Abstract: Expected utility with rank dependent probabilities is a generalization of expected utility. If such preference representations are used for the payoffs in the mixed extension of a finite game, Nash equilibrium may fail to exist. Set-valuedsolutions, however, do exist even for those more general utility functions. Such set-valued solutions can be shown to be robust to perturbations of the expected utility hypothesis, but may have certain conceptual shortcomings. The paper thus proposes an alternative set-valued solution concept, called fixed sets under the best-reply correspondence.;
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