Resumen de Outside options in coalition structures
The paper presents and axiomatizes two coalition-structure values that are meant to capture outside options of players in a cooperative game. A coalition structure is a partition on the set of players; the sets making up the partition are called components. Building on the Shapley value, several values for coalition structures have been presented in the literature, most notably by Aumann and Dreze (1974) and by Owen (1977); they are alluded to as AD-value and O-value, respectively. While the AD value assumes component efficiency, the O-value obeys overall efficiency. However, with both values, the bargaining process inside the components is dictated by the Shapley axioms. This implies that differing outside options of players within a component do not bear on the payoffs. In contrast, the two values presented in our paper deviate from the null-player axiom in order to reflect outside options. Close to the AD-approach, these values obey component efficiency (and symmetry and additivity).
Consider the following game defined by the player set N = {1, 2, 3} and the transferable-utility coalition function v : 2N �¨ R which ascribes worths v(1, 2) = v(2, 3) = 60, v(N) = 72 and vanishes elsewhere. The Shapley value of this game is (14, 44, 14) reflecting player 2�fs prominence.
Consider also the coalition structure {{1, 2} , {3}}. It leads to the AD-value (30, 30, 0) and the O-value (33, 33, 6). The two outside-option values generate the payoffs (20, 40, 0) and (15, 45, 0), respectively. They attribute a higher payoff to player 2 than to player 1, thus reflecting the outside opportunities of player 2 (v(2, 3) = 60 > 0 = v(1, 3)).
Outside option values are especially suited to analyze voting games. While the power is distributed within a government coalition (component efficiency), the possibilities of a party included in the government coalition to form potential coalitions with parties outside is to be a major factor determining this party�fs weigth.
