摘要
从概率的角度研究了可转移效用合作博弈的解的问题.通过深入分析合作博弈解的结构,发现不同合作博弈值之间的联系与区别.运用条件概率的方法,提出了一种新的合作博弈值,并证明了Shapley值与Banzhaf值分别为它的一种特例.使用概率分布解释了合作博弈解的公理化性质.指出了合作博弈解总损失的来源与局中人贡献衡量方式无关.通过概率分布揭示了不同合作博弈值适用的不同环境.最后算例分析证明了使用分步概率的方法计算合作博弈值具有高效性与统一性.
Values for cooperative games with transferable utility were studied from probability view. Different cooperative game values were compared by the deconstruction of the cooperative game value formation process. A new value for cooperative games was proposed. The Shapley value and Banzhaf value were proven to be both its special cases. Axiomatic characters were studied from the probabilistic viewpoint. Total loss is irrelevant to the measurements of players＇ contribution in cooperative games. And the essential differences between cooperative game values were revealed,providing a selection criterion for cooperative game values under different circumstances. In the final part,an example was given to exhibit the two-step probabilistic calculation method,which is highly efficient and can unify different values＇ calculation procedures.
基金
国家自然科学基金(71571171)
