Continuity and equilibrium stability

This paper examines the problem of stability of equilibrium points in normal form games in the trembling-hand framework. An equilibrium point is called perfect if it is stable against at least one sequence of trembles approaching zero. A strictly perfect equilibrium point is stable against every such sequence. eralize Okada’s sufficient condition (Okada, 1981) [12] for strict perfectness (and hence, perfectness). Particularly, we show that the continuity of the best response correspondence implies strict properness and, therefore, strict perfectness. The proposed condition is formulated in terms of the primitives of the game (payoffs and strategies), which suggests some potentially useful practical applications.