赋权合作博弈中的可行联盟结构与收益分配

Feasible coalitional structure and profit distribution in a weighted cooperative game

合作博弈的局中人由于投入或收益期望的不同,他们在联盟结构中往往具有不同的权重,因此本文提出赋权合作博弈问题。给出形成赋权合作博弈中可行联盟结构的规则:参与者为追求收益最大化而自发形成一个有加权平均最大收益的一级联盟,余下被排除在外的参与者再自发形成下一个有加权平均最大收益的二级联盟,以此类推,直至全部参与者均实现结盟。通过参与者在所有可行联盟结构中的收益确定其权益值,依此对最大联盟结构收益进行分配。最后通过一个算例验证了所提出的可行联盟结构及其收益分配方法的合理性,即参与者权益来源于个体之间的竞争,总收益最大化反映参与者全体的合作性。

Participants in a cooperative game usually have different weights in the coalitional structure because of different investments and income expectations, so this paper proposes weighted cooperative game problem. The rules to form a feasible coalitional structure in a weighted cooperative game are discussed. In order to maximize gain, a subset of players spontaneously forms a primary coalition （also called the first-level coalition） with the weighted averaged maximum gain. The remaining players spontaneously form a secondary coalition with the weighted averaged maximum revenue and so on until all players have joined the coalition. By determining the players＇ equity indexes via their profits in each feasible coalitional structure, revenue of the optimal coalitional structure is allocated. A study case demonstrates the rationality of the proposed feasible coalitional structure and profit distribution method. It shows that the rights and interests of players are from the competition among individuals and the overall maximum revenue reflects the cooperation of all players.