We argue that in extensive decision problems (extensive games with a single player) with imperfect recall care must be taken in interpreting information sets and strategies. Alternative interpretations allow for different kinds of analysis. We address the following issues: 1. randomization at information sets; 2. consistent beliefs; 3. time consistency of optimal plans; 4. the multiselves approach to decision making. We illustrate our discussion through an example that we call the ‘‘paradox of the absentminded driver.’’ Journal of Economic Literature Classification (...) Numbers: C7, D0. 1997 Academic Press. (shrink)

p. cm. — (Zeuthen lecture book series) Includes bibliographical references (p. ) and index. ISBN 0-262-18187-8 (hardcover : alk. paper). — ISBN 0-262-68100-5 (pbk. : alk. paper) 1. Decision-making. 2. Economic man. 3. Game theory. 4. Rational expectations (Economic theory) I. Title. II. Series.

The paper is a discussion of the interpretation of game theory. Game theory is viewed as an abstract inquiry into the concepts used in social reasoning when dealing with situations of conflict and not as an attempt to predict behavior. The first half of the paper..

A speaker wishes to persuade a listener to take a certain action. The conditions under which the request is justified, from the listener’s point of view, depend on the state of the world, which is known only to the speaker. Each state is characterized by a set of statements from which the speaker chooses. A persuasion rule specifies which statements the listener finds persuasive. We study persuasion rules that maximize the probability that the listener accepts the request if and only (...) if it is justified, given that the speaker maximizes the probability that his request is accepted. We prove that there always exists a persuasion rule involving no randomization and that all optimal persuasion rules are ex-post optimal. We relate our analysis to the field of pragmatics. (shrink)

Arising out of the author's lifetime fascination with the links between the formal language of mathematical models and natural language, this short book comprises five essays investigating both the economics of language and the language of economics. Ariel Rubinstein touches the structure imposed on binary relations in daily language, the evolutionary development of the meaning of words, game-theoretical considerations of pragmatics, the language of economic agents and the rhetoric of game theory. These short essays are full of challenging (...) ideas for social scientists that should help to encourage a fundamental rethinking of many of the underlying assumptions in economic theory and game theory. As a postscript two economists, Tilman Borgers and Bart Lipman, and a logician, Johan van Benthem offer comments. (shrink)

This paper is an examination of some modelling problems regarding imperfect recall within the model of extensive games. It is argued that, if the assumption of perfect recall is violated, care must be taken in interpreting the main elements of the model. Interpretations that are inconsequential under perfect recall have important implications in the analysis of games with imperfect recall.

Neuroeconomics is examined critically using data on the response times of subjects who were asked to express their preferences in the context of the Allais Paradox. Different patterns of choice are found among the fast and slow responders. This suggests that we try to identify types of economic agents by the time they take to make their choices. Nevertheless, it is argued that it is far from clear if and how neuroeconomics will change economics.

What on earth are economic theorists like me trying to accomplish? This paper discusses four dilemmas encountered by an economic theorist: The dilemma of absurd conclusions: Should we abandon a model if it produces absurd conclusions or should we regard a model as a very limited set of assumptions that will inevitably fail in some contexts? The dilemma of responding to evidence: Should our models be judged according to experimental results? The dilemma of modelless regularities: Should models provide the hypothesis (...) for testing or are they simply exercises in logic that have no use in identifying regularities? The dilemma of relevance: Do we have the right to offer advice or to make statements that are intended to influence the real world? (shrink)

Lecture audiences and students were asked to respond to virtual decision and game situations at gametheory.tau.ac.il. Several thousand observations were collected and the response time for each answer was recorded. There were significant differences in response time across responses. It is suggested that choices made instinctively, that is, on the basis of an emotional response, require less response time than choices that require the use of cognitive reasoning.

