Table of Contents
Game Theory
Volume 2013, Article ID 540487, 8 pages
Research Article

Allocation Rules for Games with Optimistic Aspirations

1Departamento de Matemáticas, Facultade de Informática, Universidade da Coruña, 15071 A Coruña, Spain
2Departamento de Estatística e IO, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
3Department of Economics, 435 PLC, University of Oregon, Eugene, OR 97403-1285, USA

Received 13 February 2013; Revised 8 July 2013; Accepted 1 August 2013

Academic Editor: Charles S. Tapiero

Copyright © 2013 Luisa Carpente et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A game with optimistic aspirations specifies two values for each coalition of players: the first value is the worth that the players in the coalition can guarantee for themselves in the event that they coordinate their actions, and the second value is the amount that the players in the coalition aspire to get under reasonable but very optimistic assumptions about the demands of the players who are not included in the coalition. In this paper, in addition to presenting this model and justifying its relevance, we introduce allocation rules and extend the properties of efficiency, additivity, symmetry, and null player property to this setting. We demonstrate that these four properties are insufficient to find a unique allocation rule and define three properties involving null players and nullifying players that allow the identification of unique allocation rules. The allocation rules we identify are the Midpoint Shapley Value and the Equal Division Rule.