Playing Games with Genetic Algorithms: Application on Price-QoS Competition in Telecommunications Market
The customers use the best compromise criterion
between price and quality of service (QoS) to select or change
their Service Provider (SP). The SPs share the same market and
are competing to attract more customers to gain more profit. Due
to the divergence of SPs interests, we believe that this situation is a
non-cooperative game of price and QoS. The game converges to an
equilibrium position known Nash Equilibrium (NE). In this work, we
formulate a game theoretic framework for the dynamical behaviors
of SPs. We use Genetic Algorithms (GAs) to find the price and
QoS strategies that maximize the profit for each SP and illustrate
the corresponding strategy in NE. In order to quantify how this NE
point is performant, we perform a detailed analysis of the price of
anarchy induced by the NE solution. Finally, we provide an extensive
numerical study to point out the importance of considering price and
QoS as a joint decision parameter.
[1] Altman, E., and Wynter, L. Equilibrium, games, and pricing in
transportation and telecommunications network. submitted to the special
issue of "Networks and Spacial Economics", on "Crossovers between
Transportation Planning and Telecommunications (2002).
[2] Altman, E., and Wynter, L. Equilibrium, games and pricing in
transportation and telecommunications networks. Networks and Spacial
Economics, special issue of on: Crossovers between Transportation
Planning and Telecommunications 4 (March 2004), 7–21.
[3] Anshelevich, E., Dasgupta, A., Tardos, E., and Wexler, T. Near-optimal
network design with sel´rsh agents. Theory of Computing 4 (2008),
77–109.
[4] Awerbuch, B., Azar, Y., and Epstein, A. The price of routing unsplittable
flow. In Proc. 16th Symp. Theoretical Aspects of Computer Science
(STACS) (2005), 331–337.
[5] Baslam, M., Azouzi, R. E., Sabir, E., and Echabbi, L. Market share
game with adversarial access providers : A neutral and a non-neutral
network analysis. Proc. of "NetGCOOP, Paris, France (October 2011).
[6] Baslam, M., Echabbi, L., Azouzi, R. E., and Sabir, E. Joint price and
qos market share game with adversarial service providers and migrating
customers. Proc. of GameNets, Shanghai, China (April 2011).
[7] Bernstein, F., and Federgruen, A. A general equilibrium model for
industries with price and service competition. Operations Research
(2004), 868–886. [8] Eidenbenz, S., Kumar, A., and Zust, S. Equilibria in topology control
games for ad-hoc networks. Mobile Networks and Applications 11
(2006), 143–159.
[9] El-Azouzi, R., Altman, E., and Wynter, L. Telecommunications network
equilibrium with price and quality-of-service characteristics. Proc. of
ITC, Berlin (September 2003).
[10] Friedman, J. The rational choice controversy. Yale University Press
(1996).
[11] Goldberg, D. E., and Holland, J. H. Genetic algorithms and machine
learning. Machine learning 3, 2 (1988), 95–99.
[12] Goodman, J. C. A note on existence and uniqueness of equilibriumpoints
for concave n-person games. In Econometrica (1980), 48–251.
[13] Gopi, E. Algorithm collections for digital signal processing applications
using Matlab. Springer Science & Business Media, 2007.
[14] Guijarro, L., Pla, V., Vidal, J., and Martinez-Bauset, J. Analysis of price
competition under peering and transit agreements in internet service
provision to peer-to-peer users. IEEE Consumer Communications and
Networking Conference (CCNC2011), Las Vegas, Nevada USA (January
2011), 9 – 12.
[15] HalldÃt’rsson, M., Halpern, J., Li, L., and Mirrokni, V. On spectrum
sharing games. In Proc. 22nd Symp. Principles of Distributed Computing
(PODC) (2004), 107–114.
[16] Holland, J. H. Adaptation in natural and artificial systems: an
introductory analysis with applications to biology, control, and artificial
intelligence. U Michigan Press, 1975.
[17] Kelly, F. Charging and rate control for elastic traffic. European Trans.
