Cycling in a stochastic learning algorithm for normal form games |
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Authors: | Martin Posch |
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Institution: | Institut für Medizinische Statistik der Universit?t Wien, Schwarzspanierstra?e 17, A-1090 Vienna, Austria (Fax: +43 1 40480/468, e-mail: poschm@pap.univie.ac.at), AT
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Abstract: | In this paper we study a stochastic learning model for 2×2 normal form games that are played repeatedly. The main emphasis
is put on the emergence of cycles. We assume that the players have neither information about the payoff matrix of their opponent
nor about their own. At every round each player can only observe his or her action and the payoff he or she receives. We prove
that the learning algorithm, which is modeled by an urn scheme proposed by Arthur (1993), leads with positive probability
to a cycling of strategy profiles if the game has a mixed Nash equilibrium. In case there are strict Nash equilibria, the
learning process converges a.s. to the set of Nash equilibria. |
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Keywords: | : Evolutionary games Learning Bounded rationality Learning algorithms |
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