On Hurwicz Preferences in Psychological Games

Giuseppe De Marco (), Maria Romaniello and Alba Roviello
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Giuseppe De Marco: Department of Management and Quantitative Sciences, University of Napoli Parthenope, Via Generale Parisi 13, 80132 Napoli, Italy
Maria Romaniello: Department of Economics, University Campania Vanvitelli, Corso Gran Priorato di Malta, 81043 Capua, Italy
Alba Roviello: Department of Economics and Statistical Sciences, University of Napoli Federico II, Via Cupa Cinthia, 80126 Napoli, Italy

Games, 2024, vol. 15, issue 4, 1-26

Abstract: The literature on strategic ambiguity in classical games provides generalized notions of equilibrium in which each player best responds to ambiguous or imprecise beliefs about his opponents’ strategic choices. In a recent paper, strategic ambiguity has been extended to psychological games , by taking into account ambiguous hierarchies of beliefs and max–min preferences. Given that this kind of preference seems too restrictive as a general method to evaluate decisions, in this paper we extend the analysis by taking into account α -max–min preferences in which decisions are evaluated by a convex combination of the worst-case (with weight α ) and the best-case (with weight 1 − α ) scenarios. We define the α -max–min psychological Nash equilibrium; an illustrative example shows that the set of equilibria is affected by the parameter α and the larger the ambiguity, the greater the effect. We also provide a result of stability of the equilibria with respect to perturbations that involve the attitudes toward ambiguity, the structure of ambiguity, and the payoff functions: converging sequences of equilibria of perturbed games converge to equilibria of the unperturbed game as the perturbation vanishes. Surprisingly, a final example shows that the existence of equilibria is not guaranteed for every value of α .

Keywords: psychological games; ambiguous beliefs; ?-MEU; equilibrium existence (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2024
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