Large games with only small players and strategy sets in Euclidean spaces

Andrzej Wieczorek
2005 Applicationes Mathematicae  
The games of type considered in the present paper (LSEgames) extend the concept of LSF-games studied by Wieczorek in [2004], both types of games being related to games with a continuum of players. LSE-games can be seen as anonymous games with finitely many types of players, their action sets included in Euclidean spaces and payoffs depending on a player's own action and finitely many integral characteristics of distributions of the players' (of all types) actions. We prove the existence of
more » ... e existence of equilibria and present a minimization problem and a complementarity problem (both nonlinear) whose solutions are exactly the same as equilibria in the given game. Examples of applications include a model of social adaptation and a model of economic efficiency enforced by taxation. 1. The basic concepts. The object of our study, large games with only small players and strategy sets in Euclidean spaces (if necessary, we refer to them as LSE-games; L for large, S for small and E for Euclidean) is more general than that considered by Wieczorek in [2004] (referred to there as LSF-games), but the present paper offers results of different kind. The LSEgames deal with situations involving a large number of anonymous players who independently choose their actions in a set included in a Euclidean space and whose payoffs depend on finitely many integral characteristics of distributions of the players' actions. This concept generalizes that of LSEgames in Wieczorek [2004] , where the sets of actions were assumed finite. Not 2000 Mathematics Subject Classification: 91A13, 91A10, 91A40, 91B38, 91B24, 91D25. Journal of Economic Literature Classification: C72, C62, E62, D51.
doi:10.4064/am32-2-6 fatcat:fui4kztiu5ejrgspcoubcldady