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Strategic complements and substitutes, and potential games. (English) Zbl 1129.91004

Summary: We show that games of strategic complements, or substitutes, with aggregation are “pseudo-potential” games. The upshot is that they possess Nash equilibria in pure strategies (NE), even if the strategy sets are not convex; and that various dynamic processes converge to NE. In particular, NE exist in Cournot oligopoly with indivisibilities in production.
Our notion of aggregation is quite general and enables us to take a unified view of several disparate models.

MSC:

91A10 Noncooperative games
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