On the existence of pure-strategy equilibria in large games

Guilherme Carmona and Konrad Podczeck

Journal of Economic Theory, 2009, vol. 144, issue 3, 1300-1319

Abstract: Over the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler [D. Schmeidler, Equilibrium points of nonatomic games, J. Stat. Phys. 4 (1973) 295-300], Rashid [S. Rashid, Equilibrium points of non-atomic games: Asymptotic results, Econ. Letters 12 (1983) 7-10], Mas-Colell [A. Mas-Colell, On a theorem by Schmeidler, J. Math. Econ. 13 (1984) 201-206], Khan and Sun [M. Khan, Y. Sun, Non-cooperative games on hyperfinite Loeb spaces, J. Math. Econ. 31 (1999) 455-492] and Podczeck [K. Podczeck, On purification of measure-valued maps, Econ. Theory 38 (2009) 399-418]. 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.

Keywords: Nash; equilibrium; Pure; strategies; Approximation; Equilibrium; distributions (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (35)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:144:y:2009:i:3:p:1300-1319

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