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Partially Specified Probabilities: Decisions and Games

Author

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  • Ehud Lehrer

Abstract

The paper develops a theory of decision making based on partially specified probabilities. It takes an axiomatic approach using Anscombe and Aumann's (1963) setting, and is based on the concave integral for capacities. This theory is then expanded to interactive models in order to extend Nash equilibrium by introducing the concept of partially specified equilibrium. (JEL C70, D81, D83)

Suggested Citation

  • Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
  • Handle: RePEc:aea:aejmic:v:4:y:2012:i:1:p:70-100
    Note: DOI: 10.1257/mic.4.1.70
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    References listed on IDEAS

    as
    1. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    4. Jiankang Zhang, 2002. "Subjective ambiguity, expected utility and Choquet expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 159-181.
    5. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    8. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    2. repec:eee:jetheo:v:175:y:2018:i:c:p:265-290 is not listed on IDEAS
    3. Ehud Lehrer & Eilon Solan, 2016. "A General Internal Regret-Free Strategy," Dynamic Games and Applications, Springer, vol. 6(1), pages 112-138, March.
    4. repec:eee:gamebe:v:114:y:2019:i:c:p:285-307 is not listed on IDEAS
    5. Giuseppe De Marco & Maria Romaniello, 2015. "On Games and Equilibria with Coherent Lower Expectations," CSEF Working Papers 397, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    7. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
    8. Giuseppe De Marco & Maria Romaniello, 2014. "Variational Preferences and Equilibria in Games under Ambiguous Beliefs Correspondences," CSEF Working Papers 363, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    9. Giuseppe De Marco, 2019. "On the convexity of preferences in decisions and games under (quasi-)convex/concave imprecise probability correspondences," CSEF Working Papers 523, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    10. De Marco, Giuseppe & Romaniello, Maria, 2013. "A limit theorem for equilibria under ambiguous belief correspondences," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 431-438.
    11. Battigalli, P. & Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2016. "Analysis of information feedback and selfconfirming equilibrium," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 40-51.
    12. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications, Elsevier.
    13. Ronald Stauber, 2019. "A strategic product for belief functions," ANU Working Papers in Economics and Econometrics 2019-668, Australian National University, College of Business and Economics, School of Economics.
    14. Giuseppe De Marco, 2016. "Ambiguous Games without a State Space and Full Rationality," CSEF Working Papers 425, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 01 Apr 2017.
    15. repec:eee:gamebe:v:116:y:2019:i:c:p:38-64 is not listed on IDEAS
    16. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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