We develop a framework for modeling choice in the presence of framing effects. An extended choice function assigns a chosen element to every pair (A, f ) where A is a set of alternatives and f is a frame. A frame includes observable information that is irrelevant in the rational assessment of the alternatives, but nonetheless affects choice. We relate the new framework to the classical model of choice correspondence. Conditions are identified under which there exists either a transitive or (...) a transitive and complete binary relation R such that an alternative x is chosen in some (A, f ) iff x is R-maximal in the set A. We then demonstrate that the framework of choice correspondence misses information, which is essential to economic modeling and which is incorporated in the extended choice function. (shrink)

A survey was carried out among two groups of undergraduate economics students and four groups of students in mathematics, law, philosophy and business administration. The main survey question involved a conflict between profit maximisation and the welfare of the workers who would be fired to achieve it. Significant differences were found between the choices of the groups. The results were reinforced by a survey conducted among readers of an Israeli business newspaper and PhD students of Harvard. It is argued that (...) the overly mathematical methods used to teach economics encourage students to lean towards profit maximisation. (shrink)

This book presents Ariel Rubinstein's lecture notes for the first part of his well-known graduate course in microeconomics.

The standard economic choice model assumes that the decision maker chooses from sets of alternatives. In contrast, we analyze a choice model in which the decision maker encounters the alternatives in the form of a list. We present two axioms similar in nature to the classical axioms of choice from sets. We show that they characterize all the choice functions from lists that involve the choice of either the first or the last optimal alternative in the list according to some (...) preference relation. We then relate choice functions from lists to the classical notions of choice correspondences and random choice functions. (shrink)

This paper studies a decision maker who tackles a choice problem by selecting a subset of (at most) two alternatives which he will consider further in the second stage of his deliberation. We focus on the first stage where he chooses the delebration set. We axiomatize three types of procedures: (i) The top two: the decision maker has in mind an ordering and chooses the two maximal alternatives. (ii) The two extremes: the decision maker has in mind an ordering and (...) chooses the maximal and the minimal alternatives. (iii) The top and the top: the decision maker has in mind two orderings and he chooses the maximal elements. (shrink)

The determination of “who is a J” within a society is treated as an aggregation of the views of the members of the society regarding this question. Methods, similar to those used in Social Choice theory are applied to axiomatize three criteria for determining who is a J: 1) a J is whoever defines oneself to be a J. 2) a J is whoever a “dictator” determines is a J. 3) a J is whoever an “oligarchy” of individuals agrees is (...) a J. (shrink)

The paper springs from a position that economic theory is an abstract investigation of the concepts and considerations involved in real life economic decision making rather than a tool for predicting or describing real behavior. It is argued that when experimental economics is motivated by theory, it should not look to verify the predictions of theory but instead should focus on verifying that the considerations contained in the economic model are sound and in common use. It is argued that when (...) theory is motivated by experiments, the theorist should not be hasty in adopting new functional forms but should try to identify the basic psychological themes which are revealed exposed by the experiment. Finally, some critical comments on the methodology of experimental economics are presented. 2001 Elsevier Science B.V. All rights reserved. (shrink)

Eye tracking is used to investigate human choice procedures. We infer from eye movement patterns in choice problems where the deliberation process is clear to deliberations in problems of choice between two lotteries. The results indicate that participants tend to compare prizes and probabilities separately. The data provide little support for the hypothesis that decision makers use an expected utility type of calculation exclusively. This is particularly true when the calculations involved in comparing the lotteries are complicated.

A speaker wishes to persuade a listener to accept a certain request. The conditions under which the request is justified, from the listener’s point of view, depend on the values of two aspects. The values of the aspects are known only to the speaker and the listener can check the value of at most one. A mechanism specifies a set of messages that the speaker can send and a rule that determines the listener’s response, namely, which aspect he checks and (...) whether he accepts or rejects the speaker’s request. We study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified, given that the speaker maximizes the probability that his request is accepted. We show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the L-principle. (shrink)

(2) Mental preferences: These describe the mental attitude of an individual toward the objects. They can be defined in contexts which do not involve actual choice. In particular, preferences can describe tastes (such as a preference for one season over another) or can refer to situations which are only hypothetical (such as the possible courses of action available to an individual were he to become Emperor of Rome) or which the individual does not fully control (such as a game situation (...) in which a player has preferences over the entire set of outcomes). (shrink)

