Recent working papers

[1] Choquet expected utility and never best reply (2024)

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 reply, 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 reply 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.