In the main result, partially answering a question of Telgársky, the following is proven: if X is a first countable R₀-space, then player β (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonempty -subspace which is of the first category in itself.
In this paper we focus on one-point (point-valued) solutions for transferable utility games (TU-games). Since each allocated profit vector is identified with an additive game, a solution can be regarded as a mapping which associates an additive game with each TU-game. Recently Kultti and Salonen proposed a minimum norm problem to find the best approximation in the set of efficient additive games for a given TU-game. They proved some interesting properties of the obtained solution. However, they...
Vagueness is one of the phenomena which cannot be separated from the real bargaining and cooperative situations. The aim of this paper is to offer a brief survey of the recent state-of-art of the modelling of vagueness in coalitional games with transferable utility. It may be recognized in two components of these games, namely, in vague structure of coalitions where each player may simultaneously participate in several of them, and in vague expectations of coalitional pay-offs. Both these cases...
The problem of choosing an optimal insurance policy for an individual has recently been better understood, particularly due to the papers by Gajek and Zagrodny. In this paper we study its multi-agent version: we assume that insureds cooperate with one another to maximize their utility function. They create coalitions by bringing their risks to the pool and purchasing a common insurance contract. The resulting outcome is divided according to a certain rule called strategy. We address the fundamental...
The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity problem...