Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T12:25:14.445Z Has data issue: false hasContentIssue false

An Application of Game Theory: Cost Allocation

Published online by Cambridge University Press:  29 August 2014

Jean Lemaire*
Affiliation:
Université Libre de Bruxelles
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The allocation of operating costs among the lines of an insurance company is one'of the toughest problems of accounting; it is first shown that most of the methods used by the accountants fail to satisfy some natural requirements. Next it is proved that a cost allocation problem is identical to the determination of the value of a cooperative game with transferable utilities, and 4 new accounting methods that originate from game theory are proposed. One of those methods, the proportional nucleus, is recommended, due to its properties. Several practical examples are discussed throughout the paper.

Type
Research Article
Copyright
Copyright © International Actuarial Association 1984

References

Billera, L., Heath, D. and Raanan, J. (1978) Internal Telephone Billing Rates: A Novel Application of Non Atomic Game Theory. Operat. Res. 956965.Google Scholar
Bogardi, I. and Szidarovski, F. (1976) Application of Game Theory in Water Management. Appl. Math. Mod. 1620.Google Scholar
Bres, E., Charnes, A., Cole Eckels, D., Hitt, S., Lyders, R., Rousseau, J., Russell, K. and Schoeman, M. (1979) Costs and Their Assessment to Users of a Medical Library: A Game Theoretic Method for Allocating Joint Fixed Costs. Applied Game Theory. Physica Verlag, 334351Google Scholar
Callen, J. (1978) Financial Cost Allocations: A Game Theoretic Approach. Acc. Rev., 303308.Google Scholar
Diaz, H. and Owen, G. (1979) Fair Subsidies for Urban Transportation Systems. Applied Game Theory. Physica Verlag, 325333.CrossRefGoogle Scholar
Gately, D. (1974) Sharing the Gains from Regional Cooperation: A Game Theeoretic Application to Planning Investment in Electric Power. Intern. Econ. Rev. 195208.Google Scholar
Hamlen, S., Hamlen, W. and Tschirhart, J. (1977) The Use of Core Theory in Evaluating Joint Cost Allocation Schemes. Acc. Rev. 616627.Google Scholar
Hamlen, S., Hamlen, W. and Tschirhart, J. (1980) The Use of Generalized Shapley Allocations in Joint Cost Allocation. Acc. Rev. 269287.Google Scholar
Heaney, J. (1979) Efficiency/Equity Analysis of Environmental Problems: A Game Theoretic Perspective. Applied Game Theory. Physica Verlag, pp. 352369.CrossRefGoogle Scholar
Inter-Agency Committee on Water Resources (1958) Proposed Practices for Economic Analysis of River Basin Projects. U.S. Government Printing Office, Washington D.C.Google Scholar
Jensen, D. (1977) A Class of Mutually Satisfactory Allocations. Acc. Rev. 842856.Google Scholar
Littlechild, S. and Vaidja, K. (1976) The Propensity to Disrupt and the Disruption Nucleolus of a Characteristic Function Game. Int. J. Game Theory 151161.Google Scholar
Littlechild, S. and Thompson, G. (1977) Aircraft Landing Fees: A Game Theory Approach. Bell J. of Economics 186204.Google Scholar
Loehmann, E., Orlando, J., Tschirhart, J. and Whinston, A. (1979) Cost Allocation for a Regional Wastewater Treatment System. Water Resources Research 193202.Google Scholar
Loughlin, J. (1977) The Efficiency and Equity of Cost Allocation Methods for Multipurpose Waterprojects. Water Resources Research 814.Google Scholar
Louderback, J. (1976). Another Approach to Allocating Joint Costs: A Comment. Acc. Rev. 683685.Google Scholar
Maschler, M., Peleg, B. and Shapley, L. (1972) The Kernel and Bargaining Set for Convex Games. Int. J. Game Theory 7393.Google Scholar
Megiddo, N. (1974) On the Non-Monotonicity of the Bargaining Set, the Kernel and the Nucleolus of a Game. SIAM J. Appl. Math. 355358.Google Scholar
Michener, E., Yuen, K. and Sakurai, M. (1981) On the Comparative Accuracy of Lexicographical Solutions in Cooperative Games. Int. J. Game Theory 7589.Google Scholar
Moriarity, S. (1975) Another Approach to Allocating Joint Costs. Acc. Rev. 791795.Google Scholar
Moriarity, S. (1976) Another Approach for Allocating Joint Costs: A Reply. Acc. Rev. 686687.Google Scholar
Ransmeier, J. (1942) The Tennessee Valley Authority : A Case Study in the Economics of Multiple Purpose Stream Planning. Vanderbilt Univ. Press, Nashville, Tennessee.Google Scholar
Sääksjärvi, M. (1976) A Cooperative Model of Wood Procurement—Profit Allocation as a Game Theoretic Problem (in Finnish). Lappeenranta University of Technology, Research Paper 2/76.Google Scholar
Sääksjärvi, M. (1982) Cost Allocation in Cooperative Wood Procurement. A Game Theoretic Approach. Helsinki School of Economics, Working paper F-46.Google Scholar
Shapley, L. (1953) A Value for n-Person Games. Contrib. to the Theory of Games. Annals of Maths Studies. Princeton, pp. 303306.Google Scholar
Shapley, L. (1971) Cores of Convex Games. Int. J. Game Theory 1126.Google Scholar
Schmeidler, D. (1969) The Nucleolus of a Characteristic Function Game. SIAM J. Appl. Math. 11631170.Google Scholar
Straffin, P. and Heaney, J. (1981) Game Theory and the Tennessee Valley Authority. Int. J. Game Theory 3543.Google Scholar
Suzuki, M. and Nakayama, M. (1976) The Cost Assignment of the Cooperative Water Resource Development: A Game Theoretical Approach. Management Science 10811086.Google Scholar
Verrechia, R. (1982) An Analysis of Two Cost Allocation Cases. Acc. Rev. 579593.Google Scholar
von Neumann, J.Morgenstern, O. (1944) Theory of Games and Economic Behaviour. Princeton.Google Scholar
Young, H., Okada, N. and Hashimoto, T. (1980) Cost Allocation in Water Resources Development. A Case Study of Sweden. 11 ASA Research report, Laxenburg.Google Scholar