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information is equivalent to implementation through (...) a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classification Number: C72. (shrink)

A number of experts receive noisy signals regarding a desirable public decision. The public target is to make the best possible decision on the basis of all the information held by the experts. We compare two ``cultures.'' In one, all experts are driven only by the public motive to increase the probability that the desirable action will be taken. In the second, each expert is also driven by a private motive: to have his recommendation accepted. We show that in the (...) first culture, every mechanism will have an equilibrium which does not achieve the public target, whereas the second culture gives rise to a mechanism whose unique equilibrium outcome does achieve the public target. Journal of Economic Literature Classification Numbers: C72, D71. (shrink)

New York University. He is the recipient of the Bruno Prize (2000), the Israel Prize (2002), the Nemmers Prize (2004).

A behavioral dataset contains various preference orderings displayed by the same individual in different payoff-irrelevant circumstances. We introduce a framework for eliciting the individual’s underlying preferences in such cases, in which it is conjectured that the variation in the observed preference orderings is the outcome of some cognitive process that distorts the underlying preferences. We then demonstrate for two cognitive processes how to elicit the individual’s underlying preferences from behavioral datasets.

Resumert Este trabajo presenta varios modelos que destacan el contraste entre las teorias de la decision y de los juegos, por una parte, y la intuicidn y los datos empiricos y experimentales, por otra. Estos ejemplos estimulan la adopcion del punto de vista de la ra-.

For me, economics is a collection of ideas and conventions which economists accept and use to reason with. Namely, it is a culture. Behavioral economics represents a transformation of that culture. Nonetheless, as pointed out by Camerer and Loewenstein (2003), its methods are pretty much the same as those introduced by the Game Theory revolution. At the core of most models in Behavioral Economics there are still agents who maximize a preference relation over some space of consequences and the solution (...) in most cases still involves standard equilibrium concepts. However, the behavioral economists are not committed to what is usually referred to as rational motivations. An economic fable (or a model as we would call it) that has at its core fairness, envy, present-bias and the like is by now not only permitted but even preferred. (shrink)

In the jungle, power and coercion govern the exchange of resources. We study a simple, stylised model of the jungle that mirrors an exchange economy. We define the notion of jungle equilibrium and demonstrate that a number of standard results of competitive markets hold in the jungle.

We study experimentally a two-player game which we find ideal for investigating k-level reasoning. Each player requests an amount of money between 11 and 20 shekels. He receives the amount that he requests and if he requests exactly one shekel less than the other player, he receives an additional 20 shekels. The best response function in this game is straightforward, the k-level strategies are invariant to the two prominent level-0 specifications (randomization or attraction to salience) and the situation calls for (...) self-interest behavior only. Therefore, we propose the game as a test for the "upper bound" for the depth of k-level reasoning in a population. We support this conjecture by studying several variations of the game which manipulate the attractiveness of the level-0 strategy and the monetary cost of undercutting the other player. Keywords: level-k thinking, salience, iterative reasoning.. (shrink)

We show that for solvable games, the calculation of the strategies which survive iterative elimination of dominated strategies in normal games is equivalent to the calculation of the backward induction outcome of some extensive game. However, whereas the normal game form does not provide information on how to carry out the elimination, the corresponding extensive game does. As a by-product, we conclude that implementation using a subgame perfect equilibrium of an extensive game with perfect information is equivalent to implementation through (...) a solution concept which we call guided iteratively elimination of dominated strategies which requires a uniform order of elimination. Journal of Economic Literature Classifica-. (shrink)

In this paper, the term ‘debate’ refers to a situation in which two parties disagree over some issue and each of them tries to persuade a third party, the listener, to adopt his position by raising arguments in his favor. We are interested in the logic behind the relative strength of the arguments and counterarguments; we therefore limit our discussion to debates in which one side is asked to argue first, with the other party having the right to respond before (...) the listener makes up his mind. (shrink)

