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On the Existence of Pure-Strategy Equilibria in Large Games

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  • Carmona, Guilherme
  • Podczeckz, Konrad

Abstract

Over 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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  1. Carmona, Guilherme, 2004. "Nash Equilibria of Games with a Continuum of Players," FEUNL Working Paper Series, Universidade Nova de Lisboa, Faculdade de Economia wp466, Universidade Nova de Lisboa, Faculdade de Economia.
  2. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
  3. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, Econometric Society, vol. 72(6), pages 1631-1665, November.
  4. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
  5. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  6. 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, Elsevier, vol. 76(1), pages 13-46, September.
  7. Carmona, Guilherme, 2008. "Large games with countable characteristics," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 344-347, February.
  8. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006. "Behavioral conformity in games with many players," Games and Economic Behavior, Elsevier, Elsevier, vol. 57(2), pages 347-360, November.
  9. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, Econometric Society, vol. 37(1), pages 25-38, January.
  10. Guilherme Carmona, 2003. "On the Purification of Nash Equilibria of Large Games," Game Theory and Information, EconWPA 0311007, EconWPA.
  11. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer, Springer, vol. 38(2), pages 399-418, February.
  12. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, Elsevier, vol. 12(1), pages 7-10.
  13. Al-Najjar, Nabil I., 2008. "Large games and the law of large numbers," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(1), pages 1-34, September.
  14. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(2), pages 437-470, February.
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Cited by:
  1. Bodoh-Creed, Aaron, 2013. "Efficiency and information aggregation in large uniform-price auctions," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(6), pages 2436-2466.
  2. M. Ali Khan & Kali P. Rath, 2011. "The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 586, The Johns Hopkins University,Department of Economics.
  3. Guilherme Carmona, 2009. "A remark on the measurability of large games," Economic Theory, Springer, Springer, vol. 39(3), pages 491-494, June.
  4. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 585, The Johns Hopkins University,Department of Economics.
  5. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer, Springer, vol. 55(2), pages 457-479, February.
  6. Carmona, Guilherme & Podczeck, Konrad, 2013. "Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions," MPRA Paper 44263, University Library of Munich, Germany.

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