Abstract
There is a wide range of situations where a group of agents (broadly interpreted as persons, departments, organizations or countries) benefit from cooperative actions, but is left with the problem of sharing the related costs. These situations range from everyday life problems such as people sharing a cab to international agreements like the Kyoto protocol where industrialized countries bargain over emission cuts. In everyday situations, like sharing a cab, there are rarely time to make use of sophisticated allocation rules even though the problem itself may be rather complex: typically the allocation becomes more or less random and people often tend to use rules of thumb.In situations like bargaining between countries over emission cuts, the final outcome will typically reflect the countries bargaining power rather than sophisticated considerations of fairness
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arin J, Kuipers J, Vermeulen D (2003) Some characterizations of egalitarian solutions on classes of TU-games. Math Soc Sci 46:327–345.
Aumann R, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36:195–213.
Bjondal E, Hamers H, Koster M (2004) Cost allocation in a bank ATM network. Math Methods Oper Res 59:405–418.
Bondareva ON (1963) Certain applications of the method of linear programming to the theory of cooperative games. Problemy Kibernitiki 10:119–139.
Charnes A, Granot D (1973) Prior solutions: extensions of convex nucleolus solutions to chance-constrained games. In: Proceedings of the Computer Science and Statistics Seventh Symposium at Iowa State University, 323–332.
Curiel I (1997) Cooperative game theory and applications. Kluwer, Dordrecht.
Curiel I, Maschler M, Tijs SH (1987) Bankruptcy games. Z Oper Res 31:A143–A159.
Dutta B (1990) The egalitarian solution and reduced game properties in convex games. Int J Game Theory 19:153–169.
Dutta B, Ray D (1989) A concept of egalitarianism under participation constraints. Econometrica 57:615–635.
Hart S, Mas-Colell A (1989) Potential, value, and consistency. Econometrica 57:589–614.
Hokari T (2000) The nucleolus is not aggregate monotonic on the class of convex games. Int J Game Theory 29:133–137.
Hougaard JL, Østerdal LP (2006) Monotonicity of social welfare optima. Games Econ Behav (to appear).
Hougaard JL, Peleg B, Thorlund-Petersen L (2001) On the set of Lorenz-maximal imputations in the core of a balanced game. Int J Game Theory 30:147–165.
Hougaard JL, Peleg B, Østerdal LP (2005) The Dutta–Ray solution on the class of convex games: a generalization and monotonicity properties. Int Game Theory Review 7:1–12.
Housman D, Clark L (1998) Core and monotonic allocation methods. Int J Game Theory 27:611–616.
Ichiishi T (1981) Super modularity: applications to convex games and the greedy algorithm. J Econ Theory 25:283–286.
Lehrer E (2002) Allocation processes in cooperative games. Int J Game Theory 31:341–351.
Littlechild SC, Thompson GF (1977) Aircraft landing fees: a game theory approach. Bell J Econ 8:186–204.
Mirghani AN, Scapens RW (1995) Cost allocation theory and practice: the continuing debate. In: Ashton, Hopper, Scapens (eds) Issues in management accounting, chap. 3. Prentice-Hall, London, pp. 39–60.
Owen G (1995) Game theory, 3rd edn. Academic, New York.
Peleg B, Sudhölter P (2003) Introduction to the theory of cooperative games. Kluwer, Dordrecht.
Ransmeier JS (1942) The Tennessee Valley Authority: a case study in the economics of multiple purpose stream planning. Vanderbilt University Press, Nashville, TN.
Schmeidler D (1969) The Nucleolus of a characteristic function game. SIAM J Appl Math 17:1163–1170.
Shapley L (1953) A value for n-person games. Ann Math Stud 28:307–318.
Shapley L (1967) On balanced sets and cores. Naval Res Logist Q 14:453–460.
Shapley L (1971) Cores of convex games. Int J Game Theory 1:11–26.
Sobolev AI (1975) The characterization of optimality principles in cooperative games by functional equations. In: Vorobiev NN (ed) Mathematical methods in social sciences, vol 6. Academy of Sciences of the Lithunian SSR, Vilnius, pp. 95–151 (in Russian).
Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ Behav 2:378–394.
Suijs J (2000) Cooperative decision-making under risk. Kluwer, New York.
Taha HA (1989) Operations research, 2nd edn. Maxwell Macmillan, New York.
Tijs SH (1981) Bounds for the core and the τ-value. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North-Holland, Amsterdam, pp. 123–132.
Tijs SH (1987) An axiomatization of the τ-value. Math Soc Sci 13:177–181.
Tijs SH, Driessen TSH (1986) Game theory and cost allocation problems. Manage Sci 32:1015–1024.
Timmer J, Borm P, Tijs S (2003) On three Shapley-like solutions for cooperative games with random payoffs. Int J Game Theory 32:595–613.
van den Nouweland A, Borm P, van den Golstein Brouwers W, Groot Bruinderink R, Tijs S (1996) A game theoretic approach to problems in telecommunication. Manage Sci 42:294–303.
(1985) Monotonic solutions of cooperative games. Int J Game Theory 14: 65–72. Please update reference Hougaard and Østerdal (2006).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hougaard, J.L. (2009). Cost Allocation as Cooperative Games. In: An Introduction to Allocation Rules. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01828-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-01828-2_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01827-5
Online ISBN: 978-3-642-01828-2
eBook Packages: Business and EconomicsEconomics and Finance (R0)