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

Andrzej Wieczorek¹

¹ Institute of Computer Science Polish Academy of Sciences Ordona 21 01-237 Warszawa, Poland

Applicationes Mathematicae, Tome 32 (2005) no. 2, pp. 183-193

Résumé

The games of type considered in the present paper (LSE-games) 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 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.

Détail

DOI : 10.4064/am32-2-6

Keywords: games type considered present paper lse games extend concept lsf games studied wieczorek types games being related games continuum players lse games seen anonymous games finitely many types players their action sets included euclidean spaces payoffs depending players own action finitely many integral characteristics distributions players types actions prove existence equilibria present minimization problem complementarity problem nonlinear whose solutions exactly equilibria given game examples applications include model social adaptation model economic efficiency enforced taxation