The α-Egalitarian Myerson value of games with communication structure

Some cooperative games may have some players whose marginal contribution is zero but are indispensable to forming the coalition. However, the marginalism-based index allocates such players with zero payoffs. It is unreasonable and inconsistent with practical cases because the rest players cannot cooperate to make more payoffs without the participation of the players with no marginal contribution. This paper studies one such type of cooperative game called games with communication structure and introduces the a-Egalitarian Myerson value. This payoff index consolidates the Myerson value and the Equal Component Division value, which not only considers the marginal contribution of players but also regards egalitarianism. The main feature of this payoff index is to protect all players' payoffs. Three axiomatic systems are provided to show the rationality of the a-Egalitarian Myerson value. An application of the theoretical results in pharmaceutical supply chain management is offered to show the efficiency of the new payoff index.