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

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

On consistent solutions for strategic games

Nash equilibrium;game theory

Discretization of Information Collecting Situations and Continuity of Compensation Rules

A canonical procedure is described, which associates to each infinite information collecting situation a related information collecting situation with finite state and action spaces, in such a way that the two corresponding IC-games are near to each other.Compensations for informants are then also near to each other in the two IC-situations, if they are based on continuous compensation rules.cooperative games;information

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

Approximate Fixed Point Theorems

Under some weakenings of the condition of the well-known fixed point theorems of Brouwer, Kakutani and Banach the existence of approximate fixed points turns out to be still guaranteed. Also an approximate fixed point theorem is given for certain nonexpansive maps