
Previous Article
Existence of the uniform value in zerosum 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 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), 605614. doi: 10.1016/j.ijindorg.2009.02.001. 
[2] 
F. Bloch and N. Quérou, Pricing in social network, Games and Economic Behavior, 80 (2013), 243261. 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, San Francisco, 2001, 5766. doi: 10.1145/502512.502525. 
[4] 
J. L. Doob, Stochastic Processes, John Wiley & Sons, New York, 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, Lecture Notes in Computer Science, 4286, Springer, BerlinHeidelberg, 2006, 162173. doi: 10.1007/11944874_16. 
[6] 
J. Hartline, V. Mirrokni and M. Sundarajan, Optimal marketing strategies over social networks, in Proceedings of WWW 2008, Beijing, China, 2008, 189198. 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, W. Newey and T. Persson), Cambridge University Press, 2005. 
[8] 
B. Julien, Competing in Network Industries: Divide and Conquer, Mimeo, IDEI and GREMAQ, 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, 137146. doi: 10.1145/956755.956769. 
[10] 
C. N. Moore, Summability of series, The American Mathematical Monthly, 39 (1932), 6271. doi: 10.2307/2302048. 
[11] 
J. Nash, Equilibrium points in $n$person games, Proceedings of the National Academy of Science, 36 (1950), 4849. 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, Edmonton, Alberta, Canada, 2002, 6170. doi: 10.1145/775056.775057. 
[13] 
P. Saaskilahti, Monopoly Pricing of Social Goods, MPRA Paper 3526, University Library of Munich, 2007. 
[14] 
S. Sahi, A note on the resolvent of a nonnegative matrix and its applications, Linear Algebra and Its Applications, 432 (2010), 25242528. doi: 10.1016/j.laa.2009.11.004. 
[15] 
J. Scott, Social Network Analysis: A Handbook, 2nd edition, Sage Publications, London, 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, R. D. Tollison and G. Tullock), College Station: Texas A & M University Press, 1980, 97112. 
show all references
References:
[1] 
A. Banerji and B. Dutta, Local network externalities and market segmentation, International Journal of Industrial Organization, 27 (2009), 605614. doi: 10.1016/j.ijindorg.2009.02.001. 
[2] 
F. Bloch and N. Quérou, Pricing in social network, Games and Economic Behavior, 80 (2013), 243261. 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, San Francisco, 2001, 5766. doi: 10.1145/502512.502525. 
[4] 
J. L. Doob, Stochastic Processes, John Wiley & Sons, New York, 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, Lecture Notes in Computer Science, 4286, Springer, BerlinHeidelberg, 2006, 162173. doi: 10.1007/11944874_16. 
[6] 
J. Hartline, V. Mirrokni and M. Sundarajan, Optimal marketing strategies over social networks, in Proceedings of WWW 2008, Beijing, China, 2008, 189198. 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, W. Newey and T. Persson), Cambridge University Press, 2005. 
[8] 
B. Julien, Competing in Network Industries: Divide and Conquer, Mimeo, IDEI and GREMAQ, 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, 137146. doi: 10.1145/956755.956769. 
[10] 
C. N. Moore, Summability of series, The American Mathematical Monthly, 39 (1932), 6271. doi: 10.2307/2302048. 
[11] 
J. Nash, Equilibrium points in $n$person games, Proceedings of the National Academy of Science, 36 (1950), 4849. 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, Edmonton, Alberta, Canada, 2002, 6170. doi: 10.1145/775056.775057. 
[13] 
P. Saaskilahti, Monopoly Pricing of Social Goods, MPRA Paper 3526, University Library of Munich, 2007. 
[14] 
S. Sahi, A note on the resolvent of a nonnegative matrix and its applications, Linear Algebra and Its Applications, 432 (2010), 25242528. doi: 10.1016/j.laa.2009.11.004. 
[15] 
J. Scott, Social Network Analysis: A Handbook, 2nd edition, Sage Publications, London, 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, R. D. Tollison and G. Tullock), College Station: Texas A & M University Press, 1980, 97112. 
