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The maximin equilibrium and the PBE under ambiguity

Author

Listed:
  • Dionysius Glycopantis

    (City, University of London)

  • Nicholas C. Yannelis

    (University of Iowa)

Abstract

This note refers to the recent work on ambiguous implementation by de Castro–Liu–Yannelis (Econ Theory 63:233–261, 2017). The authors discuss, under condition of ambiguity, the implementation as maximin equilibria of maximin individually rational and ex ante maximin efficient allocations. An explicit example is used to support their analysis. We analyse further the example used by de Castro–Liu–Yannelis (2017). We show that in the formulated game tree the proposed allocation is implementable through a backward induction argument. Also it is shown that a perfect Bayesian equilibrium (PBE) exists, leading to different allocations. Comparisons are drawn between the maximin and the PBE implementations. We consider also briefly the meaning of the incentive compatibility (IC) of proposed allocations.

Suggested Citation

  • Dionysius Glycopantis & Nicholas C. Yannelis, 2018. "The maximin equilibrium and the PBE under ambiguity," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 183-199, October.
    • Handle: RePEc:spr:etbull:v:6:y:2018:i:2:d:10.1007_s40505-018-0139-6
    DOI: 10.1007/s40505-018-0139-6
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    References listed on IDEAS

    as
    1. Thomas R. Palfrey & Sanjay Srivastava, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 193-208.
    2. Luciano I. Castro & Zhiwei Liu & Nicholas C. Yannelis, 2017. "Ambiguous implementation: the partition model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 233-261, January.
    3. Zhiwei Liu, 2014. "A note on the welfare of the maximin rational expectations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 213-218, October.
    4. Dionysius Glycopantis & Allan Muir & Nicholas C. Yannelis, 2003. "On extensive form implementation of contracts in differential information economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 495-526, March.
    5. Angelos Angelopoulos & Leonidas Koutsougeras, 2015. "Value allocation under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 147-167, May.
    6. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    7. Allan Muir & Nicholas C. Yannelis & Dionysius Glycopantis, 2001. "An extensive form interpretation of the private core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(2), pages 293-319.
    8. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 183-197, April.
    9. Luciano Castro & Marialaura Pesce & Nicholas Yannelis, 2011. "Core and equilibria under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 519-548, October.
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    More about this item

    Keywords

    Ambiguity; Maximin preferences; Maximin efficient allocations; Maximin equilibrium; Implementation; Mechanism design; Perfect Bayesian equilibrium; Nash equilibrium;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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