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Discrete Time Dynamic Games with a continuum of Players I: Decomposable Games

The purpose of this paper is to present some simple properties and applications of dynamic games with discrete time and a continuum of players. For such games relations between dynamic equilibria and families of static equilibria in the corresponding static games, as well as between dynamic and static best response sets are examined and an equivalence theorem is proven. The existence of a dynamic equilibrium is also proven. These results are counterintuitive since they differ from results that can be obtained in similar games with a finite number of players.The theoretical results are illustrated with examples describing voting and exploitation of ecological systems.