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.
Hartline, Mirrokni and Sundararajan @cite_1 study the explore and exploit framework. In their model the seller offers the product to the agents in a sequential manner, and assumes all agents are myopic , i.e., each agent is making the decision based on the known results of the previous agents in the sequence. As they have pointed out, if the pricing strategy of the seller and the private value distributions of the subsequent agents are publicly known, the agents can make more informed'' decisions than the myopic ones. In contrast to them, we consider perfect rational'' agents in the simultaneous-move game, where agents make decisions in anticipation of what others may do given their beliefs to other agents' valuations.
@cite_1
2110373679
We discuss the use of social networks in implementing viral marketing strategies. While influence maximization has been studied in this context (see Chapter 24 of [10]), we study revenue maximization, arguably, a more natural objective. In our model, a buyer's decision to buy an item is influenced by the set of other buyers that own the item and the price at which the item is offered. We focus on algorithmic question of finding revenue maximizing marketing strategies. When the buyers are completely symmetric, we can find the optimal marketing strategy in polynomial time. In the general case, motivated by hardness results, we investigate approximation algorithms for this problem. We identify a family of strategies called influence-and-exploit strategies that are based on the following idea: Initially influence the population by giving the item for free to carefully a chosen set of buyers. Then extract revenue from the remaining buyers using a 'greedy' pricing strategy. We first argue why such strategies are reasonable and then show how to use recently developed set-function maximization techniques to find the right set of buyers to influence.