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On Large Games with a Bio-Social Typology

  • M. Ali Khan
  • Kali P. Rath
  • Yeneng Sun
  • Haomiao Yu

We present a comprehensive theory of large non-anonymous games in which agents have a name and a determinate social-type and/or biological trait to resolve the dissonance of a (matching-pennies type) game with an exact pure-strategy Nash equilibrium with finite agents, but without one when modeled on the Lebesgue unit interval. We (i) establish saturated player spaces as both necessary and sufficient for an existence result for Nash equilibrium in pure strategies, (ii) clarify the relationship between pure, mixed and behavioral strategies via the exact law of large numbers in a framework of Fubini extension, (iii) illustrate corresponding asymptotic results.

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Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 585.

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Date of creation: Dec 2011
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Handle: RePEc:jhu:papers:585
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  1. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
  2. William A. Brock & Steven N. Durlauf, 2010. "Adoption Curves and Social Interactions," Journal of the European Economic Association, MIT Press, vol. 8(1), pages 232-251, 03.
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  4. Yeneng Sun, 1999. "The complete removal of individual uncertainty: multiple optimal choices and random exchange economies," Economic Theory, Springer, vol. 14(3), pages 507-544.
  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. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  7. Richard McLean & Andrew Postlewaite, . "Informational Size and Incentive Compatibility," CARESS Working Papres 99-14, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  8. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
  9. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer, vol. 34(1), pages 91-104, April.
  10. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
  11. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
  12. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  13. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 192-200, February.
  14. Carmona, Guilherme & Podczeckz, Konrad, 2008. "On the Existence of Pure-Strategy Equilibria in Large Games," FEUNL Working Paper Series wp531, Universidade Nova de Lisboa, Faculdade de Economia.
  15. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity, and the Timing of Attacks," Econometrica, Econometric Society, vol. 75(3), pages 711-756, 05.
  16. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  17. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  18. Cartwright, Edward & Wooders, Myrna, 2004. "On Purification Of Equilibrium In Bayesian Games And Ex-Post Nash Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 701, University of Warwick, Department of Economics.
  19. George A. Akerlof & Rachel E. Kranton, 2000. "Economics And Identity," The Quarterly Journal of Economics, MIT Press, vol. 115(3), pages 715-753, August.
  20. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, 09.
  21. AUMANN, Robert J. & DREZE, Jacques H., . "Rational expectations in games," CORE Discussion Papers RP -2011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  22. Peter Hammond & Yeneng Sun, 2001. "Monte Carlo Simulation of Macroeconomic Risk with a Continuum of Agents: The Symmetric Case," Working Papers 01015, Stanford University, Department of Economics.
  23. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
  24. George-Marios Angeletos & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity and Timing of Attacks," Discussion Papers 1497, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  25. Blume, Lawrence E. & Brock, William A. & Durlauf, Steven N. & Ioannides, Yannis M., 2010. "Identification of Social Interactions," Economics Series 260, Institute for Advanced Studies.
  26. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, vol. 27(1), pages 83-92.
  27. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer, vol. 45(1), pages 1-22, October.
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