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Games with imperfectly observable commitment. (English) Zbl 0899.90168
Summary: K. Bagwell [Games Econ. Behav. 8, No. 2, 271-280 (1995; Zbl 0821.90148)] claims that, in models of commitment, “the first-mover advantage is eliminated when there is a slight amount of noise associated with the observation of the first-mover’s selection”. We show that the validity of this claim depends crucially on the restriction to pure strategy equilibria. The game analyzed by Bagwell always has a mixed equilibrium that is close to the Stackelberg equilibrium when the noise is small. Furthermore, an equilibrium selection theory that combines elements from the theory of J. C. Harsanyi and R. Selten [‘A general theory of equilibrium selection in games” (1988; Zbl 0693.90098)] with elements from the theory of J. C. Harsanyi [Games Econ. Behav. 8, No. 1, 91-122 (1995; Zbl 0833.90135)], actually selects his “noisy Stackelberg equilibrium”.

MSC:
91A05 2-person games
91A65 Hierarchical games (including Stackelberg games)
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