Shapley Value를 이용한 안양천 유역 통합관리 계획에 따른 비용분담방안의 연구
A Study on Cost Division Scheme Using Shapley Value for Integrated Watershed Management Planning for Anyang-cheon, Korea
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초록
안양천은 서울의 한강에 유입되는 대표적 도시하천이다. 도시화로 인한 안양천 하천수질 악화와 건천화 문제를 개선하기 위해 유역통합관리를 위한 여러 사업이 진행되고 있다. 유역통합관리를 위해서는 관련 지자체들의 공조가 필요하게 되며, 재정분담문제가 필연적으로 발생하게 된다. 본 연구에서는 유역통합관리를 위해 제안된 사업비 261억의 4개 소유역의 비용분담 방안을 Shapley Value를 이용하여 제안하고 이를 다른 2개 분담방안들과 비교하였다. ‘분담방안 1’은 수질개선시설이 설치되는 유역의 지자체가 비용을 부담하는 방안으로, 소유역 Ⅰ지역은 0.58%, 소유역 Ⅱ지역은 29.54%, 소유역 Ⅳ지역은 0%, 그리고 소유역 Ⅴ지역은 69.88%의 비용을 분담하게 된다. ‘분담방안 2’는 각 소유역의 소하천길이에 따라 비용을 분담하는 것으로, 13개 지자체들의 교섭력이 동일하다는 것을 전제로 하고 있으며, 소유역 Ⅰ지역은 13.76%, Ⅱ지역은 7.34%,Ⅳ지역은 45.87%, Ⅴ지역은 33.03%의 분담을 해야 한다. 하지만 하천의 물 흐름은 상중하류의 각 지자체에 서로 다른 교섭력을 부여하므로, 공조적 게임의 解인 shapley Value를 이용하여 교섭력을 고려한 재정분담방안인 ‘분담방안 3’으로 비용분담체계를 설계하였다. 모든 가능한 공조체제에 있어 각 참여자들의 평균 한계기여도의 합으로 측정되는 Shapley Value에 의한 분담비율은 Ⅰ지역 0.29%, Ⅱ지역은 14.77%,Ⅳ지역 50.00%, Ⅴ지역은 34.94%이며, 이를 지자체들이 수용 가능한, ‘공정한’ 재정분담방안으로 제시하였다.
Abstract
Anyang-cheon(stream) runs through southern metropolitan area of Seoul to Han-river in Korea. Due to fast growth of Seoul, the water quality and quantity problems in Anyang-cheon have occurred. To cope with the problems, the Integrated Watershed Management program for Anyang-cheon was adopted and a KRW 26.1 billion (USD 21.8 million) pilot project (construction of 4 facilities such as reservoir) is suggested for 4 sub-watersheds of Anyang-cheon, which cost will be shared by the 12 local governments (LG). Three cost division schemes are compared. By Scheme 1, if the cost is borne by the LG in a watershed where the facilities are constructed (no cost division scheme), the LG in Ⅰ is to bear 0.58% of the total construction cost, LG in watershed Ⅱ 29.54%, LG in Ⅳ 0%, LG in Ⅴ 69.88%. In particular, LG in Ⅳ in this scheme bears no cost because no facility is constructed, even though watershed Ⅳ is the major beneficiary of the facility construction. Scheme 2 is to share the cost by length of streams in each sub-watershed and the suggested cost share for each sub-watershed is 13.76% by Ⅰ, 7.34% by Ⅱ, 45.87% by Ⅳ, and 33.03% by Ⅴ. However, this cost division scheme is fair only under the false assumption that the bargaining powers of group of LGs are identical. To suggest a better and fair division rule, Shapley Value, a cooperative game solution, is used to suggest Scheme 3. In Scheme 3, Shapley Value measures the summation of average marginal contribution of each player in all possible coalitions as cost division scheme and is known to provide a fair division considering bargaining power. In the context of Anyang-cheon, LGs in upper stream have superior bargaining position. The result suggests the cost division is fair under Scheme 3, when the cost shares are 0.29% by Ⅰ, 14.77% by Ⅱ, 50% by Ⅳ, and 34.94% by Ⅴ, respectively.
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