Nash equilibrium with strategic complementarities. (English) Zbl 0708.90094

The existence of Nash equilibrium in non-cooperative games is usually established under the assumption that payoff functions are quasiconcave. This paper starts with a different framework: more precisely, it focuses on games where action sets are lattices and payoff functions have monotonicity properties (they are “supermodular” and have “increasing differences” in the appropriate variables). This model was introduced by D. M. Topkis [SIAM J. Control Optimization 17, 773-787 (1979; Zbl 0433.90091)]. Tarski’s fixed point theorem is a basic tool for the analysis.
The results do not only concern the existence of Nash equilibria in supermodular games but also the order structure of the equilibrium set and the stability of solutions (with respect to “Cournot tâtonnement”). Some aspects of the analysis are extended to Bayesian games.
The previous approach applies in particular to games “with strategic complementarities”. This class of games is relevant to economic applications, as illustrated in the paper.
Reviewer: F.Forges


90C10 Integer programming
91A24 Positional games (pursuit and evasion, etc.)
91B24 Microeconomic theory (price theory and economic markets)


Zbl 0433.90091
Full Text: DOI


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