Limiting Price Discrimination when Selling Products with Positive Network Externalities
Assume a seller wants to sell a digital product in a social network where a buyer’s valuation of the item has positive network externalities from her neighbors that already have the item. The goal of the seller is to maximize his revenue. Previous work on this problem  studies the case where clients are offered the item in sequence and have to pay personalized prices. This is highly infeasible in large scale networks such as the Facebook graph: (1) Offering items to the clients one after the other consumes a large amount of time, and (2) price-discrimination of clients could appear unfair to them and result in negative client reaction or could conflict with legal requirements.
We study a setting dealing with these issues. Specifically, the item is offered in parallel to multiple clients at the same time and at the same price. This is called a round. We show that with O(logn) rounds, where n is the number of clients, a constant factor of the revenue with price discrimination can be achieved and that this is not possible with o(logn) rounds. Moreover we show that it is APX-hard to maximize the revenue and we give constant factor approximation algorithms for various further settings of limited price discrimination.
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- 3.Buchbinder, N., Feldman, M., Naor, J.S., Schwartz, R.: A tight linear time (1/2)-approximation for unconstrained submodular maximization. In: 53rd FOCS, pp. 649–658 (2012)Google Scholar
- 6.Haghpanah, N., Immorlica, N., Mirrokni, V., Munagala, K.: Optimal auctions with positive network externalities. ACM Transactions on Economics and Computation 1(2), 13:1–13:24 (2013)Google Scholar
- 7.Hartline, J., Mirrokni, V.S., Sundararajan, M.: Optimal marketing strategies over social networks. In: 17th WWW, pp. 189–198 (2008)Google Scholar
- 8.Kann, V., Khanna, S., Lagergren, J., Panconesi, A.: On the hardness of approximating max k-cut and its dual. Chicago Journal of Theoretical Computer Science 1997 (1997)Google Scholar