 Nash equilibria of games with a continuum of playersNova SBE Working Paper Series from Universidade Nova de Lisboa, Nova School of Business and Economics Abstract: We characterize Nash equilibria of games with a continuum of players (Mas-Colell (1984)) in terms of approximate equilibria of large finite games. For the concept of ("; ") equilibrium in which the fraction of players not " optimizing is less than " 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 ("n; "n) equilibria, with "n converging to zero. The same holds for " equilibrium in which almost all players are " optimizing provided that either players payoff functions are equicontinuous or players action space is finite. Furthermore, we give conditions under which the above results hold for all approximating sequences of games. In our characterizations, a sequence of finite games approaches the continuum game in the sense that the number of players converges to infinity and the distribution of characteristics and actions in the finite games converges to that of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance. Pages: 31 pages Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:unl:unlfep:wp466 Access Statistics for this paper More papers in Nova SBE Working Paper Series from Universidade Nova de Lisboa, Nova School of Business and Economics Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.