10.2190/G103-37W5-311K-9318 G10337W5311K9318 6 Economies of Scale Can Be Implemented by Cooperative Game: The Chain Model Case 105 115 20070614 20070614 20070614 20070614 G10337W5311K9318.pdf http://baywood.metapress.com/link.asp?target=contribution&id=G10337W5311K9318 1 Hung-Ming Peter Wu Keith D. Willett Aletheia University, Taiwan Oklahoma State University, Stillwater An important issue examined in this article is that the chain model (which solves for the optimal sitting problem of regional wastewater treatment plants) cannot be implemented if the dischargers do not have fair cost sharing. The article finds that the total treatment cost of the optimal regional treatment plant is fairly assigned to each discharger by the <i>N</i>-cooperative game-MCRS approach. Therefore, the economies of scale are implemented by cooperative game in the chain model case. X. Zhu and C. ReVelle, Siting Model for Regional Wastewater Treatment Systems: The Chain Configuration Case, <i>Water Resource Research</i>, <b>24</b>, pp. 137-144, 1988. J. P. Heaney, Efficiency/Equity Analysis of Environmental Problems—A Game Theoretic Perspective, in <i>Applied Game Theory</i>, S. J. Brams, A. Schotter, and G. Schwodiauer (eds.), Physica-Verlag, Vienna, pp. 352-369, 1979. Federal Interagency River Basin Committee, <i>Proposed Practices for Economic Analysis of River Basin Projects: Technical Report</i>, Washington, DC, 1950. Inter-Agency Committee on Water Resources, <i>Proposed Practices for Economic Analysis of River Basin Projects, Technical Report</i>, Washington, DC, 1958. J. P. Heaney and R. E. Dickinson, Methods for Appointing the Cost of a Water Resource Project, <i>Water Resources Research</i><b>18</b>:3, pp. 476-482, June 1982. T. S. H. Driessen and S. H. Tijs, The Cost Gap Method and Other Cost Allocation Methods for Multipurpose Water Projects, <i>Water Resource Research</i>, <b>21</b>:10, pp. 1469-1475, 1985. S. H. Tijs, Bounds for the Core and the τ Value, in <i>Game Theory and Mathematical Economics</i>, O. Moeschlin and D. Pallaschke (eds.), North-Holland, Amsterdam, pp. 123-132, 1981. G. R. Faulhaber, Cross-Subsidization: Pricing in Public Enterprises, <i>American Economic Review</i>, <b>65</b>, pp. 966-977, 1975. R. P. Lejanon and C. A. Davos, Cost Allocation of Multiagency Water Resource Projects: Game Theoretic Approaches and Case Study, <i>Water Resources Research</i>, <b>31</b>, pp. 1387-1393, 1995. K. E. Readnour, <i>Allocating Financial Responsibility Under CERCLA: An Empirical Model</i>, Master's thesis, Oklahoma State University, Stillwater, Oklahoma, 1996. J. P. Heaney, Coalition Formation and the Size of Regional Pollution Control Systems, in <i>Buying a Better Environment: Cost Effective Regulation Through Permit Trading</i>, E. F. Joeres and M. H. David (eds.), The University of Wisconsin Press, Ltd., Madison, Wisconsin, 1983.