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Non-additive beliefs and strategic equilibria. (English) Zbl 0962.91002
The authors introduce a notion of equilibrium under uncertainty for \(n\)-player games generalizing the notion for \(2\)-player games introduced by J. Dow and S. Ribeiro da Costa Werlang [J. Econ. Theory 64, 305-324 (1994; Zbl 0813.90132)]. In this framework, beliefs are modelled by (non-additive) capacities. For a capacity \(\nu\), we have two notions measuring the degree of uncertainty: The degree of confidence and the degree of ambiguity.
The authors show some facts about their notion: (a) mixed-strategy Nash equilibria are equilibria under uncertainty, (b) pure-strategy maximin strategy combinations are equilibria under uncertainty, (c) if the degree of confidence is sufficiently small, then an equilibrium under uncertainty induces maximin play, and (d) if the beliefs of all players are independent and consistent, then every sequence of equilibria under uncertainty whose degrees of ambiguity converge to zero converges to a Nash equilibrium.

91A06 \(n\)-person games, \(n>2\)
91A10 Noncooperative games
28A12 Contents, measures, outer measures, capacities
Full Text: DOI
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