The Nucleolus as a Power Index

• Autores: María Montero
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese, Francisco Ramón Fernández García, 2002, ISBN 84-472-0733-1, pág. 116
• Idioma: inglés
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• Resumen

  • This paper studies a situation in which n players vote on the division of a budget. Very general voting rules are considered, namely all the rules such that no two disjoint groups of agents have a majority (i.e., the associated characteristic function game is proper). A player�s expected share of the budget can be interpreted as a measure of his power. This type of power is known as P-power, as opposed to the probability of being pivotal, or I-power (see Felsenthal and Machover, 1998). This paper addresses the question of what is a good measure of P-power. From the axiomatic point of view, the answer seems to be the Shapley value. We approach this question from a strategic point of view, using an extension of Baron and Ferejohn�s (1989) noncooperative bargaining model.

    Bargaining proceeds as follows. An agent is selected at random to propose a division of the budget. If a winning coalition votes in favor of the proposal, the proposal is implemented; otherwise, a new proposer is selected at random, always using the same probability vector. Baron and Ferejohn limited themselves to symmetric majority games in which all players are selected to be proposers with equal probability; we consider arbitrary proper simple games and probability vectors. Like Baron and Ferejohn, we look at stationary subgame perfect equilibria.