Purification of Bayesian-Nash equilibria in large games with compact type and action spaces
We present a purification result for incomplete information games with a large but finite number of players that allows compact metric spaces for both actions and types. We then compare our framework and findings to the early purification theorems of Rashid (1983. Equilibrium points of non-atomic games: asymptotic results. Economics Letters 12, 7-10), Cartwright and Wooders (2002 On equilibrium in pure strategies in games with many players. University of Warwick Working Paper 686 (revised 2005)), Kalai (2004. Large robust games. Econometrica 72, 1631-1665) and Wooders, Cartwright and Selten (2006. Behavioral conformity in games with many players. Games and Economic Behavior 57, 347-360). Our proofs are elementary and rely on the Shapley-Folkman theorem.
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- Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
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- Edward Cartwright & Myrna Wooders, 2005. "On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium," Vanderbilt University Department of Economics Working Papers 0512, Vanderbilt University Department of Economics.
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Game Theory and Information
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- Carmona, Guilherme, 2003. "On the Purification of Nash Equilibria of Large Games," FEUNL Working Paper Series wp436, Universidade Nova de Lisboa, Faculdade de Economia.
- Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
- P. D., 1988. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 10(4), pages 527, July.
- Myrna Wooders & Edward Cartwright & Reinhard Selten, 2005.
"Behavioral Conformity in Games with Many Players,"
Vanderbilt University Department of Economics Working Papers
0513, Vanderbilt University Department of Economics.
- Ehud Kalai, 2002.
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1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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