广义多选择合作博弈的Shapley值

A Shapley value for multi-choice cooperative games revisited

多选择合作博弈是允许局中人有多种行动选择的合作博弈.狭义多选择合作博弈要求所有局中人的行动集相同.广义多选择合作博弈则允许不同局中人有不同的行动集.本文在广义多选择合作博弈框架下重新审视狭义多选择合作博弈的一类Shapley值,利用公理化方法给出了它在广义多选择合作博弈中的扩展,给出了详细的数值算例说明其计算过程,并指出它可用于分析供应链韧性.研究结果既丰富了多选择合作博弈理论,又可为供应链韧性分析提供新的途径.

A multi-choice cooperative game is a cooperative game that allows players to have multi-choices of actions.While a narrow multi-choice cooperative game requires all players to have the same action set,a generalized game allows different sets for different players.In this paper,under the framework of generalized games,a Shapley value of narrow games is revisited.We extend the value to generalized games with the axiomatic method,give a detailed numerical example to illustrate its calculation process,and use it to analyze supply chain resilience.