  Empirically, many strategic settings are characterized by stable outcomes in
which players' decisions are publicly observed, yet no player takes the
opportunity to deviate. To analyze such situations in the presence of
incomplete information, we build an empirical framework by introducing a novel
solution concept that we call Bayes stable equilibrium. Our framework allows
the researcher to be agnostic about players' information and the equilibrium
selection rule. The Bayes stable equilibrium identified set collapses to the
complete information pure strategy Nash equilibrium identified set under strong
assumptions on players' information. Furthermore, all else equal, it is weakly
tighter than the Bayes correlated equilibrium identified set. We also propose
computationally tractable approaches for estimation and inference. In an
application, we study the strategic entry decisions of McDonald's and Burger
King in the US. Our results highlight the identifying power of informational
assumptions and show that the Bayes stable equilibrium identified set can be
substantially tighter than the Bayes correlated equilibrium identified set. In
a counterfactual experiment, we examine the impact of increasing access to
healthy food on the market structures in Mississippi food deserts.
