基于T-联盟Shapley值的分配策略

摘要/Abstract

摘要： 考虑合作博弈中子联盟整体参与合作的情形，提出了T-联盟相关概念，对Shapley提出的公理进行拓广，并构造了T-联盟Shapley值。针对局中人在合作完成后需要分配收益的情况，利用构造的T-联盟Shapley值给出了子联盟在博弈中的利益分配方案，并分析了该分配方法的相关性质。给出了局中人接受子联盟作为整体参与合作博弈的条件。T-联盟Shapley值是经典Shapley值的扩展，该分配方法允许子联盟中的局中人作为整体参与合作，从而为局中人选择联盟的合作形式提供了理论依据。最后，通过实例分析了局中人依据T-联盟Shapley值选择合作联盟的过程。

关键词: 合作博弈, Shapley值, 哑联盟, 合伙联盟, T-联盟

Abstract: From the viewpoint of coalition payoff allocation, the definition of T-coalition is employed. The axioms of T-coalition Shapley value have been proposed. The explicit form of T-coalition Shapley value has also been given, which can be served as the payoff of the whole coalition. The fair axioms of T-coalition are an extension of crisp axioms, and the explicit form of T-coalition Shapley value is also an extension of crisp Shapley value. The properties of the T-coalition Shapley function are discussed. The condition that the cooperative game accepts the partnership is also proposed. This allocation method allows the players to participate the grand allocation in partnership form. Hence, the T-coalition Shapley function can help players to choose cooperative form. Finally, an illustrative example has been given in order to show the decision process based on T-coalition Shapley function.

Key words: Cooperative game, Shapley value, Dummy coalition, Partnership coalition, T-coalition

于晓辉张强. 基于T-联盟Shapley值的分配策略[J]. 运筹学学报.

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