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When all is said and done, how should you play and what should you expect ?

Robert Aumann and Jacques Dreze

No 2005021, CORE Discussion Papers from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Modern game theory was born in 1928, when John von Neumann published his Minimax Theorem.This theorem ascribes to all two-person zero-sum games a value - what rational players may expect - and optimal strategies? how they should play to achieve that expectation.Sev entyseven years later, strategic game theory has not gotten beyond that initial point, insofar as the basic questions of value and optimal strategies are concerned.Equilibrium theories do not tell players how to play and what to expect; even when there is a unique Nash equilibrium, it it is not at all clear that the players "should" play this equilibrium, nor that they should expect its payoff.Here, we return to square one: abandon all ideas of equilibrium and simply ask, how should rational players play, and what should they expect. We provide answers to both questions, for all n-person games in strategic form.

Date: 2005-02
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