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\(p\)-best response set. (English) Zbl 1142.91345

Summary: This paper introduces a notion of \(p\)-best response set (\(p\)-BR). We build on this notion in order to provide a new set-valued concept: the minimal \(p\)-best response set (\(p\)-MBR). After proving general existence results of the \(p\)-MBR, we show that it characterizes set-valued stability concepts in a dynamic with Poisson revision opportunities borrowed from A. Matsui and K. Matsuyama [J. Econ. Theory 65, 415–434 (1995; Zbl 0835.90121)]. Then, we study equilibrium selection. In particular, using our notion of \(p\)-BR, we generalize S. Morris et al. [ Econometrica 63, No. 1, 145–157 (1995; Zbl 0827.90138 )] that aimed to provide sufficient conditions under which a unique equilibrium is selected in the presence of higher order uncertainty.

MSC:

91A22 Evolutionary games
91A10 Noncooperative games
91A26 Rationality and learning in game theory
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