# Nash and Limit Equilibria of Games with a Continuum of Players

## Author Info

• Guilherme Carmona

## Abstract

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 $\varepsilon_n$-equilibria, with $\varepsilon_n$ converging 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 approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Also, they suggest defining a refinement 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, making limit equilibrium a natural equilibrium concept for games with a continuum of players.

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File URL: http://econwpa.repec.org/eps/game/papers/0311/0311004.pdf

## Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0311004.

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 Length: 39 pages Date of creation: 18 Nov 2003 Date of revision: Handle: RePEc:wpa:wuwpga:0311004 Note: Type of Document - pdf; prepared on win xp; to print on general; pages: 39; figures: 0. none Contact details of provider: Web page: http://econwpa.repec.org

## References

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