The 2-Shapley value for bicooperative games
针对双合作博弈（玩家分为支持变革、维持现状和弃权三类），利用反拟阵理论提出一种新的Shapley型值（2-Shapley值），给出公理化并验证其与现有解概念的一致性，为分析决策过程提供数学基础。
Abstract In this paper, we propose a new Shapley-type value (the 2-Shapley value) for bicooperative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while the remaining players abstain. To develop this new value, we employ antimatroid theory not as a structural constraint on the games, but as a methodological bridge. Specifically, we demonstrate that any bicooperative coalition structure is isomorphic to a specific antimatroid, which we term the ‘double antimatroid’. Leveraging this mathematical connection, we propose a new Shapley value, provide an axiomatization that preserves its fundamental axioms, and establish its consistency with existing solution concepts. Finally, we illustrate our theoretical proposal and the calculation of this value through an example modeling a decision-making process. This work provides a robust mathematical foundation connecting both structures, opening new perspectives for analysis within bicooperative game theory.