[1] 
Vadim Romanuke. Consistency of equilibrium stacks in finite uniform approximation of a noncooperative game played with staircasefunction strategies. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022027 
[2] 
Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics and Games, 2014, 1 (3) : 537553. doi: 10.3934/jdg.2014.1.537 
[3] 
Filipe Martins, Alberto A. Pinto, Jorge Passamani Zubelli. Nash and social welfare impact in an international trade model. Journal of Dynamics and Games, 2017, 4 (2) : 149173. doi: 10.3934/jdg.2017009 
[4] 
Junichi Minagawa. On the uniqueness of Nash equilibrium in strategicform games. Journal of Dynamics and Games, 2020, 7 (2) : 97104. doi: 10.3934/jdg.2020006 
[5] 
Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial and Management Optimization, 2014, 10 (4) : 10911108. doi: 10.3934/jimo.2014.10.1091 
[6] 
Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A penalty method for generalized Nash equilibrium problems. Journal of Industrial and Management Optimization, 2012, 8 (1) : 5165. doi: 10.3934/jimo.2012.8.51 
[7] 
Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, GerhardWilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial and Management Optimization, 2020, 16 (4) : 19271941. doi: 10.3934/jimo.2019036 
[8] 
Elvio Accinelli, Bruno Bazzano, Franco Robledo, Pablo Romero. Nash Equilibrium in evolutionary competitive models of firms and workers under external regulation. Journal of Dynamics and Games, 2015, 2 (1) : 132. doi: 10.3934/jdg.2015.2.1 
[9] 
Dean A. Carlson. Finding openloop Nash equilibrium for variational games. Conference Publications, 2005, 2005 (Special) : 153163. doi: 10.3934/proc.2005.2005.153 
[10] 
Shunfu Jin, Haixing Wu, Wuyi Yue, Yutaka Takahashi. Performance evaluation and Nash equilibrium of a cloud architecture with a sleeping mechanism and an enrollment service. Journal of Industrial and Management Optimization, 2020, 16 (5) : 24072424. doi: 10.3934/jimo.2019060 
[11] 
Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control and Optimization, 2021, 11 (2) : 209220. doi: 10.3934/naco.2020022 
[12] 
Xiaona Fan, Li Jiang, Mengsi Li. Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints. Journal of Industrial and Management Optimization, 2019, 15 (4) : 17951807. doi: 10.3934/jimo.2018123 
[13] 
Rumi Ghosh, Kristina Lerman. Rethinking centrality: The role of dynamical processes in social network analysis. Discrete and Continuous Dynamical Systems  B, 2014, 19 (5) : 13551372. doi: 10.3934/dcdsb.2014.19.1355 
[14] 
Weiping Li, Haiyan Wu, Jie Yang. Intelligent recognition algorithm for social network sensitive information based on classification technology. Discrete and Continuous Dynamical Systems  S, 2019, 12 (4&5) : 13851398. doi: 10.3934/dcdss.2019095 
[15] 
Gaidi Li, Jiating Shao, Dachuan Xu, WenQing Xu. The warehouseretailer network design game. Journal of Industrial and Management Optimization, 2015, 11 (1) : 291305. doi: 10.3934/jimo.2015.11.291 
[16] 
Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial and Management Optimization, 2010, 6 (3) : 453464. doi: 10.3934/jimo.2010.6.453 
[17] 
Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial and Management Optimization, 2007, 3 (4) : 727737. doi: 10.3934/jimo.2007.3.727 
[18] 
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 and Games, 2017, 4 (3) : 255284. doi: 10.3934/jdg.2017015 
[19] 
Ali NaimiSadigh, S. Kamal Chaharsooghi, Marzieh Mozafari. Optimal pricing and advertising decisions with suppliers' oligopoly competition: StakelbergNash game structures. Journal of Industrial and Management Optimization, 2021, 17 (3) : 14231450. doi: 10.3934/jimo.2020028 
[20] 
Moez Kallel, Maher Moakher, Anis Theljani. The Cauchy problem for a nonlinear elliptic equation: Nashgame approach and application to image inpainting. Inverse Problems and Imaging, 2015, 9 (3) : 853874. doi: 10.3934/ipi.2015.9.853 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]