On the Existence of Pure-Strategy Equilibria in Large Games

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On the Existence of Pure-Strategy Equilibria in Large Games

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Carmona, Guilherme
Podczeckz, Konrad

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Guilherme Carmona

Abstract

TOver the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler (1973), Rashid (1983), Mas-Colell (1984), Khan and Sun (1999) and Podczeck (2007a). The level of generality of each of these existence results is typically regarded as a criterion to evaluate how appropriate is the corresponding formalization of large games. In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games.

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Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp531.

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Length: 34 pages
Date of creation: 2008
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Handle: RePEc:unl:unlfep:wp531

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This paper has been announced in the following NEP Reports:

NEP-ALL-2008-11-18 (All new papers)
NEP-GTH-2008-11-18 (Game Theory)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information 0412009, EconWPA. [Downloadable!]
Other versions:
- Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series wp466, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
Carmona, Guilherme, 2004. "On the purification of Nash equilibria of large games," Economics Letters, Elsevier, vol. 85(2), pages 215-219, November. [Downloadable!] (restricted)
Other versions:
- Carmona, Guilherme, 2003. "On the Purification of Nash Equilibria of Large Games," FEUNL Working Paper Series wp436, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
- Guilherme Carmona, 2003. "On the Purification of Nash Equilibria of Large Games," Game Theory and Information 0311007, EconWPA. [Downloadable!]
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.
Other versions:
- 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. [Downloadable!] (restricted)
Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10. [Downloadable!] (restricted)
Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February. [Downloadable!] (restricted)
Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November. [Downloadable!] (restricted)
Other versions:
- Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]

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Guilherme Carmona, 2009. "A remark on the measurability of large games," Economic Theory, Springer, vol. 39(3), pages 491-494, June. [Downloadable!] (restricted)

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