With a focus on a regional joint water distribution system, this paper proposes a cost allocation scheme which guarantees an equilibrium reached by participating regions (players) who are self-organized to form appropriate cooperative relations (coalitions). Two critical properties of regional joint water distribution systems are discussed, i.e., physical and social networks. Physical networks include regional water distribution pipelines combined with treatment facilities built in regions. Social networks mean cooperative relations (linkages) among participating regions. It is pointed out that a reasonable self-enforcing cost allocation scheme, should properly reflect the manner in which participants attain an equilibrium in the dynamic evolution process of the two networks. Characteristics of cost functions are closely examined by referring to the manner in which social network structure bind the optimal (economically efficient) design of respective physical network structure. It is shown that economies of scale may not always hold for water distribution pipeline systems. Since formation of self-enforcing coalitions largely depends on such characteristics of cost functions, proper sizes and division of coalitions should eventually become stable if joint costs are to be efficiently allocated.
The notions of equilibria based on Myerson's value coupled with 'component balance' and 'equal bargaining power' are proved to serve as the intended cost allocation scheme. With a joint regional distribution system as a case study, illustrations are made to demonstrate the applicability of the proposed cost allocation scheme.