On Continuity of Robust Equilibria

Abstract

We relax the Kajii and Morris (1997a) notion of equilibrium ro-bustness by allowing approximate equilibria when information in a game becomes incomplete. The new notion is termed "approximate robustness". The approximately robust equilibrium correspondence turns out to be upper hemicontinuous, unlike the (exactly) robust equilibrium correspondence. Another distinction comes to light when we show that, as a corollary of upper hemicontinuity, approximately robust equilibria exist in all zero-sum games. Thus, although approx-imate robustness is only a small variation of the original notion, it is strictly weaker than the latter, and its adoption enriches the domain of games for which robust equilibria exist.