# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Large games with only small players and finite strategy sets

### Tom 31 / 2004

Applicationes Mathematicae 31 (2004), 79-96 MSC: 91A06, 91A13, 91B24, 91B50, 90C33, 54H25. DOI: 10.4064/am31-1-7

#### Streszczenie

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.

#### Autorzy

• Andrzej WieczorekInstitute of Computer Science