Sharing Costs Fairly. A Practical Introduction to Cooperative Game Theory

Young, H.P., Okada, N., & Hashimoto, T. (1981). Sharing Costs Fairly. A Practical Introduction to Cooperative Game Theory. IIASA Executive Report. IIASA, Laxenburg, Austria: ER-81-005

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Abstract

An IIASA executive report based on an IIASA research report by H.P. Young, N. Okada, and T. Hashimoto, who compare traditional methods of allocating costs of new water facilities with more recently developed methods involving cooperative game theory. Their purpose is to show how these methods work in actual use, and the executive report serves as practical introduction to cooperative game theory.

The authors have investigated an actual water cost allocation case in the Skane region of southern Sweden. The 18 municipalities of the area were combined into six groups. Costs of a water development project there were first allocated by two naive methods -- proportional to population and proportional to use. Then five techniques of cost allocation derived from cooperative game theory were tried -- separable costs/remaining benefits, Shapley value, nucleolus, weak nucleolus, and proportional nucleolus.

The rationale behind each of these methods is explained, and the superiority of the proportional nucleolus in this particular case is demonstrated. The authors note that as a practical matter, however, there are cases when a single numerical criterion such as apportioning costs by population or by use may be preferable to the more complicated game-theory methods.

The executive report also discusses briefly a simple method for allocating costs in such cases as the Skane water development project that is based on bidding, a noncooperative type of game that puts the burden of information gathering on the players themselves.

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