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Cooperative networks games with elastic demands

Published online by Cambridge University Press:  11 October 2007

Alain Quilliot ,
Fatiha Bendali  and
Jean Mailfert
Alain Quilliot
Affiliation:
Laboratoire LIMOS-CNRS UMR 6158, Université de Clermont II Complexe Scientifique des Cézeaux 63177 Aubière Cedex, France; [email protected], [email protected], [email protected]
Fatiha Bendali
Affiliation:
Laboratoire LIMOS-CNRS UMR 6158, Université de Clermont II Complexe Scientifique des Cézeaux 63177 Aubière Cedex, France; [email protected], [email protected], [email protected]
Jean Mailfert
Affiliation:
Laboratoire LIMOS-CNRS UMR 6158, Université de Clermont II Complexe Scientifique des Cézeaux 63177 Aubière Cedex, France; [email protected], [email protected], [email protected]
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Abstract

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.

Keywords

Cooperative gamespricingfixed pointnetwork design
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 4 , October 2007 , pp. 345 - 360
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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References

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.
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.
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.
On, C.G. BIRD cost allocation on a spanning tree: a game approach. Networks 6 (1976) 335–350.
Bondareva, O.N., Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernetica 10 (1963) 119–139.
Boulogne, T., Altman, E., Kameda, H. and Pourtallier, O., Mixed equilibrium in multiclass routing games. IEEE Trans. Aut. Cont. 47 (2002) 903–916. CrossRef
T. Boulogne, E. Altman and O. Pourtallier, Mixed equilibrium in multiclass routing games, Ann. Oper. Res. 109 (2002) 279–291.
Cao, X.R., Shen, H.X., Milito, R. and Wirth, P., Internet pricing with a game theoretical approach: concepts and examples. IEEE/ACM Transactions on Networking 10 (2002) 208–215.
C. Courcoubetis and F. Weber, Pricing communication networks-economics, technology and modelling, Wiley, New York (2003).
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.
L.A. Da Silva, Pricing of QoS enabled networks: a survey. IEEE Com. Surv. Tutorials 3 (2000).
Dubey, P. and Shapley, L.S., Totally balanced games arising from programming problems. Math. Program. 29 (1984) 245–267. CrossRef
Granot, D. and Huberman, G., On the core and nucleolus of minimum spanning tree games. Math. Program. 29 (1984) 323–347. CrossRef
Eiselt, H.A., Laporte, G. and Thisse, J.F., Competitive location models: a framework and bibliography. Transp. Sci. 27 (1993) 44–54. CrossRef
El Azouzi, R. and Altman, E., Constrained traffic equilibrium in routing. IEEE Trans. Aut. Cont. 48 (2003) 1656–1660. CrossRef
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).
Gibbens, R.P. and Kelly, F.P., Resource pricing and the evolution of congestion control. Automatica 35 (1999) 1969–1985. CrossRef
Granot, D. and Granot, F., On some network flow games. Math. Op. Res. 17 (1992) 792–841. CrossRef
Granot, D. and Maschler, M., Spanning network games. Int. J. Game Theor. 27 (1998) 467–500. CrossRef
Haurie, A. and Marcotte, P., On the relationship between Nash Cournot equilibrium and Wardrop equilibria. Networks 15 (1985) 295–308. CrossRef
M. Haviv, The Aumann-Shapley pricing mechanism for allocating congestion costs. Oper. Res. Lett. 29 211–215 (2001).
G. Huberman, The nucleolus and the essential coalitions, in Analysis and Optimization Systems. Springer Berlin (1980) 416–422.
Kalai, E. and Zemel, E., Totally balanced games and flows. Math. Oper. Res. 7 (1982) 476–478. CrossRef
F.P. Kelly, Charging and rate control for elastic traffic. Eur. Trans. Telecom. 8 (1997).
Korilis, Y.A., Lazar, A.A. and Capacity, A. Orda allocation under non cooperative routing. IEEE Trans. Aut. Cont. 42 (1997) 309–325. CrossRef
R.J. La, and V. Anantharam, Network pricing using game theoretical approach, in Proc. 38th IEEE Conf. Decision and Control 4 (1999) 4002–4007.
Lederer, P.J., A competitive network design problem with pricing. Transp. Sci. 27 (1993) 25–38. CrossRef
N. Meggido, Cost allocation for Steiner trees. Networks 8 (1978).
Nash, J., Non cooperative games. Ann. Maths 54 (1951) 286–295. CrossRef
D.R. SMART, Fixed Point Theorems. Cambridge Univ Press, Cambridge tracts in Math. 66 (1974).
Tamir, A., On the core of network synthesis games. Math. Program. 50 (1991) 123–135. CrossRef
Van Den Nouweland, A., Borm, P. and Van Golstein, W., A game theoretic approach to problems in telecommunications. Manage. Sci. 42 (1996) 294–303. CrossRef