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On Equilibria when Agents Have Multiple Priors

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  • Rose-Anne Dana

Abstract

We discuss the existence and the qualitative properties of equilibria when agents have multiple priors and there is only one good in each state of the world. We first prove a general existence result in infinite dimension economies. We then fully describe the equilibria in two special cases. We first consider the case of CEU maximizers that have same capacities. We next consider the case of no aggregate uncertainty. We prove that if agents have non-random initial endowments and are uncertainty averse and maximize the minimal expected utility according to a set of possible priors, then the existence of a common prior is equivalent to the existence of a unique equilibrium, the no-trade equilibrium. We lastly give a mild assumption for indeterminacy of equilibria and compute the dimension of indeterminacy. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Rose-Anne Dana, 2002. "On Equilibria when Agents Have Multiple Priors," Annals of Operations Research, Springer, vol. 114(1), pages 105-115, August.
  • Handle: RePEc:spr:annopr:v:114:y:2002:i:1:p:105-115:10.1023/a:1021006118400
    DOI: 10.1023/A:1021006118400
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    Cited by:

    1. Riedel, Frank & Herzberg, Frederik, 2013. "Existence of financial equilibria in continuous time with potentially complete markets," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 398-404.
    2. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    3. Dana, Rose-Anne & Riedel, Frank, 2013. "Intertemporal equilibria with Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1582-1605.
    4. Patrick Beissner & Frank Riedel, 2018. "Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty," Finance and Stochastics, Springer, vol. 22(3), pages 603-620, July.
    5. Martins-da-Rocha, V. Filipe, 2010. "Interim efficiency with MEU-preferences," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1987-2017, September.
    6. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
    7. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Kajii, Atsushi & Ui, Takashi, 2009. "Interim efficient allocations under uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 337-353, January.
    9. Rose-Anne Dana & Cuong Le Van, 2008. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Documents de travail du Centre d'Economie de la Sorbonne b08039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    10. Beißner, Patrick, 2016. "Radner Equilibria under Ambiguous Volatility," Center for Mathematical Economics Working Papers 493, Center for Mathematical Economics, Bielefeld University.
    11. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    12. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," PSE-Ecole d'économie de Paris (Postprint) halshs-00470670, HAL.
    13. Chambers, Christopher P. & Echenique, Federico, 2012. "When does aggregation reduce risk aversion?," Games and Economic Behavior, Elsevier, vol. 76(2), pages 582-595.
    14. Amarante, M & Ghossoub, M & Phelps, E, 2013. "Innovation, Entrepreneurship and Knightian Uncertainty," Working Papers 12241, Imperial College, London, Imperial College Business School.
    15. Chambers, Robert G., 2014. "Uncertain equilibria and incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 48-54.
    16. Tarik Driouchi & Lenos Trigeorgis & Raymond H. Y. So, 2018. "Option implied ambiguity and its information content: Evidence from the subprime crisis," Annals of Operations Research, Springer, vol. 262(2), pages 463-491, March.
    17. repec:ipg:wpaper:2013-016 is not listed on IDEAS
    18. repec:dau:papers:123456789/11268 is not listed on IDEAS
    19. repec:dau:papers:123456789/5375 is not listed on IDEAS
    20. repec:ipg:wpaper:16 is not listed on IDEAS
    21. Rose-Anne Dana & Cuong Le Van, 2009. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Post-Print halshs-00281582, HAL.
    22. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Post-Print halshs-00470670, HAL.
    23. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.
    24. Rigotti, Luca & Shannon, Chris, 2012. "Sharing risk and ambiguity," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2028-2039.
    25. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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