Infinite Histories and Steady Orbits in Repeated Games

Itzhak Gilboa (1) , David Schmeidler (2, 3)

1 Northwestern University [Evanston]
2 TAU - Tel Aviv University
3 OSU - Ohio State University [Columbus]

We study a model of repeated games with the following features: (a) Infinite histories. The game has been played since days of yore, or is so perceived by the players: (b) Turing machines with memory. Since regular Turing machines coincide with bounded recall strategies (in the presence of infinite histories), we endow them with "external" memory; (c) Nonstrategic players. The players ignore complicated strategic considerations and speculations about them. Instead, each player uses his/her machine to update some statistics regarding the others′ behaviour, and chooses a best response to observed behaviour. Relying on these assumptions, we define a solution concept for the one shot game, called steady orbit. The (closure of the) set of steady orbit payoffs strictly includes the convex hull of the Nash equilibria payoffs and is strictly included in the correlated equilibria payoffs. Assumptions (a)-(c) above are independent to a large extent. In particular, one may define steady orbits without explicitly dealing with histories or machines.

Mots clés: game; repeated game; model

Domaines: Economie et sciences de la décision

Itzhak Gilboa, David Schmeidler. Infinite Histories and Steady Orbits in Repeated Games. Games and Economic Behavior, 1994, vol.6, n°3, pp.370-399. ⟨10.1006/game.1994.1022⟩. ⟨hal-00481357⟩