Cooperative networks games with elastic demands

Alain Quilliot; Fatiha Bendali; Jean Mailfert

RAIRO - Operations Research (2007)

  • Volume: 41, Issue: 4, page 345-360
  • ISSN: 0399-0559

Abstract

top
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.

How to cite

top

Quilliot, Alain, Bendali, Fatiha, and Mailfert, Jean. "Cooperative networks games with elastic demands." RAIRO - Operations Research 41.4 (2007): 345-360. <http://eudml.org/doc/250112>.

@article{Quilliot2007,
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. },
author = {Quilliot, Alain, Bendali, Fatiha, Mailfert, Jean},
journal = {RAIRO - Operations Research},
keywords = {Cooperative games; pricing; fixed point; network design},
language = {eng},
month = {10},
number = {4},
pages = {345-360},
publisher = {EDP Sciences},
title = {Cooperative networks games with elastic demands},
url = {http://eudml.org/doc/250112},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Quilliot, Alain
AU - Bendali, Fatiha
AU - Mailfert, Jean
TI - Cooperative networks games with elastic demands
JO - RAIRO - Operations Research
DA - 2007/10//
PB - EDP Sciences
VL - 41
IS - 4
SP - 345
EP - 360
AB - 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.
LA - eng
KW - Cooperative games; pricing; fixed point; network design
UR - http://eudml.org/doc/250112
ER -

References

top
  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 Methods5, Birkauser, Berlin (1999) 359–376.  
  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.  Zbl1116.91310
  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.  Zbl1094.91003
  4. C.G. BIRD, On cost allocation on a spanning tree: a game approach. Networks6 (1976) 335–350.  Zbl0357.90083
  5. O.N. Bondareva, Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernetica10 (1963) 119–139.  Zbl1013.91501
  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.  Zbl1005.91003
  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 Networking10 (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. Tutorials3 (2000).  
  12. P. Dubey and L.S. Shapley, Totally balanced games arising from programming problems. Math. Program.29 (1984) 245–267.  Zbl0557.90109
  13. D. Granot and G. Huberman, On the core and nucleolus of minimum spanning tree games. Math. Program.29 (1984) 323–347.  Zbl0541.90099
  14. H.A. Eiselt, G. Laporte and J.F. Thisse, Competitive location models: a framework and bibliography. Transp. Sci.27 (1993) 44–54.  Zbl0767.90006
  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. Automatica35 (1999) 1969–1985.  Zbl0946.93028
  18. D. Granot and F. Granot, On some network flow games. Math. Op. Res.17 (1992) 792–841.  Zbl0773.90097
  19. D. Granot and M. Maschler, Spanning network games. Int. J. Game Theor.27 (1998) 467–500.  Zbl1058.91518
  20. A. Haurie and P. Marcotte, On the relationship between Nash Cournot equilibrium and Wardrop equilibria. Networks15 (1985) 295–308.  Zbl0579.90030
  21. M. Haviv, The Aumann-Shapley pricing mechanism for allocating congestion costs. Oper. Res. Lett.29 211–215 (2001).  Zbl0993.90027
  22. G. Huberman, The nucleolus and the essential coalitions, in Analysis and Optimization Systems. Springer Berlin (1980) 416–422.  
  23. E. Kalai and E. Zemel, Totally balanced games and flows. Math. Oper. Res.7 (1982) 476–478.  Zbl0498.90030
  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.  Zbl0872.90035
  26. R.J. La, and V. Anantharam, Network pricing using game theoretical approach, in Proc. 38th IEEE Conf. Decision and Control4 (1999) 4002–4007.  
  27. P.J. Lederer, A competitive network design problem with pricing. Transp. Sci.27 (1993) 25–38.  Zbl0795.90016
  28. N. Meggido, Cost allocation for Steiner trees. Networks8 (1978).  
  29. J. Nash, Non cooperative games. Ann. Maths54 (1951) 286–295.  Zbl0045.08202
  30. D.R. SMART, Fixed Point Theorems. Cambridge Univ Press, Cambridge tracts in Math.66 (1974).  Zbl0297.47042
  31. A. Tamir, On the core of network synthesis games. Math. Program.50 (1991) 123–135.  Zbl0722.90091
  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.  Zbl0881.90152

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.