Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games

Inspired by Kalai-Samet [4] and Tijs [11], weighted average lexicographic values are introduced for share sets and for cores of cooperative games using induction arguments. Continuity properties and monotonicity properties of these weighted lexicographic values are studied. For subclasses of games (convex games, simplex games, big boss games) relations are established with weighted (exact) Shapley values.Cooperative games;average lexicographic value;weighted Shapley value

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

Share Opportunity Sets and Cooperative Games

In many share problems there is a priori given a natural set of possible divisions to solve the sharing problem.Cooperative games related to such share sets are introduced, which may be helpful in solving share problems.Relations between properties of share sets and properties of games are investigated.The average lexicographic value for share sets and for cooperative games is studied.cooperative games;bankruptcy games;average lexicographic value;opportunity sets

Leximals, the Lexicore and the Average Lexicographic Value

The lexicographic vectors of a balanced game, called here leximals, are used to define a new solution concept, the lexicore, on the cone of balanced games. Properties of the lexicore and its relation with the core on some classes of games are studied. It is shown that on cones of balanced games where the core is additive, the leximals, the lexicore and the Average Lexicographic (AL-)value are additive, too. Further, it turns out that the leximals satisfy a consistency property with respect to a reduced game `a la Davis and Maschler, which implies an average consistency property of the AL-value. Explicit formulas for the AL-value on the class of k-convex games and on the class of balanced almost convex games are provided.cooperative games;the core;the AL-value;the Shapley value

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

Two Classes of Cooperative Games Related to One-Object Auction Situations

AMS classifications; 91A12; 90B05;market games;ring games;one-object auction situations;big boss games;peer group games

Weighted Component Fairness for Forest Games

We present the axiom of weighted component fairness for the class of forest games, a generalization of component fairness introduced by Herings, Talman and van der Laan (2008) in order to characterize the average tree solution. Given a system of weights, component eciency and weighted component fairness yield a unique allocation rule. We provide an analysis of the set of allocation rules generated by component eciency and weighted component fairness. This allows us to provide a new characterization of the random tree solutions.(Weighted) component fairness ; Core ; Graph games ; Alexia value ; Harsanyi solutions ; Random tree solutions.

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.

A Stroll with Alexia

This paper revisits the Alexia value, a recent solution concept for cooperative transferable utility games. We introduce the dual Alexia value and show that it coincides with the Alexia value for several classes of games. We demonstrate the importance of the notion of compromise stability for characterizing the Alexia value.Alexia value;dual Alexia value;compromise stability;bankruptcy