Evolutionary methods of equilibrium selection

Besides the famous stochastic model of KMR and Young there are other less known evolutionary models that are able to select between equilibria. In my invited talk at the First World Congress (Bilbao, July 2000) of the Game Theory Society I presented two such alternative methods:

1) the perfect foresight model introduced by Matsui and Matsuyama (JET 1995) which was further developped in [HS1, HS2, O, HOT] and can be expressed as a differential game.

2) a spatial model (in terms of a reaction diffusion equation) studied in [H1, H2, HHV].

For 2x2 games both methods select the risk-dominant equilibrium. Further selection results have been obtained for special classes of games such as potential games and supermodular games.

The selection results parallel to some extent those for the global games method of Carlsson and van Damme (1993), see the higher order beliefs web page and the survey article of Stephen Morris and Hyun Song Shin for Seattle .

[HS1] J. Hofbauer and Gerhard Sorger: Perfect foresight and equilibrium selection in symmetric potential games. J. Economic Theory 85 , 1-23 (1999).

[HS2] J. Hofbauer and G. Sorger: A differential game approach to evolutionary equilibrium selection. IGTR 4 (2002) 17-31.

[O] D. Oyama: p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics . To appear in JET.

[HOT] J.Hofbauer, D. Oyama and S. Takahashi): Monotone methods for equilibrium selection under perfect foresight dynamics. 2003.

[H1] J. Hofbauer: Equilibrium selection via travelling waves. In: Werner Leinfellner and Eckehart Köhler (eds.): Vienna Circle Institute Yearbook 5/1997 : Game Theory, Experience, Rationality. Foundations of Social Sciences, Economics and Ethics. In Honor of John C. Harsanyi. Dordrecht-Boston-London: Kluwer. pp. 245-259.

[H2] J. Hofbauer: The spatially dominant equilibrium of a game. Annals of Operations Research 89 (1999) 233-251.

[HHV] J. Hofbauer, V. Hutson, G. T. Vickers: Travelling waves for games in economics and biology. Nonlinear Analysis, Theory, Methods & Applications 30, 1235-1244 (1997).

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