Abstract
This paper deals with a linear production game with restricted communication. Based on the Owen solution (Owen in Math Progr 9:358–370, 1975), we propose a core-allocation reflecting the communication situation defined by a network. The core of a linear production game with unrestricted communication is included by that of the corresponding network restricted game. Taking this property into account, we develop a procedure for modifying the Owen solution to reflect the configuration of the enlarged core.
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References
Bird, G. C. (1976). On cost allocation for a spanning tree: A game theoretic approach. Networks, 6, 335–350.
Borm, P., Owen, G., & Tijs, S. (1992). On the position value for communication situations. SIAM Journal on Discrete Mathematics, 5, 305–320.
Curiel, I. (1997). Cooperative game theory and applications: Cooperative games arising from combinatorial optimization problems. Berlin: Kluwer Academic Publishers.
Dubey, P., & Shapley, L. S. (1984). Totally balanced games arising from controlled programming problems. Mathematical Programming, 29, 245–267.
Engelbrecht-Wiggans, R., & Granot, D. (1985). On market prices in linear production games. Mathematical Programming, 32, 366–370.
Fernández, F. R., Fiestras-Janeiro, M. G., García-Jurado, I., & Puerto, J. (2005). Competition and cooperation in non-centralized linear production games. Annals of Operations Research, 137, 91–100.
Granot, D. (1986). A generalized linear production model: A unifying model. Mathematical Programming, 34, 212–222.
Granot, D., & Huberman, G. (1981). Minimum cost spanning tree games. Mathematical Programming, 21, 1–18.
Granot, D., & Huberman, G. (1984). On the core and nucleolus of MCST games. Mathematical Programming, 29, 323–347.
Hamiache, G. (1999). A value with incomplete communication. Games and Economic Behavior, 26, 59–78.
Kalai, E., & Zemel, E. (1982a). Totally balanced games and games of flows. Mathematics of Operations Research, 7, 476–478.
Kalai, E., & Zemel, E. (1982b). Generalized network problems yielding totally balanced games. Operations Research, 30, 998–1008.
Kongo, T. (2010). Difference between the position value and the Myerson value is due to the existence of coalition structures. International Journal of Game Theory, 39, 669–675.
Llorca, N., Molina, E., Pulido, M., & Sánchez-Soriano, J. (2004). On the Owen set of transportation situations. Theory and Decision, 56, 215–228.
Megiddo, N. (1978a). Cost allocation for Steiner trees. Networks, 8, 1–6.
Megiddo, N. (1978b). Computational complexity and the game theory approach to cost allocation for a tree. Mathematics of Operations Research, 3, 189–196.
Myerson, R. (1977). Graph and cooperation in games. Mathematics of Operations Research, 2, 225–229.
Nishizaki, I., & Sakawa, M. (2000). Fuzzy cooperative games arising from linear production programming problems with fuzzy parameters. Fuzzy Sets and Systems, 114, 11–21.
Nishizaki, I., & Sakawa, M. (2001). On computational methods for solutions of multiobjective linear production programming games. European Journal of Operational Research, 129, 386–413.
Owen, G. (1975). On the core of linear production games. Mathematical Programming, 9, 358–370.
Owen, G. (1977). Values of games with a priori unions. In R. Henn & O. Moeschlin (Eds.), Mathematical economics and game theory (pp. 77–88). London: Springer.
Peleg, B. (1986). On the reduced game property and its converse. International Journal of Game Theory, 15, 187–200.
Peleg, B. (1992). Axiomatizations of the core. In R. J. Aumann & S. Hart (Eds.), Handbook of game theory with economic applications (Vol. 1, pp. 397–412). Philadelphia: Elsevier. Chapter 13.
Samet, D., & Zemel, E. (1984). On the core and dual set of linear programming games. Mathematics of Operations Research, 9, 309–316.
Slikker, M., & van den Nouweland, A. (2001). Social and economic networks in cooperative game theory. Berlin: Kluwer Academic Publishers.
Suijs, J., Borm, P., Hamers, H., Quant, M., & Koster, M. (2005). Communication and cooperation in public network situations. Annals of Operations Research, 137, 117–140.
Tamir, A. (1991). On the core of network synthesis games. Mathematical Programming, 50, 123–135.
van Gellekom, J. R. G., Potters, J. A. M., Reijnierse, J. H., Engel, M. C., & Tijs, S. H. (2000). Characterization of the Owen set of linear production processes. Games and Economic Behavior, 32, 139–156.
Vázquez-Brage, M., García-Jurado, I., & Carreras, F. (1996). The Owen value applied to games with graph-restricted communication. Games and Economic Behavior, 12, 42–53.
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This work was supported by JSPS KAKENHI Grant Number: 26282086.
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Nishizaki, I., Hayashida, T. & Shintomi, Y. A core-allocation for a network restricted linear production game. Ann Oper Res 238, 389–410 (2016). https://doi.org/10.1007/s10479-016-2109-4
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DOI: https://doi.org/10.1007/s10479-016-2109-4