Optimal Strategies in n-Person Unilaterally Competitive Games

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