Evolution of Beliefs and the Nash Equilibrium of Normal Form Games

Aoyagi, Masaki

doi:10.1006/jeth.1996.0098

Cited by 26 publications

(10 citation statements)

References 9 publications

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“…Aoyagi (1996), studied an extension of fictitious play in which agents test the history for "patterns," which are sequences of outcomes. Agents first check for the pattern of length 1 corresponding to yesterday's outcome, and count how often this outcome has occurred in the past.…”

Section: B Asymptotic Performance and Global Convergencementioning

confidence: 99%

Learning and Equilibrium

Fudenberg

Levine

2009

Annu. Rev. Econ.

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Abstract:The theory of learning in games studies how, which and what kind of equilibria might arise as a consequence of a long-run non-equilibrium process of learning, adaptation and/or imitation. If agents' strategies are completely observed at the end of each round, and agents are randomly matched with a series of anonymous opponents, fairly simple rules perform well in terms of the agent's worst-case payoffs, and also guarantee that any steady state of the system must correspond to an equilibrium.If (as in extensive-form games) players do not observe the strategies chosen by their opponents, then learning is consistent with steady states that are not Nash equilibria because players can maintain incorrect beliefs about off-path play. Beliefs can also be incorrect due to cognitive limitations and systematic inferential errors.

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Section: B Asymptotic Performance and Global Convergencementioning

confidence: 99%

Learning and Equilibrium

Fudenberg

Levine

2009

Annu. Rev. Econ.

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“…He could also use a number of categories corresponding to the number of outcomes, and categorize current outcomes according to the outcome in the previous period. This type of scheme is considered by Aoyagi [1994] and Sonsino [1995]. This method has the additional advantage of doing well when the opponents play follows cycles that are growing in length over time.…”

Section: Use Of Categorization Rulesmentioning

confidence: 99%

“…This means that if we 11 Aoyagi [1994] also considers an example where two players classify observations using different categories. However, in his example players are using exact fictitious play within categories so the player with a more refined category scheme can exploit the player with the less refined scheme.…”

Section: Calibrated Play and Correlated Equilibriummentioning

confidence: 99%

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Conditional Universal Consistency

Fudenberg

Levine

1999

Games and Economic Behavior

115

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Each period, a player must choose an action without knowing the outcome that will be chosen by "Nature," according to an unknown and possibly history-dependent stochastic rule. We discuss have a class of procedures that assign observations to categories, and prescribe a simple randomized variation of fictitious play within each category. These procedures are "conditionally consistent," in the sense of yielding almost as high a time-average payoff as could be obtained if the player chose knowing the conditional distributions of actions given categories. Moreover given any alternative procedure, there is a conditionally consistent procedure whose performance is no more than epsilon worse regardless of the discount factor. Cycles can persist if all players classify histories in the same way; however in an example, where players classify histories differently, the system converges to a Nash equilibrium. We also argue that in the long run the time-average of play should resemble a correlated equilibrium.

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“…While the message of this paper is that some degree of naivete may be unavoidable, one might still hope to construct theories of (semi-) rational learning in which players are more sophisticated than in fictitious play. For recent work along these general lines, see Fudenberg and Levine (1995b), Fudenberg and Levine (1995a), Fudenberg and Levine (1996), Aoyagi (1994), and Sonsino (1995). A feature of much of this literature is that players are modeled as using strategies that are intuitively sensible without necessarily being best responses to well-formed prior beliefs.…”

Section: Fictitious Play and (Semi-) Rational Learningmentioning

confidence: 99%