Impacts of boycotts concerning the Shapley value and extensions

Abstract

If a player boycotts another player, it means that the cooperation gains of all coalitions containing both players vanish. In the associated coalition function, both players are now disjointly productive with respect to each other. The disjointly productive players property states that a player’s payoff does not change when another player who is disjointly productive to that player is removed from the game. We show that the Shapley value is the only TU-value that satisfies efficiency and the disjointly productive players property and for which the impact of a boycott is the same for the boycotting and the boycotted player. Analogous considerations are made for the proportional Shapley value and the class of (positively) weighted Shapley values.