Strongly consistent self-confirming equilibrium. (English) Zbl 1229.91032

Kamada, Yuichiro

Econometrica 78, No. 2, 823-832 (2010).

Summary: D. Fudenberg and D. K. Levine [Econometrica 61, No. 3, 523–545 (1993; Zbl 0796.90072)] introduced the notion of self-confirming equilibrium, which is generally less restrictive than Nash equilibrium. Fudenberg and Levine also defined a concept of consistency, and claimed in their Theorem 4 that with consistency and other conditions on beliefs, a self-confirming equilibrium has a Nash equilibrium outcome. We provide a counterexample that disproves Theorem 4 and prove an alternative by replacing consistency with a more restrictive concept, which we call strong consistency. In games with observed deviators, self-confirming equilibria are strongly consistent self-confirming equilibria. Hence, our alternative theorem ensures that despite the counterexample, the corollary of Theorem 4 is still valid.

MSC:

91A10

Noncooperative games

Keywords:

self-confirming equilibrium; consistency; strong consistency; Nash equilibrium