-
Previous Article
Existence of the uniform value in zero-sum repeated games with a more informed controller
- JDG Home
- This Issue
-
Next Article
Pure and Random strategies in differential game with incomplete informations
Competing for customers in a social network
1. | Center for Game Theory in Economics, Stony Brook University, Stony Brook, NY 11794-4384, United States |
2. | Opera Solutions-India, Floor 6, Express Trade Towers 1, Plot No. 15-16, Sector 16A, Noida 201 301, New Delhi, India |
3. | PSE-Univesité Paris 1, 112 Boulevard de l'Hôpital, 75013 Paris, France |
  The connectivity of a customer is related to the money firms spend on him. This becomes particularly transparent when externalities are dominant: NE can be characterized in terms of the invariant measures on the recurrent classes of the Markov chain underlying the social network.
  When cost functions of firms are convex, instead of just linear, NE need no longer be unique as we show via an example. But uniqueness is restored if there is enough competition between firms or if their valuations of clients are anonymous.
  Finally we develop a general model of nonlinear externalities and show that existence of NE remains intact.
References:
[1] |
A. Banerji and B. Dutta, Local network externalities and market segmentation,, International Journal of Industrial Organization, 27 (2009), 605.
doi: 10.1016/j.ijindorg.2009.02.001. |
[2] |
F. Bloch and N. Quérou, Pricing in social network,, Games and Economic Behavior, 80 (2013), 243.
doi: 10.1016/j.geb.2013.03.006. |
[3] |
P. Domingos and M. Richardson, Mining the network value of customers,, in Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2001), 57.
doi: 10.1145/502512.502525. |
[4] |
J. L. Doob, Stochastic Processes,, John Wiley & Sons, (1953).
|
[5] |
P. Dubey, R. Garg and B. De Meyer, Competing for customers in a social network: The quasi-linear Case,, in Internet and Network Economics: Second International Workshop, (4286), 162.
doi: 10.1007/11944874_16. |
[6] |
J. Hartline, V. Mirrokni and M. Sundarajan, Optimal marketing strategies over social networks,, in Proceedings of WWW 2008, (2008), 189.
doi: 10.1145/1367497.1367524. |
[7] |
M. Jackson, The economics of social networks,, in Proceedings of the 9th World Congress of the Econometric Society (eds. R. Blundell, (2005). Google Scholar |
[8] |
B. Julien, Competing in Network Industries: Divide and Conquer,, Mimeo, (2001). Google Scholar |
[9] |
D. Kempe, J. Kleinberg and E. Tardos, Maximizing the spread of influence through a social network,, in Proceedings of the 9th International Conference on Knowledge Discovery and Data Mining, (2003), 137.
doi: 10.1145/956755.956769. |
[10] |
C. N. Moore, Summability of series,, The American Mathematical Monthly, 39 (1932), 62.
doi: 10.2307/2302048. |
[11] |
J. Nash, Equilibrium points in $n$-person games,, Proceedings of the National Academy of Science, 36 (1950), 48.
doi: 10.1073/pnas.36.1.48. |
[12] |
M. Richardson and P. Domingos, Mining knowledge-sharing sites for viral marketing,, in Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2002), 61.
doi: 10.1145/775056.775057. |
[13] |
P. Saaskilahti, Monopoly Pricing of Social Goods,, MPRA Paper 3526, (3526). Google Scholar |
[14] |
S. Sahi, A note on the resolvent of a nonnegative matrix and its applications,, Linear Algebra and Its Applications, 432 (2010), 2524.
doi: 10.1016/j.laa.2009.11.004. |
[15] |
J. Scott, Social Network Analysis: A Handbook,, 2nd edition, (2000). Google Scholar |
[16] |
C. Shapiro and H. R. Varian, Information Rules: A Strategic Guide to the Network Economy,, Harvard Business School Press, (1998). Google Scholar |
[17] |
O. Shy, The Economics of Network Industries,, Cambridge University Press, (2001). Google Scholar |
[18] |
G. Tullock, Efficient rent-seeking,, in Toward a Theory of the Rent-Seeking Society (eds. J. M. Buchanan, (1980), 97. Google Scholar |
show all references
References:
[1] |
A. Banerji and B. Dutta, Local network externalities and market segmentation,, International Journal of Industrial Organization, 27 (2009), 605.
doi: 10.1016/j.ijindorg.2009.02.001. |
[2] |
F. Bloch and N. Quérou, Pricing in social network,, Games and Economic Behavior, 80 (2013), 243.
doi: 10.1016/j.geb.2013.03.006. |
[3] |
P. Domingos and M. Richardson, Mining the network value of customers,, in Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2001), 57.
doi: 10.1145/502512.502525. |
[4] |
J. L. Doob, Stochastic Processes,, John Wiley & Sons, (1953).
|
[5] |
P. Dubey, R. Garg and B. De Meyer, Competing for customers in a social network: The quasi-linear Case,, in Internet and Network Economics: Second International Workshop, (4286), 162.
doi: 10.1007/11944874_16. |
[6] |
J. Hartline, V. Mirrokni and M. Sundarajan, Optimal marketing strategies over social networks,, in Proceedings of WWW 2008, (2008), 189.
