Publications

1997
Mas-Colell, Sergiu Hart, and Andreu. A Simple Adaptive Procedure Leading To Correlated Equilibrium. Discussion Papers 1997. Web. Publisher's VersionAbstract
We propose a simple adaptive procedure for playing a game. In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies (these measures are updated every period). It is shown that our adaptive procedure guaranties that with probability one, the sample distributions of play converge to the set of correlated equilibria of the game. To compute these regret measures, a player needs to know his payoff function and the history of play. We also offer a variation where every player knows only his own realized payoff history (but not his payoff function).
David Assaf, Larry Goldstein, and Ester Samuel-Cahn. A Statistical Version Of Prophet Inequalities. Discussion Papers 1997. Web. Publisher's VersionAbstract
All classical "prophet inequalities" for independent random variables hold also in the case where only a noise corrupted version of those variables is observable. That is, if the pairs (X1, Z1),...,(Xn,Zn) are independent with arbitrary, known joint distributions, and only the sequence Z1,...,Zn is observable, then all prophet inequalities which hold if the X's were directly observable still hold, even though the expected X-values (i.e. the payoffs) for both the and statistician, will be different. Our model includes, for example, the case when Zi=Xi+Yi, where the Y's are any sequence of independent random variables.
Neyman, Elon Kohlberg, and Abraham. A Strong Law Of Large Numbers For Nonexpansive Vector Valued Stochastic Processes. Discussion Papers 1997. Web. Publisher's Version
Peleg, Bezalel . Almost All Equilibria In Dominant Strategies Are Coalition-Proof. Discussion Papers 1997. Web. Publisher's VersionAbstract
Almost all equilibria in dominant strategies of finite strategic games are coalition-proof.
Peleg, Mukul Majumdar, and Bezalel. An Axiomatization Of The Walras Correspondence In Infinite Dimensional Spaces. Discussion Papers 1997. Web. Publisher's VersionAbstract
This paper presents a generalization of the results of van den Nouweland, Peleg and Tijs on the axiomatization of the Walras correspondence to generalized (pure exchange) economies where the commodity space is the positive cone in an ordered locally convex topological vector space. Our main result characterizes the Walras correspondence completely over an "acceptable" class of economies in terms of consistency, converse consistency, and weak versions of Pareto optimality and non-emptiness. Important examples of economies that are "acceptable" are given in detail.
Zamir, Eyal Winter, and Shmuel. An Experiment With Ultimatum Bargaining In A Changing Environment. Discussion Papers 1997. Web. Publisher's VersionAbstract
We have obtained experimental results on the ultimatum bargaining game that support an evolutionary explanation for subjects' behavior in the game. In these experiments we have created enviornments in which subjects interact with each other in addition to interacting with virtual players, i.e. computer programs with pre-specified stategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behavior closer to the subgame-perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behavior of real subjects depending on the type of "mutants" (virtual players) that were present in their enviornment.
Neyman, Abraham . Cooperation In Repeated Games When The Number Of Stages Is Not Commonly Known (Revision Of Discussion Paper #65). Discussion Papers 1997. Web. Publisher's Version
Pitowsky, Itamar . Correlation Polytopes And The Geometry Of Limit Laws In Probability. Discussion Papers 1997. Web. Publisher's VersionAbstract
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Samet, Dov . Counterfactuals In Wonderland. Discussion Papers 1997. Web. Publisher's VersionAbstract
The literary source of the main ideas in Aumann's article "Backward Induction and Common Knowledge of Rationality" is exposed and analyzed. The primordial archetypal images that underlie both this literary source and Aumann's work are delineated and are used to explain the great emotive impact that this work had on the community of game theorists.
Simon, Robert S. . Difference Between Common Knowledge Of Formulas And Sets, The. Discussion Papers 1997. Web. Publisher's VersionAbstract
This article concerns the interactive model propositional calculus, using the multi-agent epistemic logic S5. With regard to the space % of maximally consistent sets of formulas, the knowledge of an agent is defined by its knowledge of a set of formulas. Common knowledge can be defined in at least two ways, as the common knowledge of a set of formulas or according to the meet partition generated by the knowledge partitions of the agents. With at least two agents, this meet partition is a much finer partition of % than that generated by the common knowledge of sets of formulas, yet for some points of % the two partition members coincide. Whether the two partition members coincide has radical implications for the structure of the meet partition members.
Levy, Sergiu Hart, and Zohar, A. Efficiency Does Not Imply Immediate Agreement. Discussion Papers 1997. Web. Publisher's VersionAbstract
Gul (1989) introduces a non-cooperative bargaining procedure and claims that the payoffs of the resulting efficient stationary subgame perfect equilibria are close to the Shapley value of the underlying transferable utility game (when the discount factor is close to 1). We exhibit here an example showing that efficiency, even for strictly super-additive games, does not imply that all meetings end in agreement. Thus efficiency does not suffice to get Gul's result.
