SFB 303 Discussion Paper No. A - 183

Author: Hellwig, Martin, and Wolfgang Leininger
Title: Markov-Perfect Equilibrium in Games of Perfect Information
Abstract: We study infinite-action games of perfect information with finitely many players. Specifically, we are interested in establishing existence of subgame-perfect equilibrium (Selten (1965)) in certain "simple" strategies. The games considered in this paper allow a representation via "state variables", such that for any date t, the subgame that is played from date t onwards depends on the history (resp. state trajectory) up to tonly as this history affects the present state at t. Available results for such games ensure the existence of subgame-perfect equilibrium in general history - dependent or trajectory-dependent strategies (Harris (1985), Hellwig and Leininger (1987)). Here we consider the existence of subgame-perfect equilibrium in strategies that condition only on the respective present "state variables". Such strategies are called Markov strategies; a subgame-perfect equilibrium in Markov strategies is called Markov-perfect. Markov strategies are attractive because their structure reflects the underlying structure of the game itself. If a player uses a Markov strategy, his behaviour at any date t depends on the history of the game only as this history affects the subgame that is played from date t on. Thus, the Markov property is a necessary ingredient of what Harsanyi and Selten (1988) call subgame- consistency, i.e. the behaviour principle according to which a player's behaviour in strategically equivalent subgames should be the same, regardless of the different paths by which these subgames might be reached.
Creation-Date: July 1988
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