Abstract
In revenue maximization of selling a digital product in a social network, the utility of an agent is often considered to have two parts: a private valuation, and linearly additive influences from other agents. We study the incomplete information case where agents know a common distribution about others’ private valuations, and make decisions simultaneously. The “rational behavior” of agents in this case is captured by the well-known Bayesian Nash equilibrium.
Two challenging questions arise: how to compute an equilibrium and how to optimize a pricing strategy accordingly to maximize the revenue assuming agents follow the equilibrium? In this paper, we mainly focus on the natural model where the private valuation of each agent is sampled from a uniform distribution, which turns out to be already challenging.
Our main result is a polynomial-time algorithm that can exactly compute the equilibrium and the optimal price, when pairwise influences are non-negative. If negative influences are allowed, computing any equilibrium even approximately is PPAD-hard. Our algorithm can also be used to design an FPTAS for optimizing discriminative price profile.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akhlaghpour, H., Ghodsi, M., Haghpanah, N., Mirrokni, V.S., Mahini, H., Nikzad, A.: Optimal Iterative Pricing over Social Networks. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 415–423. Springer, Heidelberg (2010)
Arthur, D., Motwani, R., Sharma, A., Xu, Y.: Pricing Strategies for Viral Marketing on Social Networks. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 101–112. Springer, Heidelberg (2009)
Bloch, F., Quérou, N.: Pricing with local network externalities. Technical report (July 2009)
Candogan, O., Bimpikis, K., Ozdaglar, A.E.: Optimal Pricing in the Presence of Local Network Effects. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 118–132. Springer, Heidelberg (2010)
Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: SIGKDD 2009, pp. 199–208 (2009)
Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure nash equilibria. In: STOC 2004, pp. 604–612 (2004)
Goldberg, A.V., Hartline, J.D., Karlin, A.R., Saks, M., Wright, A.: Competitive auctions. Games and Economic Behavior 55(2), 242–269 (2006)
Harsanyi, J.C.: Games with incomplete information played by “bayesian” players, i-iii. part i. the basic model. Management Science 14(3), 159–182 (1967)
Hartline, J., Mirrokni, V., Sundararajan, M.: Optimal marketing strategies over social networks. In: WWW 2008, pp. 189–198 (2008)
Hartline, J.D., McGrew, R.: From optimal limited to unlimited supply auctions. In: ACM-EC 2005, pp. 175–182 (2005)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: SIGKDD 2003, pp. 137–146 (2003)
Milgrom, P., Roberts, J.: Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58(6), 1255–1277 (1990)
Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58 (1981)
Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V.: Algorithmic game theory. Cambridge University Press (2007)
Sundararajan, A.: Local network effects and complex network structure. The B.E. Journal of Theoretical Economics 7(1) (2008)
Van Zandt, T., Vives, X.: Monotone equilibria in bayesian games of strategic complementarities. Journal of Economic Theory 134(1), 339–360 (2007)
Vives, X.: Nash equilibrium with strategic complementarities. Journal of Mathematical Economics 19(3), 305–321 (1990)
Zhu, Z.A.: Two Topics on Nash Equilibrium in Algorithmic Game Theory. Bach- elor’s thesis. Tsinghua University (June 2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, W., Lu, P., Sun, X., Tang, B., Wang, Y., Zhu, Z.A. (2011). Optimal Pricing in Social Networks with Incomplete Information. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-25510-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25509-0
Online ISBN: 978-3-642-25510-6
eBook Packages: Computer ScienceComputer Science (R0)