On Hurwicz preferences in psychological games

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 hisopponents’ strategy choices. In a recent paper, strategic ambiguity has been extended topsychological games, by taking into account ambiguous hierarchies of beliefs and maxmin 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-maxmin 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 give the definition of α-maxmin Psychological Nash Equilibrium; an illustrative example shows that the set of equilibria is affected by the parameter α and the larger is ambiguity the greater is 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 existence of equilibria is not guaranteed for every value of α.