Andrzej Wieczorek

Simple large games and their applications to problems with many agents

842

Abstract

The concept of simple large (SL) games extends that of elementary large (EL) games studied by Wieczorek in 1996, both of them related to the games with a continuum of players. SL-games can be regarded 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 remaining players' actions. We prove the existence of equilibrated distributions and present a minimization problem and a complementarity problem (both nonlinear) whose solutions are exactly the same as equilibrated distributions in the given game. Examples of applications include a model of social adaptation and a model of economic efficiency enforced by taxation.

Key words: (simple) large game, SL-game, equilibrated distribution, noncooperative game, measure space of players, continuum of players, Kakutani Theorem, Cournot-Nash equilibrium, production-consumption model, competitive equilibrium, social adaptation, characteristic, taxation, efficiency.