Abstract
Economic game theorists have recently used the concept of dynamic stability to choose among the many solution concepts of noncooperative game theory. They are justifiably concerned that stability with respect to the replicator dynamic does not adequately reflect the economic assumption that players make rational decisions. The paper analyzes stability for general adjustment processes such as monotone selection that translate payoffs into an evolutionary dynamic. By the linearization technique of dynamical systems, it is shown that the replicator dynamic deserves a prominent position in questions of stability. In particular, for symmetric normal form games, stability of monotone selection dynamics at an interior rest point is completely determined by that of the replicator dynamic unless there is a trivial linearization. Linearizations are also analyzed for asymmetric normal form games and dynamic stability consequences established for evolutionarily stable strategies as well as other Nash equilibria.
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