Interval Solutions for TU-Games

Abstract

Standard solutions for TU-games assign to every TU-game a payoff vector. However, if there is uncertainty about the payoff allocation then we cannot just assign a specific payoff to every player. Therefore, in this paper we introduce interval solutions for TU-games which assign to every TU-game a vector of payoff intervals. Since the solution we propose uses marginal vectors of the interval game, we need to apply a difference operator on intervals. Applying the subtraction operator of Moore (1979), we define an interval solution for TU-games, and we provide an axiomatization.

Keywords: Cooperative TU-game, interval game, Moore subtraction, Moore-Shapley interval solution

JEL Classification: C71