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A revelation principle for correlated equilibrium under trembling-hand perfection

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  • Luo, Xiao
  • Qiao, Yongchuan
  • Sun, Yang

Abstract

Dhillon and Mertens (1996) introduce the concept of perfect correlated equilibrium (PCE) and show, using an example, that the revelation principle fails for PCE —that is, a PCE distribution may not be generated by the canonical mechanism. This failure of the revelation principle jeopardizes its applications in economics. In this paper, we show that the revelation principle holds for an alternative notion of perfect correlated equilibrium that we dub correlated equilibrium with message-dependent trembles (CEMDT). The notion of CEMDT is fully characterized by undominated correlated equilibria that involve admissible actions only. Moreover, any CEMDT distribution can be represented by an incentive-compatible direct-revelation mechanism; the set of CEMDT distributions is a convex polyhedron that contains all perfect equilibria. Our paper thus provides a strategic foundation for undominated correlated equilibrium. We also show that the CEMDT distribution is equivalent to a weak version of acceptable correlated equilibrium (ACE) as in Myerson (1986a) (and equivalent to ACE in two-person games).

Suggested Citation

  • Luo, Xiao & Qiao, Yongchuan & Sun, Yang, 2022. "A revelation principle for correlated equilibrium under trembling-hand perfection," Journal of Economic Theory, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:jetheo:v:200:y:2022:i:c:s0022053121002131
    DOI: 10.1016/j.jet.2021.105396
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    More about this item

    Keywords

    (Perfect) correlated equilibrium; Revelation principle; CEMDT; ACE; Admissibility;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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