张艳楠　孙绍荣

摘 要：部分污染型企业因自身能力有限或治污成本过高，无法达到法定环保标准。某一区域中（如工业园区）污染型企业如在环保治污设备技术的改造与提升上有一致需求和合作可能，可形成治污联盟，进行环保治污设备的成本分摊。首先，文章运用合作博弈理论，通过分析环保设备技术选择问题，构建污染型企业形成治污联盟购买使用环保治污设备技术的成本分摊合作博弈模型，并把购买使用治污设备技术的成本、设备技术运营费用、处理未被治理污染物的排污费作为总费用研究。其次，分析治污联盟中成本分摊博弈的特性，证明核心非空与线性规划松弛对偶最优解之间的关系，同时通过证明该博弈模型为子模博弈，运用子模博弈的性质求解核心解、夏普利值等，并进行算例分析。结果表明污染型企业承担的排污费是可供选择的环保治污设备技术集合的单峰函数；各个污染型企业的满意度越高，满意度差值越小，治污联盟越稳定。最后，进一步分析有附加特殊治污需求的污染型企业设备技术选择博弈，结果表明随着治污联盟成员的增加，治污联盟更加倾向于加大投入设备技术，获得较高的治污效率及附加治污效率。

关键词：合作博弈；治污联盟；成本分摊；核心解

中图分类号：F253.9 文献标识码：A

Abstract： Some polluting enterprises not meeting the statutory environmental standards have become a great problem of government management because of limited ability or high pollution-control cost. Polluting enterprises in an area（such as industrial park）can develop a pollution-control alliance to allocate the cost of pollution-control equipment if common demand and possibility of cooperation are existed. First of all， game model of cost allocation on polluting enterprises purchasing pollution-control equipment is constructed through analyzing equipment-selection problem using cooperative game theory. Total cost including purchasing pollution-control equipment expense， operating cost and pollutant charge is studied as well. Moreover， character of cost allocation game model is discussed， covering relationship of core and optimal solution in dual relaxation of linear programming and also function relationship of pollutant charge and pollution-control equipment. At the same time， property of submodular game can be used to calculate core and Shapley value after the game model above proved to be submodular game. Then， relationship between satisfaction survey and stability is given to verify the conclusions， numerical example as well. In the end， equipment-section game with additional pollution-control request demonstrates the influence on demand of pollution-control equipment due to adding numbers in a alliance.

Key words： cooperative game； pollution-control alliance； cost allocation； core

0 引 言

21世纪以来，我国已经进入企业建立与发展的高峰期。其中一部分企业因自身性质的原因，其生产或运作过程中对外界环境产生一定的破坏作用。……