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On the Relation Among Some Definitions of Strategic Stability

Department of Economics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
Department of Mathematics, University of Nÿmegan, Toernooiveld 1, 6525 ED Nÿmegan, The Netherlands
Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
j.hillas{at}auckland.ac.nz
m.jansen{at}ke.unimaas.nl
potters{at}sci.kun.nl
d.vermeulen{at}ke.unimaas.nl

In this paper we examine a number of different definitions of strategic stability and the relations among them. In particular, we show that the stability requirement given by Hillas (1990) is weaker than the requirements involved in the various definitions of stability in Mertens' reformulation of stability (Mertens 1989, 1991). To this end, we introduce a new definition of 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 results that were originally claimed (and incorrectly "proved") in Hillas (1990).

Key Words: Game theory; strategic stability
History: Received: September 21, 1999; revision received: March 8, 2000;revision received: January 4, 2001;

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