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On Purification Of Equilibrium In Bayesian Games And Ex-Post Nash Equilibrium

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  • Cartwright, Edward

    (EUREQUA, Paris 1)

  • Wooders, Myrna

    (Department of Economics, University of Warwick)

Abstract

We demonstrate that if any realization of a strategy for a Bayesiangame is, with high probability, an approximate Nash equilibrium of the induced game of complete information, then there is purification of that strategy that is an approximate equilibrium of the original Bayesian game. We also provide two examples demonstrating, amongst other things, that the bound we obtain on the distance of the purification from satisfying the requirements for an exact equilibrium is tight.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp701.pdf
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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 701.

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Length: 10 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:wrk:warwec:701

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Keywords: purification ; expost Nash ; Bayesian games;

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References

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  1. Cartwright, Edward & Wooders, Myrna, 2003. "On Equilibrium in Pure Stategies in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 686, University of Warwick, Department of Economics.
  2. M Ali Khan & Yeneng Sun, 2002. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 482, The Johns Hopkins University,Department of Economics.
  3. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
  4. 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, vol. 76(1), pages 13-46, September.
  5. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, vol. 55(1), pages 69-94, January.
  6. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
  7. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
  8. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer, vol. 27(1), pages 83-92.
  9. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
  10. 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.
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Citations

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Cited by:
  1. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer, vol. 38(1), pages 137-153, March.
  2. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.
  3. 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.
  4. Carmona, Guilherme, 2008. "Purification of Bayesian-Nash equilibria in large games with compact type and action spaces," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1302-1311, December.

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