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Belief Free Incomplete Information Games

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Abstract

We consider the following belief free solution concepts for games with incomplete information: (i) incomplete information rationalizability, (ii) incomplete information correlated equilibrium and (iii) ex post equilibrium. We present epistemic foundations for these solution concepts and establish relationships between them. The properties of these solution concepts are further developed in supermodular games and potential games.

Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1629
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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
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    7. 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 345-361, March.
    8. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
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    10. d'Aspremont, Claude & Gerard-Varet, Louis-Andre, 1979. "Incentives and incomplete information," Journal of Public Economics, Elsevier, vol. 11(1), pages 25-45, February.
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    12. Battigalli, P., 1999. "Rationalizability in Incomplete Information Games," Economics Working Papers eco99/17, European University Institute.
    13. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," CORE Discussion Papers 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    17. Börgers Tilman M & McQuade Timothy, 2007. "Information-Invariant Equilibria of Extensive Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-31, December.
    18. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    19. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(2), pages 223-227.
    20. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
    21. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Cited by:

    1. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    2. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2007. "Interactive epistemology in games with payoff uncertainty," Research in Economics, Elsevier, vol. 61(4), pages 165-184, December.
    3. Besanko, David & Tong, Jian & Wu, Jianjun, 2016. "Subsidizing research programs with "if" and "when" uncertainty in the face of severe informational constraints," Discussion Paper Series In Economics And Econometrics 1605, Economics Division, School of Social Sciences, University of Southampton.
    4. Dirk Bergemann & Stephen Morris, 2011. "Correlated Equilibrium in Games with Incomplete Information," Cowles Foundation Discussion Papers 1822, Cowles Foundation for Research in Economics, Yale University.
    5. Igal Milchtaich, 2014. "Implementability of correlated and communication equilibrium outcomes in incomplete information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 283-350, May.
    6. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    7. repec:eee:gamebe:v:104:y:2017:i:c:p:744-759 is not listed on IDEAS
    8. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    9. Dirk Bergemann & Stephen Morris, 2008. "The Role of the Common Prior in Robust Implementation," Journal of the European Economic Association, MIT Press, vol. 6(2-3), pages 551-559, 04-05.
    10. Yang, Jianxia & Wu, John, 2013. "Strategic correlativity and network games," Economic Modelling, Elsevier, vol. 30(C), pages 663-669.
    11. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
    12. Yamashita, Takuro, 2015. "Strategic and structural uncertainty in robust implementation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 267-279.

    More about this item

    Keywords

    Correlated equilibrium; Rationalizability; Ex post equilibrium; Belief free types; Payo types; Belief types; Supermodular games; Potential games;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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