C. M. Manuel García, D. Martín García
The aim of this paper is to extend the Myerson value to situations in which players in a TU-game, in addition to having cooperation possibilities restricted by a graph, they also have different bargaining abilities. Then, we will associate to each player in a communication situation a weight in the interval [0,1] that measures his bargaining ability. We modify the original TU-game to a new game which is, in turn, a modification of the Myerson's graph-restricted game. We will assume that the reduction in the willing to cooperate implies that players can not obtain the total dividend of the connected coalitions which must be discounted by an appropriated factor. Then, we propose as solution for these situations the Shapley value of the modified game. The obtained value extends the Myerson one, satisfies monotonicity in the weights, and admits several characterizations using bargaining component efficiency, fairness, balanced contributions and balanced bargaining ability contributions.
Keywords: Game Theory, Communication Situations, Weighted Game, Bargaining Abilities, Myerson Value.
Scheduled
TJ-2 Game Theory
September 6, 2019 11:20 AM
I3L1. Georgina Blanes building