Stability of Alliances between Service Providers

Three service providers in competition, try to optimize their quality of service / content level and their service access price. But, they have to deal with uncertainty on the consumers- preferences. To reduce their uncertainty, they have the opportunity to buy information and to build alliances. We determine the Shapley value which is a fair way to allocate the grand coalition-s revenue between the service providers. Then, we identify the values of β (consumers- sensitivity coefficient to the quality of service / contents) for which allocating the grand coalition-s revenue using the Shapley value guarantees the system stability. For other values of β, we prove that it is possible for the regulator to impose a per-period interest rate maximizing the market coverage under equal allocation rules.

Authors:

• Helene Le Cadre

Keywords:

• Alliance
• Shapley value
• Stability
• Repeated game
• Interest rate.

References:

[1] El Omri A., Cooperation in Supply chains: Alliance Formation and Profit
Allocation among Independent Firms, Ph.D. thesis, Ecole Centrale de
Paris, 2009
[2] Bourreau M., Coaltion, Industrial organization course, master IREN, 2010
[3] de Man A.-P., Roijakkers N., de Graauw H., Managing dynamics through
robust alliance governance structures: The case of KLM and Northwest
Airlines, European Management journal, in press, 2010
[4] Dupuit J., On the measurement of the utility of public works, Annales
des Ponts et Chauss'ees, 1952
[5] Gulati R., Khanna T., Nohria N., Unilateral Commitments and the
Importance of Process in Alliances, Sloan Management Review, MIT,
1994
[6] Johnson J., Myatt D., On the Simple Economics of Advertising, Marketing,
and Product Design, American Economic Review, American
Economic Association, vol. 96, pp. 756-784, 2006
[7] Grzybowski L., Karamti C., Competition in Mobile Telephony in France
and Germany, working Paper 07-24, NET Institute, 2007
[8] Koessler F., Th'eorie des jeux, cours de Paris School of Economics, 2009
[9] Le Cadre H., Bouhtou M., An Interconnection Game between Mobile
Network Operators: Hidden Information Forecasting using Expert Advice
Fusion, Computer Networks, to appear, 2010
[10] MacAvoy P. W., Tacit Collusion under Regulation in the Pricing of
Interstate Long-Distance Telephone Services, Journal of Economics and
Management Strategy, vol.2, pp.147-185, 1995
[11] Myerson R., Game Theory, Analysis of Conflict, Harvard University
Press, 6 − th Edition, 2004
[12] P'enard T., Structures de march'e et Pratiques facilitant la collusion: une
approche par la th'eorie des jeux r'ep'et'es, CREREG working paper, 2003
[13] Pohjola O.-P., Kilkky K., Value-based methodology to analyze communication
services, Netnomics, vol.8, pp.135-151, 2007
[14] Rubinstein R., The Cross-Entropy Method, Springer Information Science
and Statistics, 2004
[15] Saad W., Debbah M., Hjorungnes A., Basar T., Coalitional Game Theory
for Communication networks, IEEE Signal Processing Magazine Tutorial,
2009
[16] Schlee E., The Value of Information About Product Quality, Rand
Journal of Economics, the RAND Corporation, vol.27, pp.803-815, 1996
[17] Tijms A., A First Course in Stochastic Models, Wiley Interscience, 2003
[18] Yildizoglu M., Introduction `a la th'eorie des jeux, Manuel et Exercices
corrig'es, Dunod, 2003