We analyze the problem of existence of undominated pure strategy Nash
equilibria in games with strategic complementarities. A Nash equilibri
um is undominated if no player's equilibrium strategy is weakly domina
ted by another pure strategy. We show the existence of the least and t
he greatest undominated equilibrium. The equilibrium strategies of the
se extremal equilibria are undominated against mixed strategies as wel
l and have nice comparative statics properties. (C) 1997 Academic Pres
s.