Abstract
We extend the generic equivalence result of Blume and Zame (Econometrica 62:783–794, 1994) to a broader context of perfectly and sequentially rational strategic behavior (including equilibrium and nonequilibrium behavior) through a unifying solution concept of “mutually acceptable course of action” (MACA) proposed by Greenberg et al. (Econ Theory 40:91–112, 2009. https://doi.org/10.1007/s00199-008-0349-5 ). As a by-product, we show, in the affirmative, Dekel et al.’s (J Econ Theory 89:165–185, 1999) conjecture on the generic equivalence between the sequential and perfect versions of rationalizable self-confirming equilibrium.
Highlights
In dealing with the imperfection in extensive-form games, Selten (1975) introduced the notion of perfect equilibrium
Kreps and Wilson (1982) pointed out that the two concepts lead to similar prescriptions for equilibrium play–that is, for each particular game form and for almost all assignments of payoffs to the terminal nodes, almost all sequential equilibria are perfect equilibria, and the sets of sequential and perfect equilibria fail to coincide only at payoffs where the perfect equilibrium correspondence fails to be upper hemi-continuous
In the spirit of Kreps and Wilson (1982), we provide a useful characterization of perfect rationality and sequential rationality respectively by the closure and vertical closure of Ri
Summary
In dealing with the imperfection in extensive-form games (with perfect recall), Selten (1975) introduced the notion of perfect equilibrium. Our analysis is solely based on the semi-algebraic property of the elementary set Ri ; it is feasible and applicable to a variety of game-theoretic solution concepts, as long as the trembling sequence in the analysis of perfectly and sequentially rational behavior is confirmed to be concordant with the belief structure adopted in an extensive-form game.
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