M. A. Puente del Campo, J. M. Giménez Pradales
Introduced in 1974 by Aumann and Drèze, the notion of game with a coalition structure gave a new impulsion to the development of value theory. These authors extended the Shapley value to this new framework.
In 1977, a second approach was used by Owen, when introducing the first coalitional value, called now the Owen value. This value is the result of a two-step procedure: first, the unions play a quotient game among themselves, and each one receives a payoff which, in turn, is shared among its players in an internal game. Both payoffs, in the quotient game for unions and within each union for its players, are given by the Shapley value.
In 1982, Owen applied the same procedure to the Banzhaf value and obtained the Owen--Banzhaf value. In this case the payoffs at both levels are given by the Banzhaf value.
The present work focuses on giving a new computational procedure for these coalitional values by means of the multilinear extension of the game. A political example is also studied.
Keywords: Cooperative games; Shapley value, Banzhaf value, coalition structure, multilinear extension.
Scheduled
TJ-1 Game Theory
September 6, 2019 9:30 AM
I3L1. Georgina Blanes building