Geodesic
An extension of a class of cost sharing methods to two-person cooperative games solutions
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 3, pp. 93-127.

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Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents [4] is extended to a class of solutions for two-person cooperative games that are larger than both cost-sharing and surplus-sharing problems, since cooperative games have no no restrictions on positivity of costs and surpluses. The tool of the extension is a new invariance axiom – self covariance [1] – that can be applied both to cost-sharing methods and to cooperative game solutions. In particular, this axiom replaces the Lower composition axiom which is not applicable to methods for profit sharing problems.
Keywords: cooperative game with transferable utilities, cost/surplus sharing method, self-covariance
Mots-clés : solution. 
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Elena B. Yanovskaya. An extension of a class of cost sharing methods to two-person cooperative games solutions. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 3, pp. 93-127. http://geodesic.mathdoc.fr/item/MGTA_2017_9_3_a3/

[1] Yanovskaya E. B., “Sovmestnaya aksiomatizatsiya pred $n$-yadra i resheniya Dutty–Reya dlya vypuklykh igr”, Matematicheskaya teoriya igr i ee prilozheniya, 4:2 (2012), 96–123 | Zbl

[2] Arín J., Iñarra E., “Egalitarian sets for TU-games”, International Game Theory Review, 4:3 (2002), 183–199 | DOI | MR | Zbl

[3] Dutta B., “The egalitarian solution and the reduced game property in convex games”, International Journal of Game Theory, 19 (1990), 153–159 | DOI | MR

[4] Moulin H., “Priority rules and other asymmetric methods”, Econometrica, 68:3 (2000), 643–684 | DOI | MR | Zbl

[5] Moulin H., “Axiomatic cost and surplus sharing”, Handbook of social choice and welfare, chapter 6, v. 1, ed. 1, eds. K. J. Arrow, A. K. Set, K. Suzumura, 2002, 289–357 | DOI | MR

[6] Thomson W., “Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey”, Mathematical Social Sciences, 45 (2003), 249–297 | DOI | MR | Zbl

[7] Yanovskaya E. B., Self-Covariant Solutions To Cooperative Games With Transferable Utilities, Preprint HSE, Series: Economics, WP BRP 85/EC/2014, 2014

[8] Yanovskaya E., An extension of a class of cost sharing methods to the solutions of the class of two-person cooperative games, Preprint NRY Higher School of Economics, Series: Economics No 127, 2014