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Strategic behavior in non-atomic games

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  • Barlo, Mehmet
  • Carmona, Guilherme

Abstract

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player's belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 35549.

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Date of creation: 13 Dec 2011
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Handle: RePEc:pra:mprapa:35549

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Keywords: Strategic equilibrium; Games with a continuum of players; Equilibrium distributions;

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References

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  1. V.V. Chari & Patrick J. Kehoe, 1989. "Sustainable plans and mutual default," Staff Report, Federal Reserve Bank of Minneapolis 124, Federal Reserve Bank of Minneapolis.
  2. Carmona, Guilherme, 2008. "Large games with countable characteristics," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 344-347, February.
  3. Chari V. V. & Kehoe Patrick J., 1993. "Sustainable Plans and Debt," Journal of Economic Theory, Elsevier, Elsevier, vol. 61(2), pages 230-261, December.
  4. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1161-80, September.
  5. 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, The Johns Hopkins University,Department of Economics 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
  6. Chari, V V & Kehoe, Patrick J, 1990. "Sustainable Plans," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 98(4), pages 783-802, August.
  7. 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.
  8. Sabourian, Hamid, 1990. "Anonymous repeated games with a large number of players and random outcomes," Journal of Economic Theory, Elsevier, Elsevier, vol. 51(1), pages 92-110, June.
  9. Wolfgang Pesendorfer & David Levine, 1992. "When are Agents Negligible?," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1018, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Guilherme Carmona, 2009. "A remark on the measurability of large games," Economic Theory, Springer, Springer, vol. 39(3), pages 491-494, June.
  11. Damme, E.E.C. van & Kühn, H. & Harsanyi, J. & Selten, R. & Weibull, J. & Nash Jr., J. & Hammerstein, P., 1996. "The work of John Nash in game theory," Open Access publications from Tilburg University urn:nbn:nl:ui:12-73413, Tilburg University.
  12. 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.
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Cited by:
  1. Carmona, Guilherme, 2004. "On the Existence of Equilibrium Bank Runs in a Diamond-Dybvig Environment," FEUNL Working Paper Series wp448, Universidade Nova de Lisboa, Faculdade de Economia.
  2. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information, EconWPA 0311004, EconWPA.
  3. Guilherme Carmona, 2004. "Nash Equilibria of Games with a Continuum of Players," Game Theory and Information, EconWPA 0412009, EconWPA.
  4. Alioğulları, Zeynel Harun & Barlo, Mehmet, 2012. "Entropic selection of Nash equilibrium," MPRA Paper 37132, University Library of Munich, Germany.
  5. Carmona, Guilherme, 2003. "A Re-Interpretation of the Concept of Nash Equilibrium Based on the Notion of Social Institutions," FEUNL Working Paper Series wp425, Universidade Nova de Lisboa, Faculdade de Economia.
  6. Guilherme Carmona, 2003. "A Re-Interpretation of Nash Equilibrium Based on the Notion of Social Institutions," Game Theory and Information, EconWPA 0311005, EconWPA.

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