A revelation principle for correlated equilibrium under trembling-hand perfection

Xiao Luo, Yongchuan Qiao and Yang Sun

Journal of Economic Theory, 2022, vol. 200, issue C

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).

Keywords: (Perfect) correlated equilibrium; Revelation principle; CEMDT; ACE; Admissibility (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:200:y:2022:i:c:s0022053121002131

DOI: 10.1016/j.jet.2021.105396

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