[1] Choquet expected utility and never best choice (2025)
Christopher Kops, Hans Peters, Dries Vermeulen
Abstract Given a set of capacities describing uncertainty over a set of states, and a set of acts, the question is considered when an act is never a best choice, i.e., when for every capacity there is another act with higher Choquet expected utility. This question is answered for several sets of capacities, distinguished by their supports, where the focus is on four different definitions of a support. One consequence of the analysis is that an act is never a best choice against the set of all capacities if and only if it is strictly dominated by a convex combination of the comonotonized versions of the other acts. This result can be seen as the counterpart of the analogous result for additive capacities, such as mixed strategies in games.
[2] On perspective invariance in bargaining (2024)
Hans Peters
Abstract Nalebuff (Management Science, 2021) discusses a Perspective Invariant approach to Nash bargaining, meaning that it should not matter for the outcome whether gains with respect to the disagreement payoffs or sacrifices with respect to the ideal payoffs are considered. We propose an alternative version of Nash's Contraction Independence condition that allows for an extension of the Nash bargaining solution which is Perspective Invariant, in contrast with the version considered in Nalebuff (2021). We also study a condition of Restricted Monotonicity, resulting, among other solutions, in a Perspective-Invariant version of the Kalai-Smorodinsky solution.
[3] Abstention, multiple issues, and the Banzhaf power index (2025)
Qianqian Kong, Hans Peters
Abstract This paper considers voting systems in which abstention is possible, and in which the power of coalitions may depend on the issues under consideration. A class of issue-based Banzhaf power indices is axiomatically characterized for such systems, using effectivity functions rather than relying directly on simple games. As a by-product, this approach also yields several new characterizations of (nonnegative multiples of) the Banzhaf power index.
[4] About the Sugeno integral in bimatrix games (2025)
Hans Peters
Abstract We consider bimatrix games where the strategies of theplayers are described by capacities, and the payoffs are determined by the Sugeno integral. In this model we establish when a row or column is never a best reply. We also study a version of Nash equilibrium, called Sugeno-Nash equilibrium, and show its existence. Finally, we characterize the cooperative payoff space of a bimatrix game attainable by capacities defined on the set of all payoff pairs in the bimatrix game.
[5] On revealed preference in individual and collective choice (2024)
Hans Peters
Abstract We provide a selection of results from the theory of preference revealed by choice, with contraction independence and its variations as a main condition on choice functions. Choice can be individual, as in consumer theory, or collective, as in cooperative and noncooperative games. It can be single-valued - the main case considered in this overview, multi-valued, or probabilistic.
[6] The excess prebargaining set for cooperative games (2025)
Qianqian Kong, Hans Peters, Hao Sun
Abstract The excess prebargaining set is a novel solution concept for cooperative games. It is a refinement of existing prebargaining set solutions, notably the reactive, semireactive, and Aumann-Maschler prebargaining sets. It contains the prekernel, and coincides with that solution on simple games except possibly on balanced simple games with all individual worths equal to zero. An axiomatic characterization based on reduced game properties is
provided as well.