Tarification par des jeux coopératifs avec demandes élastiques
RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 3, pp. 367-381.

Nous proposons ici un modèle de Tarification basé sur une extension du formalisme des Jeux Coopératifs et qui prend en compte la notion d'Élasticité de la Demande. Nous présentons pour ce modèle un résultat d'existence ainsi qu'un algorithme de calcul associé. Nous interprétons enfin ce nouveau concept dans le cas d'un problème de production et nous le prolongeons au cas d'un problème de transport.

We propose here a pricing Model which is an extension of the Cooperative Game concept and which includes a notion of Elastic Demand. We present some existence results as well as some algorithms. We conclude by discussing this model in the context of some Production and Transportation problems.

Mots-clés : programmation linéaire, jeux coopératifs, point fixe, flots, transport, production 
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     author = {Bendali, F. and Mailfert, J. and Quilliot, A.},
     title = {Tarification par des jeux coop\'eratifs avec demandes \'elastiques},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {367--381},
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Bendali, F.; Mailfert, J.; Quilliot, A. Tarification par des jeux coopératifs avec demandes élastiques. RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 3, pp. 367-381. http://www.numdam.org/item/RO_2001__35_3_367_0/

[1] K.J. Arrow, Choix Collectifs et Préférences Individuelles. Calmann-Levy (1975).

[2] C. Berge, Théorie des Jeux à n personnes. Gauthier-Villars, Paris, Memorial Sciences Math. 138 (1957). | Numdam | MR | Zbl

[3] C.G. Bird, On cost allocation on a spanning tree : A game theoretical approach. Networks 6 (1976) 335-350. | MR | Zbl

[4] O.N. Bondareva, Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernetica 10 (1963) 119-139. | MR | Zbl

[5] G. Bruyneel, Computation of the nucleolus of a game by means of minimal balanced sets. Oper. Res. Verfahren 34 (1979) 35-51. | MR | Zbl

[6] N. Curien, Cost allocation and pricing policy : the case of french telecommunications, in Cost Allocation : Methods, Principles, Applications, edited H.P. Young, Chap. 9, Elsevier Sciences (1985) 167-178.

[7] M. Davis, M. Maschler, The kernel of a cooperative game. Naval Res. Logist. Quarterly 12 (1965) 223-259. | MR | Zbl

[8] D. Granot, G. Huberman, On the core and nucleolus of minimum cost spanning tree games. Math. Programming 29 (1984) 323-347. | MR | Zbl

[9] P. Dubey, L.S. Shapley, Totally balanced games arising from controlled programming problems. Math. Programming 29 (1984) 245-267. | MR | Zbl

[10] H.A. Eiselt, G. Laporte, J.F. Thisse, Competitive location model : a framework and bibliography. Transportation Sci. 27 (1993) 44-54. | Zbl

[11] I. Ekeland, La Théorie des Jeux et ses Applications à l'Economie Mathématique. Presses Universitaires de France (1974).

[12] F.M. Fisher, Games economists play : A non cooperatice view. Rand J. Econom. 20 (1989) 113-124. | MR

[13] D. Fudemberg, J. Tirole, Game Theory. MIT Press (1991). | MR

[14] D. Granot, A generalized linear production model : A unifying model. Math. Programming 34 (1986) 212-222. | MR | Zbl

[15] D. Granot, F. Granot, On some network flow games. Math. Oper. Res. 17 (1992) 792-841. | MR | Zbl

[16] G. Huberman, The nucleolus and the essential coalitions, in Analysis and Optimization Systems. Springer, Berlin (1980) 416-422. | MR | Zbl

[17] E. Kalai, E. Zemel, Totally balanced games and games of flows. Math. Oper. Res. 7 (1982) 476-478. | MR | Zbl

[18] P.J. Lederer, A competitive network design problem with pricing. Transportation Sci. 27 (1993) 25-38. | Zbl

[19] J. Nash, Non-Cooperative games. Ann. of Math. 54 (1951) 286-295. | MR | Zbl

[20] A. Orda, R. Rom, N. Shimkin, Competitive routing in multiuser communication networks. IEEE/ACM Trans. Networking 1 (1993) 510-521.

[21] G. Owen, On the core of linear production games. Math. Prog. 9 (1975) 358-370. | MR | Zbl

[22] G. Owen, Game Theory. Academic Press (1982). | MR | Zbl

[23] L.S. Shapley, On balanced sets and cores. Naval Res. Logist. Quarlerly 14 (1967) 453-460.

[24] L.S. Shapley, Cores of convex games. Int. J. Game Theory 1 (1971) 11-26. | MR | Zbl

[25] D.R. Smart, Fixed Point Theorems. Cambridge University Press, Cambridge Tracts in Math. 66 (1974). | MR | Zbl

[26] A. Tamir, On the core of network synthesis games. Math. Programming 50 (1991) 123-135. | MR | Zbl

[27] J. Von Neuman, O. Morgenstern, Theory of Games and Economic Behaviour. Princeton University Press (1947). | MR | Zbl