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DEA production games and Owen allocations. (English) Zbl 1347.91022

Summary: DEA production games have recently been introduced in a paper by S. Lozano [Eur. J. Oper. Res. 231, No. 2, 405–413 (2013; Zbl 1317.90106)]. In the present paper we further investigate these cooperative games. We establish the links between the class of DEA production games and the classes of linear programming games and linear production games. We also analyse the Owen set of DEA production games and discuss the interpretation of these allocations for different levels of cooperation between agents.

MSC:

91A12 Cooperative games
91B38 Production theory, theory of the firm
90C05 Linear programming
91A80 Applications of game theory

Citations:

Zbl 1317.90106
Full Text: DOI

References:

[1] Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092 (1984) · Zbl 0552.90055
[2] Csóka, P.; Herings, P. J.J.; Kóczy, L. A., Stable allocations of risk, Games and Economic Behavior, 67, 266-276 (2009) · Zbl 1168.91410
[3] Curiel, I. J., Cooperative game theory and applications (1997), Kluwer Academic Publisher: Kluwer Academic Publisher The Netherlands · Zbl 0956.91501
[4] Dubey, P.; Shapley, L. S., Totally balanced games arising from controlled programming problems, Mathematical Programming, 29, 245-267 (1984) · Zbl 0557.90109
[5] Feltkamp, V.; van den Nouweland, A.; Borm, P.; Tijs, S.; Koster, A., Linear production with transport of products. resources and technology, ZOR - Methods and Models of Operations Research, 38, 153-162 (1993) · Zbl 0802.90009
[6] Fernández, F. R.; Fiestras-Janeiro, M. G.; García-Jurado, I.; Puerto, J., Competition and cooperation in non-centralized linear production games, Annals of Operations Research, 137, 91-100 (2005) · Zbl 1138.91307
[7] Fukuda, E.; Ishijara, S.; Muto, S.; Tijs, S. H.; Brânzei, R., Cooperative fuzzy games arising from economic situations, Fuzzy Economic Review, 10, 1, 3-15 (2005)
[8] González-Díaz, J.; Garcia-Jurado, I.; Fiestras-Janeiro, M. G., An introductory course on mathematical game theory, Graduate Studies in Mathematics, 115 (2010) · Zbl 1191.91002
[9] Granot, D., A generalized linear production model: a unifying model, Mathematical Programming, 34, 212-222 (1986) · Zbl 0604.90142
[10] Jahanshahloo, G. R.; Soleimani-damanech, M.; Mostafaee, A., On the computational complexity of cost-efficiency analysis models, Applied Mathematicas and Computation, 188, 638-640 (2007) · Zbl 1137.90612
[11] Kalai, E.; Zemel, E., Totally balanced games and games of flow, Mathamtics of Operations Research, 7, 476-478 (1982) · Zbl 0498.90030
[12] Kalai, E.; Zemel, E., Generalized network problems yielding totally balanced games, Operations Research, 30, 998-1008 (1982) · Zbl 0493.90032
[13] Lozano, S., DEA production games, European Journal of Operational Research, 231, 405-413 (2013) · Zbl 1317.90106
[14] Nishizaki, I.; Sakawa, M., Fuzzy cooperative games arising from linear production programming problems with fuzzy parameters, Fuzzy Sets and Systems, 114, 11-21 (2000) · Zbl 0963.91006
[15] Owen, G., On the core of linear production games, Mathematical Programming, 9, 358-370 (1975) · Zbl 0318.90060
[16] Schmeidler, D., The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, 17, 1163-1170 (1969) · Zbl 0191.49502
[17] Seiford, L. M.; Zhu, J., An investigation of returns to scale in data envelopment analysis, Omega, International Journal of Management Science, 27, 1-11 (1999)
[18] Shapley, L. S., A value for n-person games, Annals of Mathematics Studies, 28, 307-317 (1953) · Zbl 0050.14404
[19] Shapley, L. S.; Shubik, M., On market games, Journal of Economic Theory, 1, 9-25 (1969)
[20] Timmer, J.; Borm, P.; Suijs, J., Linear transformation of products: games and economies, Journal of Optimization Theory and Applications, 105, 677-706 (2000) · Zbl 0962.91005
[21] van Gellekoom, J. R.G.; Potter, J. A.M.; Reijnierse, J. H.; Engel, M. C.; Tijs, S. H., Characterization of the Owen set of linear production processes, Games and Economic Behavior, 32, 139-156 (2000) · Zbl 0973.91003
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