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 in\ufb02uences from other agents. We study the incomplete information case where agents know a common distribution about others\u2019 private valuations, and make decisions simultaneously. The \u201crational behavior\u201d 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 in\ufb02uences are nonnegative. If negative in\ufb02uences are allowed, computing any equilibrium even approximately is PPAD-hard. Our algorithm can also be used to design an FPTAS for optimizing discriminative price pro\ufb01le.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 in\ufb02uences from other agents. We study the incomplete information case where agents know a common distribution about others\u2019 private valuations, and make decisions simultaneously. The […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-246557","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"In Proceedings of the 7th Workshop on Internet and Network Economics (WINE'2011), Singapore, December 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