Cycling with a Generalized Urn Scheme and a Learning Algorithm for 2X2 Games

Posch, M. (1994). Cycling with a Generalized Urn Scheme and a Learning Algorithm for 2X2 Games. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-94-076

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Abstract

In this paper we explore a learning algorithm for 2x2 games. We assume that the players neither know the payoff matrix of their opponent nor their own and can only observe their own actions and their own payoffs. We prove that the learning process, which is modelled by a generalized urn scheme, converges to a pure strategy profile if the game has at least one strict Nash equilibrium. In case there is no strict Nash equilibrium, the learning algorithm exhibits oscillations. We derive sufficient conditions that cycling occurs in a generalized urn scheme.

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