Telecommunications 8 (1997), 33–37.
[18] Low, S., and Lapsley, D. Optimization flow control, i: Basic algorithm
and convergence. IEEE/ACM Transactions on Networking 7 (1999),
961âA˘ S¸874.
[19] MaillÃl’, P., Naldi, M., and Tuffin, B. Price war with migrating
customers. In: 17th Annual Meeting of the IEEE/ACM International
Symposium on Modelling, Analysis and Simulation of Computer and
Telecommunication Systems (MASCOTS 2009), IEEE Computer Society,
London, UK (September 2009).
[20] Maille, P., and Tuffin, B. Analysis of price competition in a slotted
resource allocation game. in Proc. of IEEE INFOCOM (2008).
[21] Michalewicz, Z. Genetic algorithms+ data structures= evolution
programs. Springer Science & Business Media, 1996.
[22] Orda, A. Competitive routing in multi-user environments.
IEEE/ACMTrans. on Netw. (1993), 510–521.
[23] Papadimitriou, K., and Koutsoupias, E. Worst-case equilibria. in STACS
(1999), 404–413.
[24] Rosen, J. Existence and uniqueness of equilibrium points for concave
n-person games. Econometrica 33 (1965), 520–534.
[25] Varian, H. Microeconomic analysis. Norton New York (1992).
[26] Vetta, A. Nash equilibria in competitive societies with application to
facility location. In Proc. 43th Symp. Foundations of Computer Science
(FOCS) (2002), 416.
[27] von Neumann, J., and Morgenstern, O. Theory of games and economic
behavior. Princeton University Press (1944).
[28] Wright, A. H. Genetic algorithms for real parameter optimization.
Foundation of Genetic Algorithms, G. J. E (1991), 205âA˘ S¸218.
[29] Wynter, L. Optimizing proportionally fair prices. INRIA RR. 4311
(2001).
[1] Altman, E., and Wynter, L. Equilibrium, games, and pricing in
transportation and telecommunications network. submitted to the special
issue of "Networks and Spacial Economics", on "Crossovers between
Transportation Planning and Telecommunications (2002).
[2] Altman, E., and Wynter, L. Equilibrium, games and pricing in
transportation and telecommunications networks. Networks and Spacial
Economics, special issue of on: Crossovers between Transportation
Planning and Telecommunications 4 (March 2004), 7–21.
[3] Anshelevich, E., Dasgupta, A., Tardos, E., and Wexler, T. Near-optimal
network design with sel´rsh agents. Theory of Computing 4 (2008),
77–109.
[4] Awerbuch, B., Azar, Y., and Epstein, A. The price of routing unsplittable
flow. In Proc. 16th Symp. Theoretical Aspects of Computer Science
(STACS) (2005), 331–337.
[5] Baslam, M., Azouzi, R. E., Sabir, E., and Echabbi, L. Market share
game with adversarial access providers : A neutral and a non-neutral
network analysis. Proc. of "NetGCOOP, Paris, France (October 2011).
[6] Baslam, M., Echabbi, L., Azouzi, R. E., and Sabir, E. Joint price and
qos market share game with adversarial service providers and migrating
customers. Proc. of GameNets, Shanghai, China (April 2011).
[7] Bernstein, F., and Federgruen, A. A general equilibrium model for
industries with price and service competition. Operations Research
(2004), 868–886. [8] Eidenbenz, S., Kumar, A., and Zust, S. Equilibria in topology control
games for ad-hoc networks. Mobile Networks and Applications 11
(2006), 143–159.
[9] El-Azouzi, R., Altman, E., and Wynter, L. Telecommunications network
equilibrium with price and quality-of-service characteristics. Proc. of
ITC, Berlin (September 2003).
[10] Friedman, J. The rational choice controversy. Yale University Press
(1996).
[11] Goldberg, D. E., and Holland, J. H. Genetic algorithms and machine
learning. Machine learning 3, 2 (1988), 95–99.
[12] Goodman, J. C. A note on existence and uniqueness of equilibriumpoints
for concave n-person games. In Econometrica (1980), 48–251.
