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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 453168, 9 pages
Research Article

Learning in General Games with Nature’s Moves

Kedge Business School, Domaine de Luminy, BP 921, 13 288 Marseille Cedex 9, France

Received 10 October 2013; Accepted 21 December 2013; Published 19 January 2014

Academic Editor: Takashi Matsuhisa

Copyright © 2014 Patrick L. Leoni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates simultaneous learning about both nature and others’ actions in repeated games and identifies a set of sufficient conditions for which Harsanyi’s doctrine holds. Players have a utility function over infinite histories that are continuous for the sup-norm topology. Nature’s drawing after any history may depend on any past actions. Provided that (1) every player maximizes her expected payoff against her own beliefs, (2) every player updates her beliefs in a Bayesian manner, (3) prior beliefs about both nature and other players’ strategies have a grain of truth, and (4) beliefs about nature are independent of actions chosen during the game, we construct a Nash equilibrium, that is, realization-equivalent to the actual plays, where Harsanyi’s doctrine holds. Those assumptions are shown to be tight.