A coalitional compromised solution for cooperative games

Abstract

The paper aims to study a kind of revenue allocation system with a guarantee of basic interests, which integrates the egalitarianism with the marginalism. This means that a player’s payoff consists of two parts, the basic interests and the performance-based payoff. In cooperative games with coalition structure setting, the Owen value puts emphasis on the individuals’ marginal contribution, in contrast, the equal coalitional division value (ECD-value) gives priority to the egalitarianism. Through introducing the guarantee coefficient $\alpha$, we propose the compromised solution which is established as the corresponding convex combination of the Owen value and the ECD-value. We call it $\alpha$-egalitarian Owen value, as the solution degenerates to the corresponding $\alpha$-egalitarian Shapley value when the coalition structure is trivial. Furthermore, we provide three approaches to characterize an $\alpha$-egalitarian Owen value, including axiomatization, potential function and implementation.