Cooperative networks games with elastic demands
RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 345-360.

We present 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 an algorithm, and we conclude by discussing a specific problem related to network pricing.

DOI : 10.1051/ro:2007034
Classification : 91A12, 91B24
Mots-clés : cooperative games, pricing, fixed point, network design
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Quilliot, Alain; Bendali, Fatiha; Mailfert, Jean. Cooperative networks games with elastic demands. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 345-360. doi : 10.1051/ro:2007034. http://archive.numdam.org/articles/10.1051/ro:2007034/

[1] E. Altman and A Markov, game approach for optimal routing in a queing network, in Annal. of Dynamic Games, Stochastic and Differential Games, Theory and Numeric Methods 5, Birkauser, Berlin (1999) 359-376. | Zbl

[2] E. Altman, T. Boulogne, R. El Azouzi, T. Jimenez and L. Wynter, A survey on networking games in telecommunications. Comput. Oper. Res. (2004) 47 p. | MR

[3] E. Altman and L. Wynter, Equilibrium, games and pricing in transportation and telecommunication networks, in Networks and Spatial Economics: special issue on crossovers between transportation and telecommunication modelling, edited by L. Altman and L. Wynter (2004) 7-21. | Zbl

[4] C.G. BIRD, On cost allocation on a spanning tree: a game approach. Networks 6 (1976) 335-350. | Zbl

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

[6] T. Boulogne, E. Altman, H. Kameda and O. Pourtallier, Mixed equilibrium in multiclass routing games. IEEE Trans. Aut. Cont. 47 (2002) 903-916.

[7] T. Boulogne, E. Altman and O. Pourtallier, Mixed equilibrium in multiclass routing games, Ann. Oper. Res. 109 (2002) 279-291. | Zbl

[8] X.R. Cao, H.X. Shen, R. Milito and P. Wirth, Internet pricing with a game theoretical approach: concepts and examples. IEEE/ACM Transactions on Networking 10 (2002) 208-215.

[9] C. Courcoubetis and F. Weber, Pricing communication networks-economics, technology and modelling, Wiley, New York (2003).

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

[11] L.A. Da Silva, Pricing of QoS enabled networks: a survey. IEEE Com. Surv. Tutorials 3 (2000).

[12] P. Dubey and L.S. Shapley, Totally balanced games arising from programming problems. Math. Program. 29 (1984) 245-267. | Zbl

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

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

[15] R. El Azouzi and E. Altman, Constrained traffic equilibrium in routing. IEEE Trans. Aut. Cont. 48 (2003) 1656-1660.

[16] R. El Azouzi, E. Altman and L. Wynter, Telecommunication network equilibrium with price and quality of service characteristics, in Proc. of Internat. Conf. on Teletraffic ITC, Berlin (2003).

[17] R.P. Gibbens and F.P. Kelly, Resource pricing and the evolution of congestion control. Automatica 35 (1999) 1969-1985. | Zbl

[18] D. Granot and F. Granot, On some network flow games. Math. Op. Res. 17 (1992) 792-841. | Zbl

[19] D. Granot and M. Maschler, Spanning network games. Int. J. Game Theor. 27 (1998) 467-500. | Zbl

[20] A. Haurie and P. Marcotte, On the relationship between Nash Cournot equilibrium and Wardrop equilibria. Networks 15 (1985) 295-308. | Zbl

[21] M. Haviv, The Aumann-Shapley pricing mechanism for allocating congestion costs. Oper. Res. Lett. 29 211-215 (2001). | Zbl

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

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

[24] F.P. Kelly, Charging and rate control for elastic traffic. Eur. Trans. Telecom. 8 (1997).

[25] Y.A. Korilis, A.A. Lazar and A. Orda, Capacity allocation under non cooperative routing. IEEE Trans. Aut. Cont. 42 (1997) 309-325. | Zbl

[26] R.J. La, and V. Anantharam, Network pricing using game theoretical approach, in Proc. 38th IEEE Conf. Decision and Control 4 (1999) 4002-4007.

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

[28] N. Meggido, Cost allocation for Steiner trees. Networks 8 (1978). | MR | Zbl

[29] J. Nash, Non cooperative games. Ann. Maths 54 (1951) 286-295. | Zbl

[30] D.R. SMART, Fixed Point Theorems. Cambridge Univ Press, Cambridge tracts in Math. 66 (1974). | MR | Zbl

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

[32] A. Van Den Nouweland, P. Borm and W. Van Golstein, A game theoretic approach to problems in telecommunications. Manage. Sci. 42 (1996) 294-303. | Zbl

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