Nash and Limit Equilibria of Games with a Continuum of Players,” Universidade Nova de

We show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an εn-equilibria, with εn converg-ing to zero. In our characterization, the sequence of finite games approaches the continuum game in the sense that the set of players and the distribution of characteristics and actions in the finite games converge to those of the continuum game. These results render ap-proximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Also, they suggest defining a re-finement of Nash equilibria for games with a continuum of agents as limit points of equilibria of finite games. This allows us to discard those Nash equilibria that are artifacts of the continuum model, mak-ing limit equilibrium a natural equilibrium concept for games with a continuum of players