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Large Games with a Bio-Social Typology

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Author Info

  • M. Ali Khan

    (Department of Economics, Johns Hopkins University)

  • Kali P. Rath

    (Department of Economics, University of Notre Dame)

  • Yeneng Sun

    ()
    (Department of Economics, National University of Singapore)

  • Haomiao Yu

    ()
    (Department of Economics, Ryerson University)

Abstract

We present a comprehensive theory of large games in which players have names and determinate social-types and/or biological traits, and identify through four decisive examples, essentially based on a matching-pennies type game, pathologies arising from the use of a Lebesgue interval for player's names. In a sufficiently general context of traits and actions, we address this dissonance by showing a saturated probability space as being a necessary and sufficient name-space for the existence and upper hemi-continuity of pure-strategy Nash equilibria in large games with traits. We illustrate the idealized results by corresponding asymptotic results for an increasing sequence of finite games.

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Bibliographic Info

Paper provided by Ryerson University, Department of Economics in its series Working Papers with number 035.

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Date of creation: Oct 2012
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Handle: RePEc:rye:wpaper:wp035

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Related research

Keywords: Large games; social-type; traits; idealized limit game; saturated probability space; pure-strategy Nash equilibrium; closed-graph property; upper hemi-continuity; asymptotic implementation;

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References

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  1. Rath, Kali P., 1996. "Existence and upper hemicontinuity of equilibrium distributions of anonymous games with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 305-324.
  2. 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.
  3. 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.
  4. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-27, January.
  5. Wang, Jianwei & Zhang, Yongchao, 2010. "Purification, Saturation and the Exact Law of Large Numbers," MPRA Paper 22119, University Library of Munich, Germany.
  6. M Ali Khan & Kali P Rath & Yeneng Sun, 1998. "Pure-Strategy Nash Equilibrium Points in Large Non-Anonymous Games," Economics Working Paper Archive 393, The Johns Hopkins University,Department of Economics.
  7. Sun, Yeneng & Zhang, Yongchao, 2008. "Individual Risk and Lebesgue Extension without Aggregate Uncertainty," MPRA Paper 7448, University Library of Munich, Germany.
  8. George A. Akerlof & Rachel E. Kranton, 2000. "Economics And Identity," The Quarterly Journal of Economics, MIT Press, vol. 115(3), pages 715-753, August.
  9. 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.
  10. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  11. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457 Elsevier.
  12. 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.
  13. Lawrence E. Blume & William A. Brock & Steven N. Durlauf & Yannis M. Ioannides, 2010. "Identification of Social Interactions," Discussion Papers Series, Department of Economics, Tufts University 0754, Department of Economics, Tufts University.
  14. 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.
  15. Steven N. Durlauf & Yannis M. Ioannides, 2009. "Social Interactions," Discussion Papers Series, Department of Economics, Tufts University 0739, Department of Economics, Tufts University.
  16. Khan, A. & Sun, Y., 2000. "Non-Cooperative Games with Many Players," Papiers d'Economie Mathématique et Applications 2000.80, Université Panthéon-Sorbonne (Paris 1).
  17. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
  23. George A. Akerlof & Rachel E. Kranton, 2002. "Identity and Schooling: Some Lessons for the Economics of Education," Journal of Economic Literature, American Economic Association, vol. 40(4), pages 1167-1201, December.
  24. Carmona, Guilherme, 2008. "Large games with countable characteristics," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 344-347, February.
  25. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
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Citations

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Cited by:
  1. Yu, Haomiao & Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 0. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society.
  2. M. Ali Khan & Kali P. Rath & Haomiao Yu & Yongchao Zhang, 2012. "Large Distributional Games with Traits," Working Papers 037, Ryerson University, Department of Economics.

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