doi: 10.1145/1367497.1367524. |
[7] |
M. Jackson, The economics of social networks,, in Proceedings of the 9th World Congress of the Econometric Society (eds. R. Blundell, (2005). Google Scholar |
[8] |
B. Julien, Competing in Network Industries: Divide and Conquer,, Mimeo, (2001). Google Scholar |
[9] |
D. Kempe, J. Kleinberg and E. Tardos, Maximizing the spread of influence through a social network,, in Proceedings of the 9th International Conference on Knowledge Discovery and Data Mining, (2003), 137.
doi: 10.1145/956755.956769. |
[10] |
C. N. Moore, Summability of series,, The American Mathematical Monthly, 39 (1932), 62.
doi: 10.2307/2302048. |
[11] |
J. Nash, Equilibrium points in $n$-person games,, Proceedings of the National Academy of Science, 36 (1950), 48.
doi: 10.1073/pnas.36.1.48. |
[12] |
M. Richardson and P. Domingos, Mining knowledge-sharing sites for viral marketing,, in Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2002), 61.
doi: 10.1145/775056.775057. |
[13] |
P. Saaskilahti, Monopoly Pricing of Social Goods,, MPRA Paper 3526, (3526). Google Scholar |
[14] |
S. Sahi, A note on the resolvent of a nonnegative matrix and its applications,, Linear Algebra and Its Applications, 432 (2010), 2524.
doi: 10.1016/j.laa.2009.11.004. |
[15] |
J. Scott, Social Network Analysis: A Handbook,, 2nd edition, (2000). Google Scholar |
[16] |
C. Shapiro and H. R. Varian, Information Rules: A Strategic Guide to the Network Economy,, Harvard Business School Press, (1998). Google Scholar |
[17] |
O. Shy, The Economics of Network Industries,, Cambridge University Press, (2001). Google Scholar |
[18] |
G. Tullock, Efficient rent-seeking,, in Toward a Theory of the Rent-Seeking Society (eds. J. M. Buchanan, (1980), 97. Google Scholar |
[1] |
Manuel Friedrich, Martin Kružík, Ulisse Stefanelli. Equilibrium of immersed hyperelastic solids. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021003 |
[2] |
Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020172 |
[3] |
Guo Zhou, Yongquan Zhou, Ruxin Zhao. Hybrid social spider optimization algorithm with differential mutation operator for the job-shop scheduling problem. Journal of Industrial & Management Optimization, 2021, 17 (2) : 533-548. doi: 10.3934/jimo.2019122 |
[4] |
Qiang Fu, Yanlong Zhang, Yushu Zhu, Ting Li. Network centralities, demographic disparities, and voluntary participation. Mathematical Foundations of Computing, 2020, 3 (4) : 249-262. doi: 10.3934/mfc.2020011 |
[5] |
Shipra Singh, Aviv Gibali, Xiaolong Qin. Cooperation in traffic network problems via evolutionary split variational inequalities. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020170 |
[6] |
Evelyn Sander, Thomas Wanner. Equilibrium validation in models for pattern formation based on Sobolev embeddings. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 603-632. doi: 10.3934/dcdsb.2020260 |
[7] |
Yicheng Liu, Yipeng Chen, Jun Wu, Xiao Wang. Periodic consensus in network systems with general distributed processing delays. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2021002 |
[8] |
Rajendra K C Khatri, Brendan J Caseria, Yifei Lou, Guanghua Xiao, Yan Cao. Automatic extraction of cell nuclei using dilated convolutional network. Inverse Problems & Imaging, 2021, 15 (1) : 27-40. doi: 10.3934/ipi.2020049 |
[9] |
Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020047 |
[10] |
David W. K. Yeung, Yingxuan Zhang, Hongtao Bai, Sardar M. N. Islam. Collaborative environmental management for transboundary air pollution problems: A differential levies game. Journal of Industrial & Management Optimization, 2021, 17 (2) : 517-531. doi: 10.3934/jimo.2019121 |
[11] |
Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051 |
[12] |
Shasha Hu, Yihong Xu, Yuhan Zhang. Second-Order characterizations for set-valued equilibrium problems with variable ordering structures. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020164 |
[13] |
Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 1641-1660. doi: 10.3934/era.2020084 |
[14] |
Editorial Office. Retraction: Honggang Yu, An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 901-901. doi: 10.3934/dcdss.2019060 |
[15] |
Yu-Jhe Huang, Zhong-Fu Huang, Jonq Juang, Yu-Hao Liang. Flocking of non-identical Cucker-Smale models on general coupling network. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1111-1127. doi: 10.3934/dcdsb.2020155 |
[16] |
Gheorghe Craciun, Jiaxin Jin, Casian Pantea, Adrian Tudorascu. Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1305-1335. doi: 10.3934/dcdsb.2020164 |
[17] |
Jingjing Wang, Zaiyun Peng, Zhi Lin, Daqiong Zhou. On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set. Journal of Industrial & Management Optimization, 2021, 17 (2) : 869-887. doi: 10.3934/jimo.2020002 |
[18] |
Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133 |
[19] |
Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020347 |
[20] |
Alain Bensoussan, Xinwei Feng, Jianhui Huang. Linear-quadratic-Gaussian mean-field-game with partial observation and common noise. Mathematical Control & Related Fields, 2021, 11 (1) : 23-46. doi: 10.3934/mcrf.2020025 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]