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102
Epistemic conditions for Nash equilibrium
, 1991
"... According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if ..."
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Cited by 226 (6 self)
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According to conventional wisdom, Nash equilibrium in a game “involves” common knowledge of the payoff functions, of the rationality of the players, and of the strategies played. The basis for this wisdom is explored, and it turns out that considerably weaker conditions suffice. First, note that if each player is rational and knows his own payoff function, and the strategy choices of the players are mutually known, then these choices form a Nash equilibrium. The other two results treat the mixed strategies of a player not as conscious randomization of that player, but as conjectures of the other players about what he will do. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures yields Nash equilibrium. When n ≥ 3, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures yield Nash equilibrium when there is a common prior. Examples are provided showing these results to be sharp.
On Ambiguities In The Interpretation Of Game Trees
 Games and Economic Behavior
, 1996
"... Piccione and Rubinstein have pointed out ambiguities in the interpretation of games of imperfect recall. They focus on the notion of time consistency, and argue that a player in a game of imperfect recall may be time inconsistent, changing his strategy despite no new information and no change in his ..."
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Cited by 34 (14 self)
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Piccione and Rubinstein have pointed out ambiguities in the interpretation of games of imperfect recall. They focus on the notion of time consistency, and argue that a player in a game of imperfect recall may be time inconsistent, changing his strategy despite no new information and no change in his preferences. In this paper, it is argued that the apparent time inconsistency arises from implicit assumptions made in the definition about what the driver knows when he reconsiders his strategy and what he will remember if he changes his strategy, and about how the node at which reconsideration takes place is chosen. A model is proposed, based on earlier work in the computer science literature, that allows usindeed, almost forces usto make these issues explicit. Once these issues are made explicit, time inconsistency seems less inconsistent. Most of this work was carried out while I was at the IBM Almaden Research Center. I gratefully acknowledge IBM's support. This version of the ...
Decision theory without logical omniscience: Towards an axiomatic framework for bounded rationality
 Review of Economic Studies
, 1999
"... I propose modelling boundedly rational agents as agents who are not logically omniscientthat is, who do not know all logical or mathematical implications of what they know. I show how a subjective state space can be derived as part of a subjective expected utility representation of the agent's ..."
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Cited by 27 (2 self)
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I propose modelling boundedly rational agents as agents who are not logically omniscientthat is, who do not know all logical or mathematical implications of what they know. I show how a subjective state space can be derived as part of a subjective expected utility representation of the agent's preferences. The representation exists under very weak conditions. The representation uses the familiar language of probability, utility, and states of the world in the hope that this makes this model of bounded rationality easier to use in applications.
On the convergence of fictitious play
 Mathematics of Operations Research
, 1998
"... We study the continuous time BrownRobinson ctitious play process for nonzero sum games. We show that, in general, ctitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies. 1 ..."
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Cited by 20 (0 self)
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We study the continuous time BrownRobinson ctitious play process for nonzero sum games. We show that, in general, ctitious play cannot converge cyclically to a mixed strategy equilibrium in which both players use more than two pure strategies. 1
AwarenessDependent Subjective Expected Utility
 International Journal of Game Theory
, 2011
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Modeling the Economic Interaction of Agents with Diverse Abilities to Recognize Equilibrium Patterns
"... 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 ca ..."
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Cited by 16 (4 self)
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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.
Reputations, Relationships and the Enforcement of Incomplete Contracts
, 2006
"... This paper discusses the literature on the enforcement of incomplete contracts. It compares legal enforcement to enforcement via relationships and reputations. A number of mechanisms, such as the repeat purchase mechanism (Klein and Leffler (1981)) and efficiency wages (Shapiro and Stiglitz (1984)), ..."
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Cited by 16 (0 self)
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This paper discusses the literature on the enforcement of incomplete contracts. It compares legal enforcement to enforcement via relationships and reputations. A number of mechanisms, such as the repeat purchase mechanism (Klein and Leffler (1981)) and efficiency wages (Shapiro and Stiglitz (1984)), have been o ered as solutions to the problem of enforcing an incomplete contract. It is shown that the efficiency of these solutions is very sensitive to the characteristics of the good or service exchanged. In general, neither the repeat purchase mechanism nor efficiency wages is the most efficient in the set of possible relational contracts. In many situations, total output may be increased through the use of performance pay and through increasing the quality of law.
An Experimental Investigation of Unprofitable Games
, 2002
"... We investigate behavior in two unprofitable games—where Maxmin strategies do not form a Nash equilibrium yet guarantee the same payoff as Nash equilibrium strategies—that vary in the riskiness of the Nash strategy. We find that arguments for the implausibility of Nash equilibrium are confirmed by ou ..."
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Cited by 13 (0 self)
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We investigate behavior in two unprofitable games—where Maxmin strategies do not form a Nash equilibrium yet guarantee the same payoff as Nash equilibrium strategies—that vary in the riskiness of the Nash strategy. We find that arguments for the implausibility of Nash equilibrium are confirmed by our experiments; however, claims that this will lead to Maxmin play are not. Neither solution concept accounts for more than 53 % of choices in either game. The results indicate that the tension between the Nash and Maxmin strategies does not resolve itself over the course of the experiment. Moreover, the relative performance of the solution concepts is sensitive to the riskiness of the Nash strategy.
DEDUCTIVE REASONING IN EXTENSIVE GAMES
, 2003
"... We justify the application to extensive games of a model of deductive reasoning based on three key features: ‘caution’, ‘full belief of opponent rationality’, and ‘no extraneous restrictions on beliefs’. We apply the model to several examples, and show that it yields novel economic insights. The app ..."
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Cited by 10 (1 self)
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We justify the application to extensive games of a model of deductive reasoning based on three key features: ‘caution’, ‘full belief of opponent rationality’, and ‘no extraneous restrictions on beliefs’. We apply the model to several examples, and show that it yields novel economic insights. The approach supports forward induction, without necessarily promoting backward induction.