A mean value for games with communication structures

Int J Game Theory (2003) 32: 533544DOI 10.1007/s001820400175A mean value for games with communication

structuresGerard HamiacheGREMARS, Universite de Lille III, Domaine universitaire du Pont de Bois,

B.P. 149, 59653 Villeneuve dAscq Cedex, FranceReceived: April 2002/Accepted: February 2004Abstracts. The mean value is a new extension of the Shapley value for games

with communication structure representable by a simple graph; only pairwise

meetings can occur, although some of them might not be permitted. The new

value is characterized by a set of axioms of which the one with the most farreaching eect is an associated consistency property already used in various

contexts. The mean value of an n-player unanimity game is the arithmetic

average of the mean values of n 1-player unanimity games with connected

support, which means games in which the deleted players are not articulation

point of the considered graph.Key words: Shapley value, communication structure, associated game, consistency, graph1. IntroductionThe aim of this paper is to present a new extension of the Shapley value

(Shapley, 1953) for cooperative games with incomplete communication. We

are interested in situations in which only pairwise meetings can occur,

although some of them might not be permitted. These communication

structures are usually represented by simple graphs, also called undirected

graphs or networks. The nodes represent the players, the links represent the

possibility for adjacent players to communicate, and missing links indicate

that no direct communication is permitted between the players in question.

This approach was introduced by Myerson (1977), see also Owen (1986).

Following Myersons result, for (unanimity) games in which only theI wish to thank the anonymous referees for their helpful remarks. The usual disclaimer applies.534 G. Hamiachecooperation of all players generates some wealth, all players receive the same

payment regardless of their position on the graph. Considering a position on

a network to be an economic resource, we would like better connected players

to be better rewarded. The position value (Borm et al., 1992), and a previous

value (that we shall call F-value) proposed by the author (Hamiache, 1999)

are dierent ways to solve this problem. The extension of the Shapley value

for games with communication structure discussed herein, is another solution.

The non-cooperative approach in Calvo-Armengol (2001) where power

indices are determined in network situations is also...