Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.

Coalitional Games and Contracts Based on Individual Deviations

We study what coalitions form and how the members of each coalition split the coalition value in coalitional games in which only individual deviations are allowed. In this context we employ three stability notions: individual, contractual, and compensational stability. These notions differ in terms of the underlying contractual assumptions. We characterize the coalitional games in which individually stable outcomes exist by means of the top-partition property. Furthermore, we show that any coalition structure of maximum social worth is both contractually and compensationally stable.