Fictitious Play in 2×n Games

Ulrich Berger

doi:10.1016/j.jet.2004.02.003

Fictitious Play in 2×n Games

Ulrich Berger

Department für Volkswirtschaft (Berger)

Publikation: Wissenschaftliche Fachzeitschrift › Originalbeitrag in Fachzeitschrift › Begutachtung

Abstract

It is known that every discrete-time fictitious play process approaches equilibrium in nondegenerate 2×2 games, and that every continuous-time fictitious play process approaches equilibrium in nondegenerate 2×2 and 2×3 games. It has also been conjectured that convergence to the set of equilibria holds generally for nondegenerate 2×n games. We give a simple geometric proof of this for the continuous-time process, and also extend the result to discrete-time fictitious play.

Originalsprache	Englisch
Seiten (von - bis)	139 - 154
Fachzeitschrift	Journal of Economic Theory
Volume	120
Ausgabenummer	2
DOIs	https://doi.org/10.1016/j.jet.2004.02.003
Publikationsstatus	Veröffentlicht - 2005

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Zitat

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title = "Fictitious Play in 2{\texttimes}n Games",

abstract = "It is known that every discrete-time fictitious play process approaches equilibrium in nondegenerate 2{\texttimes}2 games, and that every continuous-time fictitious play process approaches equilibrium in nondegenerate 2{\texttimes}2 and 2{\texttimes}3 games. It has also been conjectured that convergence to the set of equilibria holds generally for nondegenerate 2{\texttimes}n games. We give a simple geometric proof of this for the continuous-time process, and also extend the result to discrete-time fictitious play.",

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AB - It is known that every discrete-time fictitious play process approaches equilibrium in nondegenerate 2×2 games, and that every continuous-time fictitious play process approaches equilibrium in nondegenerate 2×2 and 2×3 games. It has also been conjectured that convergence to the set of equilibria holds generally for nondegenerate 2×n games. We give a simple geometric proof of this for the continuous-time process, and also extend the result to discrete-time fictitious play.

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M3 - Journal article

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