The paper presents a simple game-theoretic model in which players decide on search procedures for a prize located in one of a set of labeled boxes. The prize is awarded to the player who finds it first. A player can decide on the number of (costly) search units he employs and on the order in which he conducts the search. It is shown that in equilibrium, the players employ an equal number of search units and conduct a completely random search. (...) The paper demonstrates that the search procedure is intrinsically inefficient. Journal of Economic Literature Classification.. (shrink)

We model economic environments in which individual choice sets are fixed and the level of a specific parameter that systematically modifies the preferences of all agents is determined endogenously to achieve equilibrium. The equilibrium concept, Biased Preferences Equilibrium, is reminiscent of competitive equilibrium: agents’ choice sets and their preferences are independent of the behaviour of other agents, the combined choices must satisfy overall feasibility constraints and the endogenous adjustment of the equilibrating preference parameter is analogous to equilibrating price adjustment. The (...) concept is applied in a number of economic examples. (shrink)

Colonel Blotto “secret files” are opened and Information about the way that people play the game is revealed. The files rely on web-based experiments, which involve a tournament version of the Colonel Blotto Game. A total of 6,500 subjects from two diverse populations participated in the tournaments. The results are analyzed in light of a novel procedure of multi-dimensional iterative reasoning. According to the procedure, a player decides separately about different features of his strategy using iterative reasoning. Measuring the response (...) time of the subjects assists in interpreting the reasoning procedure behind the choices. Common properties of the successful strategies in the tournament are exposed. Keywords: Colonel Blotto, Multi-dimensional iterative reasoning, Response Time.. (shrink)

In many decision scenarios, one has to choose an element from a set S given some reference point e. For the case where S is a subset of a Euclidean space, we axiomatize the choice method that selects the point in S that is closest to e. © 1999 Elsevier Science B.V. All rights reserved.

A preference relation is definable in a language if there is a formula in this language which is satisfied precisely for those pairs which satisfy the relation. The paper suggests that definability is a natural category of requirements of preferences in economic models.

Framing effects have a significant influence on the finitely repeated matching pennies game. The combination of being labelled "a guesser", and having the objective of matching the opponent’s action, appears to be advantageous. We find that being a player who aims to match the opponent’s action is advantageous irrespective of whether the player moves first or second. We examine alternative explanations for our results and relate them to Edgar Allan Poe’s "The Purloined Letter". We propose a behavioral model which generates (...) the observed asymmetry in the players’ performance. (shrink)

The paper deals with multiple decision problems, which are similar to the task of guessing the color outcomes of five independent spinnings of a roulette wheel, 60% of whose slots are red and 40% white. Each correct guess yields a prize of $1. The guess of 5 Reds clearly first order stochastic dominates any other strategy. In contrast, subjects diversify their choices when facing a multiple decision problem in which the choice is between lotteries with clear objective probabilities. The diversification (...) is stronger when the subjects face uncertainty without objective probabilities and weaker when the choice problem involves real life actions. c 2002 Elsevier Science B.V. All rights reserved. (shrink)

During the past two decades non-cooperative game theory has become a central topic in economic theory. Many scholars have contributed to this revolution, none more than John Nash. Following the publication of von Neumann and Morgenstern's book, it was Nash's papers in the early fifties which pointed the way for future research in game theory. The notion of Nash equilibrium is indispensable. Nash's formulation of the bargaining problem and the Nash bargaining solution constitute the cornerstone of modern bargaining theory. His (...) insights into the non-cooperative foundations of cooperative game theory initiated an area of research known as the Nash program. Nash's analysis of the demand game in which he uses a perturbation of a game to select an equilibrium inspired the construction of several refinements of the notion of Nash equilibrium. A scholar's influence does not necessarily qualify him for a Nobel prize. One may argue that such awards are a social institution established to serve social goals. It is legitimate to ask what message the Swedish Academy sends to the scientific community and the rest of the world. (shrink)

