent game forms; and (ii) it satisfies an extra simple condition (our (3.1) or (4.2)). (Nash consistent game forms have already been characterized by their effectivity functions in Peleg et al. (2001).) As a corollary of our characterization we show that every acceptable game form violates minimal liberalism.
Gilula, Gary Bornstein, and Zohar, A. Effect Of Between-Group Communication On Conflict Resolution In The Assurance And Chicken Team Games, The. Discussion Papers 2002. Web. Publisher's VersionAbstract
We studied conflict resolution in two types of intergroup conflicts modeled as team games, a game of Assurance where the groups incentive to compete is purely fear, and a game of Chicken where the groups incentive to compete is purely greed. The games were operationalized as competitions between two groups with three players in each group. The players discussed the game with other ingroup members, after which they met with the members of the outgroup for a between group discussion, and finally had a within-group discussion before deciding individually whether to participate in their group s collective effort vis-a-vis the other group. We found that all groups playing the Assurance game managed to achieve the collectively efficient outcome of zero participation, whereas groups playing the Chicken game maintained a highly inefficient participation rate of 78%. We conclude that communication between groups is very effective in bringing about a peaceful resolution if the conflict is motivated by mutual fear and practically useless if the conflict is motivated by mutual greed.
Weiss, Gusztav Morvai, and Benjamin, Nathans. Forecasting For Stationary Times Series. Discussion Papers 2002. Web. Publisher's VersionAbstract
The forecasting problem for a stationary and ergodic binary time series Xn is to estimate the probability that Xn+1 = 1 based on the observations Xi, 0 i n without prior knowledge of the distribution of the process Xn. It is known that this is not possible if one estimates at all values of n. We present a simple procedure which will attempt to make such a prediction infinitely often at carefully selected stopping times chosen by the algorithm. We show that the proposed procedure is consistent under certain conditions, and we estimate the growth rate of the stopping times.
Aumann, Robert J. . Game Theory, Bilbao 2000. Discussion Papers 2002. Web. Publisher's VersionAbstract
The Presidential Address at the First International Congress of the Game Theory Society, held in Bilbao, Spain, in July of 2000. The address contains a discussion of the Congress, of the functions and activities of the Society, of the Logo of the Society, of past accomplishments of the discipline, and of some future directions for research. The address is preceded by an introduction by David Kreps.
Gary Bornstein, Tamar Kugler, and Anthony Ziegelmeyer. Individual And Group Decisions In The Centipede Game: Are Groups More Rational  Players?. Discussion Papers 2002. Web. Publisher's VersionAbstract
Two experiments compared the Centipede game played either by 2 individuals or by 2 (3-person) groups. The 2 competitors alternate in deciding whether to take the larger portion of an increasing (or constant) pile of money, and as soon as one takes  the game ends. Assuming that both sides are concerned only with maximizing their own payoffs (and that this is common knowledge), the game theoretic solution, derived by backward induction, is for the first mover to exit the game at the first decision node. Both experiments found that although neither individuals nor groups fully complied with this solution, groups did exit the game significantly earlier than individuals. The study of experimental games has uncovered many instances in which individuals deviate systematically from the game theoretic solution. This study is in accord with other recent experiments in suggesting that game theory may provide a better description of group behavior.
Sunstein, Edna Ullmann-Margalit, and Cass R. Inequality And Indignation. Discussion Papers 2002. Web. Publisher's VersionAbstract
Inequalities often persist because both the advantaged and the disadvantaged stand to lose from change. Despite the probability of loss, moral indignation can lead the disadvantaged to seek to alter the status quo, by encouraging them to sacrifice their material self-interest for the sake of equality. Experimental research shows that moral indignation, understood as a willingness to suffer in order to punish unfair treatment by others, is widespread. It also indicates that a propensity to apparently self-defeating moral indignation can turn out to promote people's material self-interest, if and because others will anticipate their actions. But potential rebels face collective action problems. Some of these can be reduced through the acts of "indignation entrepreneurs," giving appropriate signals, organizing discussions by like-minded people, and engaging in acts of self-sacrifice. Law is relevant as well. By legitimating moral indignation and dissipating pluralistic ignorance, law can intensify and spread that indignation, thus increasing its expression. Alternatively, law can delegitimate moral indignation, or at least raise the cost of its expression, thus stabilizing a status quo of inequality. But the effects of law are unpredictable, in part because it will have moral authority for some but not for others; here too heterogeneity is an issue both for indignation entrepreneurs and their opponents. Examples are given from a range of areas, including labor-management relations, sexual harassment, civil rights, and domestic violence.
Bornstein, Gary . Intergroup Conflict: Individual, Group And Collective Interests.. Discussion Papers 2002. Web. Publisher's VersionAbstract
Intergroup conflicts generally involve conflicts of interests within the competing groups as well. This paper outlines a taxonomy of games, called team games, which incorporate the intragroup and intergroup levels of conflict. Its aims are to provide a coherent framework for analyzing the prototypical problems of cooperation and competition that arise within and between groups, and to review an extensive research program which has utilized this framework to study individual and group behavior in the laboratory. Depending on the game's payoff structure, contradictions or conflicts were created between the rational choices at the individual, group, and collective levels – a generalization of the contradiction between individual and collective rationality occurring in the traditional mixed-motive games. These contradictions were studied so as to identify the theoretical and behavioral conditions that determine which level of rationality prevails.
Hart, Robert J. Aumann, and Sergiu. Long Cheap Talk. Discussion Papers 2002. Web. Publisher's VersionAbstract
With cheap talk, more can be achieved by long conversations than by a single message - even when one side is strictly better informed than the other.
Tam, Yosef Rinott, and Michael, Howlett. Monotone Regrouping, Regression, And Simpson S Paradox. Discussion Papers 2002. Web. Publisher's VersionAbstract
We show in a general setup that if data Y are grouped by a covariate X in a certain way, then under a condition of monotone regression of Y on X, a Simpson s type paradox is natural rather than surprising. This model was motivated by an observation on recent SAT data which are presented.