Unternehmensforschung

In this paper we introduce a new consistency condition and provide characterizations for several solution concepts in TU cooperative game theory. Our new consistency condition, which we call the random reduction consistency, requires the consistency of payoff vectors assigned by a solution concept when one of the players is removed with some probability. We show that the random reduction consistency and other standard properties characterize the Weber set, the convex hull of the marginal contribution vectors. Another salient feature of random reduction consistency is that, by slightly changing its definition, we can characterize the core and the anti-core in a parallel manner. Our result enables us to compare the difference between the three solution concepts from the viewpoint of consistency.

In this paper we investigate the asymptotic stability of dynamic, multiple-objective linear programs. In particular, we show that a generalization of the optimal partition stabilizes for a large class of data functions. This result is based on a new theorem about asymptotic sign-solvable systems. The stability properties of the generalized optimal partition are used to address a dynamic version of the nonsubstitution theorem.

This work deals with the weighted excesses of players in cooperative games which are obtained by summing up all the weighted excesses of all coalitions to which they belong. We first show that the resulting payoff vector is the corresponding least square value by lexicographically minimizing the individual weighted excesses of players over the preimputation set, and thus give an alternative characterization of the least square values. Second, we show that these results give rise to lower and upper bounds for the core payoff vectors and, using these bounds, we show that the least square values can be seen as the center of a polyhedron defined by these bounds. This provides a second new characterization of the least square values. Third, we show that the individually rational least square value is the solution that lexicographically minimizes the individual weighted excesses of players over the imputation set.

In this paper, zero duality gap conditions in nonconvex optimization are investigated. It is considered that dual problems can be constructed with respect to the weak conjugate functions, and/or directly by using an augmented Lagrangian formulation. Both of these approaches and the related strong duality theorems are studied and compared in this paper. By using the weak conjugate functions approach, special cases related to the optimization problems with equality and inequality constraints are studied and the zero duality gap conditions in terms of objective and constraint functions, are established. Illustrative examples are provided.

In this paper, we provide two characterizations in the context of NTU games: of the consistent egalitarian solution and of the core. The first characterization is based on reduced games and contraction and expansion independence. The second one is based on reduced games and sub-reduced games.