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Correlated equilibrium existence for infinite games with type-dependent strategies

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  • Stinchcombe, Maxwell B.

Abstract

Under study are games in which players receive private signals and then simultaneously choose actions from compact sets. Payoffs are measurable in signals and jointly continuous in actions. This paper gives a counter-example to the main step in Cotter[modifier letter apostrophe]s [K. Cotter, Correlated equilibrium in games with type-dependent strategies, J. Econ. Theory 54 (1991) 48-69] argument for correlated equilibrium existence for this class of games, and supplies an alternative proof.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 2 (March)
Pages: 638-655

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:2:p:638-655

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Infinite games Correlated equilibrium existence Informational commonalities Nonstandard analysis;

References

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  1. Simon, Leo K. & Zame, William R., 1987. "Discontinous Games and Endogenous Sharing Rules," Department of Economics, Working Paper Series qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  2. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07.
  4. Maxwell B. Stinchcombe, 1994. "Countably Additive Subjective Probabilities," CARE Working Papers 9403, The University of Texas at Austin, Center for Applied Research in Economics.
  5. Stinchcombe, Maxwell B., 2005. "Nash equilibrium and generalized integration for infinite normal form games," Games and Economic Behavior, Elsevier, vol. 50(2), pages 332-365, February.
  6. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
  7. Manelli, Alejandro M, 1996. "Cheap Talk and Sequential Equilibria in Signaling Games," Econometrica, Econometric Society, vol. 64(4), pages 917-42, July.
  8. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, 01.
  9. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
  10. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
  11. 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.
  12. Harris, Christopher J. & Stinchcombe, Maxwell B. & Zame, William R., 2005. "Nearly compact and continuous normal form games: characterizations and equilibrium existence," Games and Economic Behavior, Elsevier, vol. 50(2), pages 208-224, February.
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Cited by:
  1. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
  2. Stinchcombe, Maxwell B., 2011. "Balance and discontinuities in infinite games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 146(2), pages 656-671, March.

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