On the Existence of Pure Strategy Nash Equilibria in Large Games
Over the years, several formalizations of games with a continuum of players have been given. These include those of Schmeidler (1973), Mas-Colell (1984) and Khan and Sun (1999). Unlike the others, Khan and Sun (1999) also addressed the equilibrium problem of large ¯- nite games, establishing the existence of a pure strategy approximate equilibrium in su±ciently large games. This ability for their formal- ization to yield asymptotic results led them to argue for it as the right approach to games with a continuum of players. We challenge this view by establishing an equivalent asymptotic theorem based only on Mas-Colell's formalization. Furthermore, we show that it is equivalent to Mas-Colell's existence theorem. Thus, in contrast to Khan and Sun (1999), we conclude that Mas-Colell's for- malization is as good as theirs for the development of the equilibrium theory of large ¯nite games.
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- Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
- Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
- Ehud Kalai, 2001. "Ex-Post Stability in Large Games," Discussion Papers 1351, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Guilherme Carmona, 2004.
"Nash Equilibria of Games with a Continuum of Players,"
Game Theory and Information
- Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp466, Universidade Nova de Lisboa, Faculdade de Economia.
- Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997.
"On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players,"
Journal of Economic Theory,
Elsevier, vol. 76(1), pages 13-46, September.
- M Ali Khan & Kali P Rath & Yeneng Sun, 1994. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economics Working Paper Archive 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
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