Large games with only small players and finite strategy sets

Andrzej Wieczorek¹

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

Applicationes Mathematicae, Tome 31 (2004) no. 1, pp. 79-96.

Résumé

Large games of kind considered in the present paper (LSF-games) directly generalize the usual concept of $n$-matrix games; the notion is related to games with a continuum of players and anonymous games with finitely many types of players, finitely many available actions and distribution dependent payoffs; however, there is no need to introduce a distribution on the set of types. Relevant features of equilibrium distributions are studied by means of fixed point, nonlinear complementarity and constrained optimization procedures in Euclidean spaces. The games are shown to fit well the voting procedures and evolutionary processes. As an example of application, we present a model of production and consumption by infinitely many households; a competitive equilibrium is obtained via a reduction to an LSF-game; the equilibrating market mechanism is modelled by actions of infinitely many small corrective powers.

Détail

DOI : 10.4064/am31-1-7

Keywords: large games kind considered present paper lsf games directly generalize usual concept n matrix games notion related games continuum players anonymous games finitely many types players finitely many available actions distribution dependent payoffs however there introduce distribution set types relevant features equilibrium distributions studied means fixed point nonlinear complementarity constrained optimization procedures euclidean spaces games shown fit voting procedures evolutionary processes example application present model production consumption infinitely many households competitive equilibrium obtained via reduction lsf game equilibrating market mechanism modelled actions infinitely many small corrective powers