The General Compromise Value for Cooperative Games With Transferable Utility

doi:10.1007/s11424-023-1159-3

Journal of Systems Science and Complexity ›› 2023, Vol. 36 ›› Issue (1): 375-392.DOI: 10.1007/s11424-023-1159-3

Previous Articles Next Articles

The General Compromise Value for Cooperative Games With Transferable Utility

SUN Panfei, HOU Dongshuang, SUN Hao

chool of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710101, China

Received:2021-05-16 Revised:2022-02-18 Online:2023-01-25 Published:2023-02-09
Supported by:
This paper is supported by the National Natural Science Foundation of China under Grant Nos. 72001172, 71871180 and 72071158, the Fundamental Research Funds for the Central Universities under Grant No. 310201911qd052 and Natural Science Basic Research Plan in Shaanxi Province of China under Grant No. 2020JQ-225.

PDF ( 2 ) Cited

SUN Panfei, HOU Dongshuang, SUN Hao. The General Compromise Value for Cooperative Games With Transferable Utility[J]. Journal of Systems Science and Complexity, 2023, 36(1): 375-392.

The authors introduce the general compromise value for cooperative games with transferable utility. With respect to a set of potential payoffs of which the maximal and minimal potential payoff vectors are regarded as the upper and lower bounds for players, the unique pre-imputation lying on the straight line segment with these two vectors as the extreme points is defined as the general compromise value. Potential-consistency and maximal proportional property are introduced to characterize the general compromise value.

Key words: Axiomatization, compromise value, cooperative game, solution concept

[1] von Neumann J and Morgenstern O, Theory of Games Anf Economic Behavior, Princeton University Press, Princeton, 1944.
[2] Tijs S H and Otten G J, Compromise values in cooperative game theory, Top, 1993, 1:1-35.
[3] Gillies D B, Some Theorems on n Person Games, Ph.D. Thesis, Princeton University Press, Princeton, New Jersey, 1953.
[4] Tijs S H, Bounds for the core and the τ-value, Game Theory and Mathematical Economics, NorthHolland Publishing Company, Amsterdam, 1981, 123-132.
[5] Berganti nos G and Massó J, Notes on a new compromise value:The χ-value, Optimization, 1996, 38(3):277-286.
[6] Berganti nos G and Massó J, The χ-compromise value for non-transferable utility games, Mathematical Methods of Operations Research, 2002, 56(2):269-286.
[7] Borm P, Keiding H, Mclean R P, et al., The compromise value for NTU-games, International Journal of Game Theory, 1992, 21(2):175-189.
[8] Aumann R J and Peleg B, Von Neumann-Morgenstern solutions to cooperative games without side payments, Bulletin of the American Mathematical Society, 1960, 66:173-179.
[9] Nash J F, The bargaining problem, Econometrica, 1950, 18(2):155-162.
[10] Raiffa H, Arbitration schemes for generalized two-person games, Annals of Mathematics Studies, 1953, 28(2):361-387.
[11] Kalai E and Somrodinsky M, Other solutions to nash's bargaining problem, Econometrica, 1975, 43(3):513-518.
[12] Sánchez-Soriano J, A note on compromise values, Mathematical Methods of Operations Research, 2000, 51(3):471-478.
[13] Timmer J, The compromise value for cooperative games with random payoffs, Mathematical Methods of Operations Research, 2006, 64(1):95-106.
[14] Ransmeier J S, The Tennessee Valley Authority:A Case Study in the Economics of Multiple Purpose Stream Planning, The Vanderbilt University Press, Nashcille, Tennessee, 1942.
[15] Driessen T and Funaki Y, Coincidence of and collinearity between game theoretic solutions, OR Spectrum, 1991, 13(1):15-30.
[16] Xu G, Dai H, and Shi H, Axiomatizations and a noncooperative interpretation of the α-CIS value, Asia Pacific Journal of Operational Research, 2015, 32(5):1550031.
[17] Moulin H, The separability axiom and equal-sharing methods, Journal of Economic Theory, 1985, 36(1):120-148.
[18] Sun P, Hou D, Sun H, et al., Process and optimization implementation of the α-ENSC value, Mathematical Methods of Operations Research, 2017, 86(5):1-16.
[19] González-dıaz J and Sánchez-Rodrıguez E, From Set-Valued Solutions to Single-Valued Solutions:The Centroid and the Core-Center, Working Paper 3-9, Reports in Statistics and Operations Research, Universidad de Santiago de Compostela, 2003.
[20] González-Dıaz J, Borm P, Hendrickx R, et al., A geometric characterisation of the compromise value, Mathematical Methods of Operations Research, 2005, 61(3):483-500.
[21] González-Dıaz J and Sánchez-Rodrıguez E, A natural selection from the core of a TU game:The core-center, International Journal of Game Theory, 2007, 36(1):27-46.
[22] Driessen T, Cooperative Games, Solutions and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988.
[23] Shapley L S, On balanced sets and cores, Naval Research Logistics, 1967, 14(4):453-460.
[24] Tijs S H, The τ-value as a feasible compromise between uptopia and disagreement, Axiomatica and Pragamatics of Conflict Analysis, Gower Publishing Company, Aldershot, England, 1987, 142-156.
[25] Milnor J W, Reasonable outcomes for n-person games, Reasearch Memorandum RM-916, the RAND Coporation, Santa Monica, 1952.
[26] Branzei R, Dimitrov D, and Tijs S H, Shapley-like values for interval bankruptcy games, Economics Bulletin, 2003, 3:1-8.
[27] Alcalde-Unzu J, Góez-Rúa M, and Molis E, Sharing the cost of cleaning a river:The Upstream Responsibility rule, Games and Economic Behavior, 2015, 90(1):134-150.
[28] Branzei R, Branzei O, Alparslan Gök S Z, et al., Cooperative interval games:A survey, Central European Journal of Operations Research, 2010, 18(3):397-411.
[29] Han W, Sun H, and Xu G, A new approach of cooperative interval games:The interval core and Shapley value revisited, Operations Research Letters, 2012, 40(6):462-468.
[30] Driessen T and Tijs S H, The τ-value, the nucleolus and the core for a subclass of games, Methods of Operations Research, 1983, 46:395-406.
[31] Schmeidler D, The nucleolus of a characteristic function game, SIAM Journal on Applied Mathematics, 1969, 17(6):1163-1170.
[32] Shapley L S, A value for n-person games, Annals of Mathematics Studies, 1953, 28(7):307-317.
[33] Shapley L S, Cores of convex games, International Journal of Game Theory, 1971, 1(1):11-26.
[34] van Heumen H, The μ-value:A Solution Concept for Cooperative Games, Master's Thesis (in Dutch), Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands, 1984.
[35] Tijs S H, An axiomatization of the τ-value, Mathmatical Social Sciences, 1987, 13(2):177-181.
[36] Nowak A and Radzik T, A solidarity value for n-person TU games, International Journal of Game Theory, 1994, 23(1):43-48.
[37] Driessen T, On the reduced game property for and the axiomatization of the τ-value of TU-games, TOP, 1996, 4(1):165-185.

[1]	Fanyong MENG, Qiang ZHANG. COOPERATIVE GAMES ON CONVEX GEOMETRIES WITH A COALITION STRUCTURE [J]. Journal of Systems Science and Complexity, 2012, 25(5): 909-925.

Viewed

Full text

Abstract