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

Tom 32 / 2005

Andrzej Wieczorek Applicationes Mathematicae 32 (2005), 183-193 MSC: 91A13, 91A10, 91A40, 91B38, 91B24, 91D25. DOI: 10.4064/am32-2-6


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.


  • Andrzej WieczorekInstitute of Computer Science
    Polish Academy of Sciences
    Ordona 21
    01-237 Warszawa, Poland

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