On the relation among some definitions of strategic stability

In this paper we examine a number of different definitions of strategic sta bility and the relations among them. In particular, we show that the stabil ity requirement given by Hillas (1990) is weaker than the requirements invo lved in the various definitions of stability in Mertens' reformulation of s tability (Mertens 1989, 1991). To this end, we introduce a new definition o f stability and show that it is equivalent to (a variant of) the definition given by Hillas (1990). We also use the equivalence of our new definition with the definition of Hillas to provide correct proofs of some of the resu lts that were originally claimed (and incorrectly "proved") in Hillas (1990 ).