[13] Gopi, E. Algorithm collections for digital signal processing applications
using Matlab. Springer Science & Business Media, 2007.
[14] Guijarro, L., Pla, V., Vidal, J., and Martinez-Bauset, J. Analysis of price
competition under peering and transit agreements in internet service
provision to peer-to-peer users. IEEE Consumer Communications and
Networking Conference (CCNC2011), Las Vegas, Nevada USA (January
2011), 9 – 12.
[15] HalldÃt’rsson, M., Halpern, J., Li, L., and Mirrokni, V. On spectrum
sharing games. In Proc. 22nd Symp. Principles of Distributed Computing
(PODC) (2004), 107–114.
[16] Holland, J. H. Adaptation in natural and artificial systems: an
introductory analysis with applications to biology, control, and artificial
intelligence. U Michigan Press, 1975.
[17] Kelly, F. Charging and rate control for elastic traffic. European Trans.
Telecommunications 8 (1997), 33–37.
[18] Low, S., and Lapsley, D. Optimization flow control, i: Basic algorithm
and convergence. IEEE/ACM Transactions on Networking 7 (1999),
961âA˘ S¸874.
[19] MaillÃl’, P., Naldi, M., and Tuffin, B. Price war with migrating
customers. In: 17th Annual Meeting of the IEEE/ACM International
Symposium on Modelling, Analysis and Simulation of Computer and
Telecommunication Systems (MASCOTS 2009), IEEE Computer Society,
London, UK (September 2009).
[20] Maille, P., and Tuffin, B. Analysis of price competition in a slotted
resource allocation game. in Proc. of IEEE INFOCOM (2008).
[21] Michalewicz, Z. Genetic algorithms+ data structures= evolution
programs. Springer Science & Business Media, 1996.
[22] Orda, A. Competitive routing in multi-user environments.
IEEE/ACMTrans. on Netw. (1993), 510–521.
[23] Papadimitriou, K., and Koutsoupias, E. Worst-case equilibria. in STACS
(1999), 404–413.
[24] Rosen, J. Existence and uniqueness of equilibrium points for concave
n-person games. Econometrica 33 (1965), 520–534.
[25] Varian, H. Microeconomic analysis. Norton New York (1992).
[26] Vetta, A. Nash equilibria in competitive societies with application to
facility location. In Proc. 43th Symp. Foundations of Computer Science
(FOCS) (2002), 416.
[27] von Neumann, J., and Morgenstern, O. Theory of games and economic
behavior. Princeton University Press (1944).
[28] Wright, A. H. Genetic algorithms for real parameter optimization.
Foundation of Genetic Algorithms, G. J. E (1991), 205âA˘ S¸218.
[29] Wynter, L. Optimizing proportionally fair prices. INRIA RR. 4311
(2001).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:71433", author = "M’hamed Outanoute and Mohamed Baslam and Belaid Bouikhalene", title = "Playing Games with Genetic Algorithms: Application on Price-QoS Competition in Telecommunications Market", abstract = "The customers use the best compromise criterion
between price and quality of service (QoS) to select or change
their Service Provider (SP). The SPs share the same market and
are competing to attract more customers to gain more profit. Due
to the divergence of SPs interests, we believe that this situation is a
non-cooperative game of price and QoS. The game converges to an
equilibrium position known Nash Equilibrium (NE). In this work, we
formulate a game theoretic framework for the dynamical behaviors
of SPs. We use Genetic Algorithms (GAs) to find the price and
QoS strategies that maximize the profit for each SP and illustrate
the corresponding strategy in NE. In order to quantify how this NE
point is performant, we perform a detailed analysis of the price of
anarchy induced by the NE solution. Finally, we provide an extensive
numerical study to point out the importance of considering price and
QoS as a joint decision parameter.
", keywords = "Pricing, QoS, Market share game, Genetic algorithms,
Nash equilibrium, Learning, Price of anarchy.", volume = "9", number = "6", pages = "342-8", }
