The First Steps with Alexia, the Average Lexicographic Value

The new value AL for balanced games is discussed, which is based on averaging of lexicographic maxima of the core.Exactifications of games play a special role to find interesting relations of AL with other solution concepts for various classes of games as convex games, big boss games, simplex games etc. Also exactifications are helpful to associate fully defined games to partially defined games and to develop solution concepts there.cooperative games;average lexicographic value;exact games;partially defined games

Finite Coverings by Cones

This paper considers analogues of statements concerning compactness and finite coverings, in which the roles of spheres are replaced by cones. Furthermore, one of the finite covering results provides an application in Multi-Objective Programming; infinite sets of alternatives are reduced to finite sets.cones;finite coverings

Compromise values in cooperative game theory

Bargaining;game theory

The consistency principle for games in strategic form

Game Theory

General Aggregation of Demand and Cost Sharing Methods

econometric models;demand;cost sharing

A Vertex Oriented Approach to Minimum Cost Spanning Tree Problems

In this paper we consider spanning tree problems, where n players want to be connected to a source as cheap as possible. We introduce and analyze (n!) vertex oriented construct and charge procedures for such spanning tree situations leading in n steps to a minimum cost spanning tree and a cost sharing where each player pays the edge which he chooses in the procedure. The main result of the paper is that the average of the n! cost sharings provided by our procedure is equal to the P-value for minimum cost spanning tree situations introduced and characterized by Branzei et al. (2004). As a side product, we find a new method, the vertex oriented procedure, to construct minimum cost spanning trees.Minimum cost spanning tree games;algorithm;value;cost sharing

Additive Stable Solutions on Perfect Cones of Cooperative Games

Closed kernel systems of the coalition matrix turn out to correspond to cones of games on which the core correspondence is additive and on which the related canonical barycentric solution is additive, stable and continuous. Different perfect cones corresponding to closed kernel systems are described.cooperative games;core;barycenter of the core;perfect cone of games