On the existence of pure-strategy equilibria in large games

Abstract

Over the years, several formalizations and existence results for games with a continuum of players have been given. In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games. Journal of Economic Literature Classification Numbers: C72

Population Games and Deterministic Evolutionary Dynamics

“…Research on population games is distinguished from the literature on large noncooperative games(Schmeidler, 1973;Khan and Sun, 2002;Balder, 2002;Carmona and Podczeck, 2009) by both the limited diversity assumption and the central role played by disequilibrium dynamics.…”

Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

“…Matyszkiel [17], Carmona and Podczeck [28], and Balbus et al [29]. The general theory of dynamic games with a continuum of players is still being developed by, e.g., Wiszniewska-Matyszkiel [20] for games with a common global state variable, Lasry and Lions [30] for stochastic mean field games where each player is associated with a private state variable and Wiszniewska-Matyszkiel [31] for games with both common global and private state variables.…”

Approximation and characterization of Nash equilibria of large games

“…Previously, in Carmona and Podczeck (2009), we have shown, among other things, that the existence of equilibrium in games with a continuum of players is equivalent to the existence of approximate equilibria in games with a large finite number of players (relative to some class of games). In the present paper, we take a closer look at this equivalence.…”