Perry, Vijay Krishna, and Motty. Efficient Mechanism Design. Discussion Papers 1997. Web. Publisher's VersionAbstract
We study Bayesian mechanism design in the context of multidimensional types and quasi-linear preferences. We first show that any two incentive compatible mechanisms which implement the same allocation rule must be payoff equivalent up to an additive constant. This result is then applied to study multiple object auctions. We show that the Vickrey-Clarke-Groves auction maximizes the seller's expected revenue among all efficient auctions.
Tang, Rosemarie Nagel, and Fang-Fang. Experimental Results On The Centipede Game In Normal Form: An Investigation On Learning. Discussion Papers 1997. Web. Publisher's VersionAbstract
We analyze behavior of an experiment on the repeated centipede game played in the reduced normal form. In this game 2 players decide simultaneously when to split a cake. The longer both players wait, the higher the total gain for both. The player who is less patient to wait obtains the larger share of the pie while the other obtains the lower share of the pie. In all standard game theoretic predictions the outcome is that the pie is split immediately. We compare several static models and ouantative learning models, among them quantal response, reinforcement models and fictitious play. Furthermore, we structure behavior from period to period according to a simple cognitive process, called learning direction theory. It is shown that there is a significant difference in behavior whether a player has observed that he got the larger share of the pie or whether he got the smaller share of the pie.
Armando Gomes, Sergiu Hart, and Andreu Mas-Colell. Finite Horizon Bargaining And The Consistent Field. Discussion Papers 1997. Web. Publisher's VersionAbstract
This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show the for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent field converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.
Neyman, Abraham . Finitely Repeated Games With Finite Automata (Revision Of Discussion Paper #69). Discussion Papers 1997. Web. Publisher's VersionAbstract
{The paper studies the implications 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 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 state 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 set of equilibrium payoffs of a sequence of such games. G(n)
Simon, Robert S. . Generation Of Formulas Held In Common Knowledge, The. Discussion Papers 1997. Web. Publisher's VersionAbstract
This ariticle concerns the interactive modal propositional calculus, using the multi-agent epistemic logic S5. With regard to the space of maximally consistent sets of formulas, the relations between three aspects of common knowledge are investigated: 1) whether common knowledge defined semantically is determined by the set of formulas held in common knowledge, 2) the partial order by inclusion of the sets of formulas that can be held in common knowledge, and 3) the cardinality of a generating set of formulas for those held in common knowledge. Additionally, assuming at least two agents, it is shown that the number of connected components of holding only the tautologies in common knowledge has the cardinality of the continuum.
Daniel Rothenstein, . Imperfect Inspection Games Over Time. Discussion Papers 1997. Web. Publisher's VersionAbstract
We consider an inspection game played on a finite time interval. The inspector wishes to detect a violation as soon as possible after it has been made by the operator. The loss to the inspector is assumed to be linear in the duration of the time elapsed between the violation and its detection. The inspection is not observed by the operator unless the inspector calls an alarm. The inspection is imperfect; it has a Type One Error which means that the inspector may call a false alarm (with probability alfa), and a Type Two Error which means that inspection may fail to detect (with probability beta) a violation which did occur. We first solve the game when alfa and beta are fixed and given. Then we consider the more general model in which the error probability alfa is chosen strategically by the inspector and may depend on the time of inspection. This yields two equilibria; one with constant alfa (and beta) and one with alfa increasing in time. The latter cannot be solved analytically. Consequently we solve a numerical example in which the inspction consist of obsderving a normally distributed signal.
Peleg, Bezalel . Implementation Of The Core Of A Marriage Problem. Discussion Papers 1997. Web. Publisher's VersionAbstract
We consider the prosaic system of matching which is specified by the following two common rules: (i) Each woman (man) proposes to at most one man (woman). (ii) A man and a woman marry each other if they propose to each other. Weprove that this system implements the correspondence of stable matchings by strong Nash Equilibria. We also find a simple extensive game form which implements the same correspondence by subgame perfect equilibria.
Yaniv, Gary Bornstein, and Ilan. Individual And Group Behavior In The Ultimatum Game: Are Groups More 'Rational' Players?. Discussion Papers 1997. Web. Publisher's VersionAbstract
This paper reports two ultimatum game experiments comparing the behavior of individuals with that of three-person groups. Group members conducted a short face-to-face discussion in order to decide, as a collective, on a proposed division or on whether to accept or reject a proposal. Both experiments found that groups offered significantly less than individuals. But, as indicated by the low rejection rate in both treatments, groups were also willing to accept less.
Ullmann-Margalit, Edna . Invisible Hand And The Cunning Of Reason, The. Discussion Papers 1997. Web. Publisher's VersionAbstract
This paper traces the ideological career of the notion of the invisible hand, from the 18th century to the 20th. Two main models of invisible-hand explanations are distinguished: the aggregative and the evolutionary. The argument is made that the contemporary use of the idea of the invisible hand by conservatives as against liberals and social planners springs from not distinguishing between these two models. The latter part of the paper draws a comparison between the idea of the invisaible hand and Hegel's historically-related idea of the cunning of reason.