
Previous Article
Pure and Random strategies in differential game with incomplete informations
 JDG Home
 This Issue

Next Article
Existence of the uniform value in zerosum repeated games with a more informed controller
Competing for customers in a social network
1.  Center for Game Theory in Economics, Stony Brook University, Stony Brook, NY 117944384, United States 
2.  Opera SolutionsIndia, Floor 6, Express Trade Towers 1, Plot No. 1516, Sector 16A, Noida 201 301, New Delhi, India 
3.  PSEUnivesité 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 quasilinear 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). 
[8] 
B. Julien, Competing in Network Industries: Divide and Conquer,, Mimeo, (2001). 
[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 knowledgesharing 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). 
[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). 
[16] 
C. Shapiro and H. R. Varian, Information Rules: A Strategic Guide to the Network Economy,, Harvard Business School Press, (1998). 
[17] 
O. Shy, The Economics of Network Industries,, Cambridge University Press, (2001). 
[18] 
G. Tullock, Efficient rentseeking,, in Toward a Theory of the RentSeeking Society (eds. J. M. Buchanan, (1980), 97. 
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 quasilinear 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). 
[8] 
B. Julien, Competing in Network Industries: Divide and Conquer,, Mimeo, (2001). 
[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 knowledgesharing 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). 
[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). 
[16] 
C. Shapiro and H. R. Varian, Information Rules: A Strategic Guide to the Network Economy,, Harvard Business School Press, (1998). 
[17] 
O. Shy, The Economics of Network Industries,, Cambridge University Press, (2001). 
[18] 
G. Tullock, Efficient rentseeking,, in Toward a Theory of the RentSeeking Society (eds. J. M. Buchanan, (1980), 97. 
[1] 
Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics & Games, 2014, 1 (3) : 537553. doi: 10.3934/jdg.2014.1.537 
[2] 
Filipe Martins, Alberto A. Pinto, Jorge Passamani Zubelli. Nash and social welfare impact in an international trade model. Journal of Dynamics & Games, 2017, 4 (2) : 149173. doi: 10.3934/jdg.2017009 
[3] 
Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2014, 10 (4) : 10911108. doi: 10.3934/jimo.2014.10.1091 
[4] 
Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A penalty method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2012, 8 (1) : 5165. doi: 10.3934/jimo.2012.8.51 
[5] 
Gaidi Li, Jiating Shao, Dachuan Xu, WenQing Xu. The warehouseretailer network design game. Journal of Industrial & Management Optimization, 2015, 11 (1) : 291305. doi: 10.3934/jimo.2015.11.291 
[6] 
Elvio Accinelli, Bruno Bazzano, Franco Robledo, Pablo Romero. Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation. Journal of Dynamics & Games, 2015, 2 (1) : 132. doi: 10.3934/jdg.2015.2.1 
[7] 
Dean A. Carlson. Finding openloop Nash equilibrium for variational games. Conference Publications, 2005, 2005 (Special) : 153163. doi: 10.3934/proc.2005.2005.153 
[8] 
Xiaona Fan, Li Jiang, Mengsi Li. Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints. Journal of Industrial & Management Optimization, 2017, 13 (5) : 113. doi: 10.3934/jimo.2018123 
[9] 
Rumi Ghosh, Kristina Lerman. Rethinking centrality: The role of dynamical processes in social network analysis. Discrete & Continuous Dynamical Systems  B, 2014, 19 (5) : 13551372. doi: 10.3934/dcdsb.2014.19.1355 
[10] 
Sheri M. Markose. Complex type 4 structure changing dynamics of digital agents: Nash equilibria of a game with arms race in innovations. Journal of Dynamics & Games, 2017, 4 (3) : 255284. doi: 10.3934/jdg.2017015 
[11] 
Moez Kallel, Maher Moakher, Anis Theljani. The Cauchy problem for a nonlinear elliptic equation: Nashgame approach and application to image inpainting. Inverse Problems & Imaging, 2015, 9 (3) : 853874. doi: 10.3934/ipi.2015.9.853 
[12] 
Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial & Management Optimization, 2010, 6 (3) : 453464. doi: 10.3934/jimo.2010.6.453 
[13] 
Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial & Management Optimization, 2007, 3 (4) : 727737. doi: 10.3934/jimo.2007.3.727 
[14] 
Mark Broom, Chris Cannings. Game theoretical modelling of a dynamically evolving network Ⅰ: General target sequences. Journal of Dynamics & Games, 2017, 4 (4) : 285318. doi: 10.3934/jdg.2017016 
[15] 
Xiaolin Xu, Xiaoqiang Cai. Price and deliverytime competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial & Management Optimization, 2008, 4 (4) : 843859. doi: 10.3934/jimo.2008.4.843 
[16] 
Rui Mu, Zhen Wu. Nash equilibrium points of recursive nonzerosum stochastic differential games with unbounded coefficients and related multiple\\ dimensional BSDEs. Mathematical Control & Related Fields, 2017, 7 (2) : 289304. doi: 10.3934/mcrf.2017010 
[17] 
Mei Ju Luo, Yi Zeng Chen. Smoothing and sample average approximation methods for solving stochastic generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 115. doi: 10.3934/jimo.2016.12.1 
[18] 
Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A smoothing Newton method for generalized Nash equilibrium problems with secondorder cone constraints. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 118. doi: 10.3934/naco.2012.2.1 
[19] 
Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zerosum linearquadratic differential game: Saddlepoint equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 120. doi: 10.3934/naco.2017001 
[20] 
Enrique R. Casares, Lucia A. RuizGalindo, María Guadalupe GarcíaSalazar. Transitional dynamics, externalities, optimal subsidy, and growth. Journal of Dynamics & Games, 2018, 5 (1) : 4159. doi: 10.3934/jdg.2018005 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]