Strategic Response with Perfect Information

Dubey, P. (1981). Strategic Response with Perfect Information. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-81-077

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Abstract

Take a game in extensive form with perfect information. Start with an arbitrary choice of strategies by the players. Now let each player -- if he can -- deviate unilaterally to a strategy that will improve his payoff, on the assumption that the others stay put with their choices. This gives rise to a new revised choice of strategies. Iterate the process. We will show that the sequence of strategic choices thus generated becomes stationary, and (of course) constitutes a Nash Equilibrium (N.E.) of the game. This result is embarrassingly simple to prove but seems to us to merit being on record. It does somewhat more than re-establish the classical existence of an N.E. for such games. It shows that the N.E.'s are obtained under the simple dynamic of unilateral strategic improvements. Such improvements underlie the very notion of an N.E. (which is defined to occur when they cannot be made), and so it is natural to use them to set up an associated dynamic.

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