Large games with only small players and finite strategy sets

Abstract

Abstract. Large games of kind considered in the present paper (LSFgames) 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.

Open and Closed Loop Nash Equilibria in Games with a Continuum of Players

“…Some theoretical works on large games are Schmeidler [19], Mas-Colell [20], Balder [21], Wieczorek [22,23], Wieczorek and Wiszniewska [24], WiszniewskaMatyszkiel [25]. An extensive survey of such games is Khan and Sun [26].…”

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

“…All of them are difficult to solve in the general case but special cases can often be solved by methods specific to a particular problem. Wieczorek in [2004] (reported earlier in [1996]) by a specification of positive integers n, k 1 , . .…”

“…A model of production and consumption, presented by Wieczorek in [2004] and also studied by Ekes (Roman) and Wieczorek [1999] and Ekes [2003], deals with infinitely many agents who first face the choice among k activities (the choice of the jth activity by an agent yields the production of a fixed amount of the jth good only) and then consume the goods jointly produced. The existence of a competitive equilibrium has been proven in Wieczorek [2004] by a reduction of the model to an LSF-game. The model itself can be easily extended to the more general case where the production process has more complex character, i.e.…”

“…The LSEgames deal with situations involving a large number of anonymous players who independently choose their actions in a set included in a Euclidean space and whose payoffs depend on finitely many integral characteristics of distributions of the players' actions. This concept generalizes that of LSEgames in Wieczorek [2004], where the sets of actions were assumed finite. Not …”

Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information

“…Some theoretical works on large games are Schmeidler (1973), Mas-Colell (1984), Balder (1995), Wieczorek (2004) and Wieczorek (2005), Wieczorek and Wiszniewska (1999) and Wiszniewska-Matyszkiel (2000).…”