Optimal strategies in n-person unilaterally competitive games

Olivier de Wolf
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Olivier de Wolf: Facultés Universitaires Saint-Louis (FUSL), B-1000, Brussels, Belgium and Center for Operations Research and Econometrics (CORE) at Université Catholique de Louvain (UCL), B-1348 Louvain-la-Neuve, Belgium

No 1999049, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, we prove that the concept of value traditionally defined in the class of two-person zero-sum games can be adequately generalized to the class of n-person weakly unilaterally competitive games introduced by Kats & Thisse [KT92b]. We subsequently establish that if there exists an equilibrium in a game belonging to the latter class, then every player possesses at least an optimal strategy (i.e., a strategy yielding at least the value to this player). Furthermore, we show that, in all unilaterally competitive games that have a Nash equilibrium profile, a strategy profile is an equilibrium if and only if it is an optimal profile. From these results, we deduce a very strong foundation to the Nash equilibrium concept in unilaterally competitive games

Date: 1999-09-08
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Citations: View citations in EconPapers (4)

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