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A Learning Theory for the Harsanyi's Doctrine in Repeated Games


Leoni, Patrick (2004). A Learning Theory for the Harsanyi's Doctrine in Repeated Games. Working paper series / Institute for Empirical Research in Economics No. 196, University of Zurich.

Abstract

This paper investigates simultaneous learning about both nature and others' actions in repeated games, and identifies a set of sufficient conditions assuring that equilibrium actions converge to a Nash equilibrium.nPlayers have each an utility function over infinite histories continuous for the product topology. Nature' drawing after any history can depend on any past actions, or can be independent of them.nProvided 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 show that after some finite time the equilibrium outcome of the above game is arbitrarily close to a Nash equilibrium.nThose assumptions are shown to be tight.

Abstract

This paper investigates simultaneous learning about both nature and others' actions in repeated games, and identifies a set of sufficient conditions assuring that equilibrium actions converge to a Nash equilibrium.nPlayers have each an utility function over infinite histories continuous for the product topology. Nature' drawing after any history can depend on any past actions, or can be independent of them.nProvided 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 show that after some finite time the equilibrium outcome of the above game is arbitrarily close to a Nash equilibrium.nThose assumptions are shown to be tight.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Institute for Empirical Research in Economics (former)
Dewey Decimal Classification:330 Economics
Language:English
Date:August 2004
Deposited On:29 Nov 2011 22:32
Last Modified:05 Apr 2017 23:12
Series Name:Working paper series / Institute for Empirical Research in Economics
ISSN:1424-0459
Official URL:http://www.econ.uzh.ch/wp.html

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