The aim of this paper is to extend the Myerson value (Myerson in Math Oper Res 2:225–229, 1977) to situations in which players in a TU-game, in addition to having cooperation possibilities restricted by a graph, also have different bargaining abilities. Then, we will associate to each player in a communication situation a weight in the interval [0, 1] that measures his bargaining ability. A unitary weight corresponds to a fully cooperative player whereas a null weight corresponds to a player that is not willing to cooperate in any way. Intermediate values modulate the bargaining ability. We modify the original TU-game to a new game which is, in turn, a modification of the Myerson’s graph-restricted game. We will assume that the reduction in the will to cooperate implies that players can not obtain the total dividend of the connected coalitions which must be discounted by an appropriate factor. Then, we propose as a solution for these situations the Shapley value (Shapley, in: Kuhn, Tucker (eds) Annals of mathematics studies, Princeton University Press, Princeton, 1953) of the modified game. This solution extends the Myerson value (and also the Shapley value). Moreover it satisfies monotonicity in the weights. Different characterizations of this rule can be obtained. They are based on properties as bargaining component efficiency, fairness, balanced contributions and balanced bargaining ability contributions, and thus they are parallel to those more prominent existing in the literature for the Myerson value.

中文翻译：

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与具有不同讨价还价能力的玩家沟通情况的价值

本文的目的是将 Myerson 值（Myerson in Math Oper Res 2:225–229, 1977）扩展到 TU 游戏中的玩家除了具有受图限制的合作可能性之外，还具有不同的情况。议价能力。然后，我们将在通信情况下为每个参与者关联一个区间 [0, 1] 中的权重来衡量他的讨价还价能力。单一权重对应于完全合作的玩家，而空权重对应于不愿意以任何方式合作的玩家。中间值调节讨价还价能力。我们将原始 TU 游戏修改为一个新游戏，而后者又是对 Myerson 图形限制游戏的修改。我们将假设合作意愿的减少意味着参与者无法获得必须通过适当因素贴现的连接联盟的总红利。然后，我们提出了修改后的游戏的 Shapley 值（Shapley，在：Kuhn，Tucker (eds) Annals ofmath Studies，普林斯顿大学出版社，普林斯顿，1953）作为这些情况的解决方案。此解决方案扩展了 Myerson 值（以及 Shapley 值）。此外，它满足权重的单调性。可以获得该规则的不同特征。它们基于议价成分效率、公平性、均衡贡献和均衡议价能力贡献等特性，因此它们与文献中存在的更突出的迈尔森值平行。