透過合作結盟策略之應用以提升決策品質之研究

在合作賽局中，各方參與者是否願意加入合作賽局，取決於合作結盟後利益之分配。若利益分配公平且各方皆可接受，則合作結盟方能成形。但何謂公平且可接受之利益分配原則，是一亟需探討之議題。本研究運用學者Shapley（1953）提出之夏普利值（Shapley value）公式，探討成本分攤及利益分配問題。考量現實情境中，可能存在不可行之合作結盟排列方式，因此提出改良後之Shapley value公式，讓參與者在合理且公平之情境下，分配其利益或分攤其成本。由應用範例可知，合作結盟下的成本分攤或利益分配是一極為關鍵之議題，傳統上係採比例原則進行分配，但未考慮合作結盟下各種排列組合之邊際成本或邊際利益之平均值，是其缺點，故Shapley提出φ_i公式是其主要貢獻。

關鍵字

合作結盟；夏普利值；利益分配

並列摘要

In the cooperative game, whether the participants are willing to join the cooperative game depends on the distribution of interests after the alliance. If the distribution of benefits is fair and acceptable to all parties, the cooperative alliance can take shape. But what is a fair and acceptable principle of the distribution of benefits is an issue that needs to be discussed. This study uses the Shapley value formula proposed by the Shapley to explore the issue of cost sharing and benefit distribution. Considering the realistic situation, there may be an infeasible arrangement of cooperative alliances. Therefore, the improved Shapley value formula proposed to allow participants to allocate their benefits or share their costs in a reasonable and fair situation. From the application examples, the cost sharing or benefit allocation under the cooperative alliance is an extremely critical issue. Traditionally, the allocation principle is proportionality, but the principle is not so reasonable in some cases. Therefore, Shapley proposed the φ_i formula that the average value of the marginal cost or marginal benefit of various permutations under the cooperative alliance is considered. It is the main contribution of Shapley formula of φ_i.

並列關鍵字

cooperation alliance ； Shapley value ； benefit distribution

參考文獻

Béal, S., Ferrières, S., Rémila, E. and Solal, P., 2018, The proportional Shapley value and applications, Games and Economic Behavior, 108, 93-112. doi:10.1016/j.geb.2017.08.010

Hou, D., Xu, G., Sun, P. and Driessen, T., 2018, The Shapley value for the probability game, Operations Research Letters, 46(4), 457-461. doi:10.1016/j.orl.2018.06.004

Kim, S., 2016, Asymptotic shapley value based resource allocation scheme for IoT services, Computer Networks, 100, 55-63. doi:10.1016/j.comnet.2016.02.021

Krawczyk, P. and Płatkowski, T., 2018, Shapley value redistribution of social wealth fosters cooperation in social dilemmas, Physica A: Statistical Mechanics and its Applications, 492, 2111-2122. doi:10.1016/j.physa.2017.11.128

Lindsay, L., 2018, Shapley value based pricing for auctions and exchanges, Games and Economic Behavior, 108, 170-181. doi:10.1016/j.geb.2017.10.020

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透過合作結盟策略之應用以提升決策品質之研究

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