Nash Equilibria of Games with a Continuum of Players
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.
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- Drew Fudenberg & David Levine, 1983.
"Limit Games and Limit Equilibria,"
UCLA Economics Working Papers
289, UCLA Department of Economics.
- Carmona, Guilherme, 2006.
"On the Existence of Pure Strategy Nash Equilibria in Large Games,"
FEUNL Working Paper Series
wp487, Universidade Nova de Lisboa, Faculdade de Economia.
- Carmona, Guilherme, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," FEUNL Working Paper Series wp465, Universidade Nova de Lisboa, Faculdade de Economia.
- Guilherme Carmona, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," Game Theory and Information 0412008, EconWPA.
- 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.
- 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.
- Guilherme Carmona, 2003.
"Symmetric Approximate Equilibrium Distributions with Finite Support,"
Game Theory and Information
- Carmona, Guilherme, 2004. "Symmetric Approximate Equilibrium Distributions with Finite Support," FEUNL Working Paper Series wp441, 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.
- Green, Edward J, 1984.
"Continuum and Finite-Player Noncooperative Models of Competition,"
Econometric Society, vol. 52(4), pages 975-993, July.
- Green, Edward J., 1982. "Continuum and Finite-Player Noncooperative Models of Competition," Working Papers 418, California Institute of Technology, Division of the Humanities and Social Sciences.
- Barlo, Mehmet & Carmona, Guilherme, 2015.
"Strategic behavior in non-atomic games,"
Journal of Mathematical Economics,
Elsevier, vol. 60(C), pages 134-144.
- Wooders, M. & Selten, R. & Cartwright, E., 2001. "Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies," The Warwick Economics Research Paper Series (TWERPS) 589, University of Warwick, Department of Economics.
- Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April.
- Hildenbrand, W & Mertens, J F, 1972.
"Upper Hemi-Continuity of the Equilibrium-Set Correspondence for Pure Exchange Economies,"
Econometric Society, vol. 40(1), pages 99-108, January.
- HILDENBRAND, Werner & MERTENS, Jean-François, "undated". "Upper hemi-continuity of the equilibrium set correspondence for pure exchange economies," CORE Discussion Papers RP 109, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Mas-Colell, Andreu, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part I: Mixed strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 153-170, June.
- Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June.
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