A number of experts receive noisy signals regarding a desirable public decision. The public target is to make the best possible decision on the basis of all the information held by the experts. We compare two ``cultures.'' In one, all experts are driven only by the public motive to increase the probability that the desirable action will be taken. In the second, each expert is also driven by a private motive: to have his recommendation accepted. We show that in the (...) first culture, every mechanism will have an equilibrium which does not achieve the public target, whereas the second culture gives rise to a mechanism whose unique equilibrium outcome does achieve the public target. Journal of Economic Literature Classification Numbers: C72, D71. 1998 Academic Press.. (shrink)

Agents who employ non-rational choice procedures are often vulnerable to exploitation, in the sense that a profit-seeking trader can offer them a harmful transaction which they will nevertheless accept. We examine the vulnerability of a procedure for deciding whether to buy a lottery: observe another agent who already bought it and buy the lottery if that agent’s experience was positive. We show that the exploitation of such agents can be embedded in an inter-temporal market mechanism, in the form of speculative (...) trade in an asset of no intrinsic value. (JEL: D84). (shrink)

We model differences among agents in their ability to recognize temporal patterns of prices. Using the concept of DeBruijn sequences in two dynamic models of markets, we demonstrate the existence of equilibria in which prices fluctuate in a pattern that is independent of the fundamentals and that can be recognized only by the more competent agents. (JEL: C7, D4.

I love cafés. It’s where academic life meets passion. The noise and tumult veils the soul from the world and enables deeper concentration than a large, wellappointed office affords. There’s just one problem: I hate coffee. The aroma gives me a headache. The bitter taste makes my facial muscles contract. My ideal coffee recipe would be: take a quarter teaspoon of coffee from the large round red container (the one that replaced the blue container as a symbol of Zionism), add (...) a bit of milk and fill to the brim with boiling water. (shrink)

We investigate the procedure of "random sampling" where the alternatives are random variables. When comparing any two alternatives, the decision maker samples each of the alternatives once and ranks them according to the comparison between the two realizations. Our main result is that when applied to three alternatives, the procedure yields a cycle with a probability bounded above by 8 27 . Bounds are also obtained for other related procedures.

about Smith, who usually emerges as a loveable if eccentric bachelor, trying—not always It would be no exaggeration to state that succeeding—to do the proper thing.

Let me start with what you should not do. Do not attend too many seminars in your own field. Otherwise you may simply end up adding a comment to the existing literature, which is mostly made up of comments on previous comments which were themselves only marginal comments. If you want a good idea, look at the world around you or take courses in other disciplines. Some of the papers in my own dissertation (like my 1979 paper on a principal-agent (...) problem with moral hazard and an infinite horizon) were thought of while daydreaming in some law courses I took. (shrink)

The paper presents an approach to selecting among the many subgame-perfect equilibria that exist in a standard concession game with complete information. We extend the description of a game to include a specific 'irrational' (mixed) strategy for each player. Depending on the irrational strategies chosen, we demonstrate that this approach may select a unique equilibrium in which the weaker player concedes immediately. A player is weaker either if he is more impatient or if his irrational strategy is to wait in (...) any period with the higher.. (shrink)

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win (...) the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.  2003 Elsevier Inc. All rights reserved. (shrink)

from now on , was to point out that the model commonly used to describe . a decision problem with imperfect recall suffers from major ambiguities in its interpretation. We claimed that several issues which were immaterial in decision problems with perfect recall may be of importance in the analysis of decision problems with imperfect recall. The issues that we raised can be summarized by the following questions.

In strategic situations, being wealthy andpowerful is consid eredto be advantageous. However, imagine a world where being powerful means being able to seize control of the assets heldandaccumulatedby others. Then, being wealthy might attract the attention of those who are powerful andbe detrimental to one’s wealth. So is being powerful, as those who seize control of the wealth of others will in turn become a desirable target for those who are in a position to seize their acquired wealth. In this (...) short paper, we identify a class of situations where one agent is stronger than another andyet ends up being poorer. (shrink)