Learning by Forgetful Players

Hurkens, Sjaak

doi:10.1006/game.1995.1053

Cited by 75 publications

(64 citation statements)

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“…There is a handful such models in the economics literature. Some of these have been shown to converge to minimal curb sets, see Young (1993Young ( , 1998, Hurkens (1995) and Sanchirico (1996). In the same vein, Kets and Voorneveld (2008) establish convergence to minimal prep sets (see Remark 1) when individuals tend to favor recently used strategies-a form of habit formation.…”

Section: Resultsmentioning

confidence: 92%

Tenable Strategy Blocks and Settled Equilibria

Myerson¹,

Weibull²

2015

Econometrica

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Abstract.When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set-valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal-form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal-form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff-equivalent equilibrium, a property that other related concepts have not satisfied.

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Section: Resultsmentioning

confidence: 92%

Tenable Strategy Blocks and Settled Equilibria

Myerson¹,

Weibull²

2015

Econometrica

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“…Models of evolution with incomplete sampling have also been considered by Young (1993aYoung ( , 1993b, Hurkens (1995), Kaniovski andYoung (1995), andSáez-Martí andWeibull (1999). In these models, players choose best responses to an incomplete memory of past play rather than an incomplete sample of current behavior.…”

Section: Theorem: If S I Ismentioning

confidence: 99%

Almost global convergence to p -dominant equilibrium

Sandholm

2001

International Journal of Game Theory

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A population of players repeatedly plays an n strategy symmetric game. Players update their strategies by sampling the behavior of k opponents and playing a best response to the distribution of strategies in the sample. Suppose the game possesses a 1 k -dominant strategy which is initially played by a positive fraction of the population. Then if the population size is large enough, play converges to the 1 k -dominant equilibrium with arbitrarily high probability.

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“…It is within these minimal curb sets that many intuitive models of strategic adjustment settle down (Young, 1993, Hurkens, 1995, Kosfeld et al, 2002. Moreover, in several classes of relevant games, minimal curb sets yield nice results.…”

Section: Introductionmentioning

confidence: 94%

The Cutting Power of Preparation

Tercieux¹,

Voorneveld

2005

SSRN Journal

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In a strategic game, a curb set [Basu and Weibull, Econ. Letters 36 (1991) 141] is a product set of pure strategies containing all best responses to every possible belief restricted to this set. Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403] relax this condition by only requiring the presence of at least one best response to such a belief.The purpose of this paper is to provide economically interesting classes of games in which minimal prep sets give sharp predictions, whereas in relevant subclasses of these games, minimal curb sets have no cutting power whatsoever and simply consist of the entire strategy space. These classes include potential games, congestion games with playerspecific payoffs, and supermodular games. JEL classification: C72

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Learning by Forgetful Players

Cited by 75 publications

References 0 publications

Tenable Strategy Blocks and Settled Equilibria

Tenable Strategy Blocks and Settled Equilibria

Almost global convergence to p -dominant equilibrium

The Cutting Power of Preparation

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