pp-Best response set

This paper introduces a notion of pp-best response set (pp-BR). We build on this notion in order to provide a new set-valued concept: the minimal pp-best response set (pp-MBR). After proving general existence results of the pp-MBR, we show that it characterizes set-valued stability concepts in a dynamic with Poisson revision opportunities borrowed from Matsui and Matsuyama [An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415–434.] Then, we study equilibrium selection. In particular, using our notion of pp-BR, we generalize Morris et al. [pp-Dominance and belief potential, Econometrica 63 (1995) 145–157.] that aimed to provide sufficient conditions under which a unique equilibrium is selected in the presence of higher order uncertainty.