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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 |
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