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.
@cite_0 also use the explore and exploit framework, and study a similar problem; potential buyers do not arrive sequentially as in @cite_1 , but can choose to buy the product with some probability only if being recommended by friends.
@cite_0 @cite_1
2952466854 2406185007 2015290529 2296066287
We study the use of viral marketing strategies on social networks to maximize revenue from the sale of a single product. We propose a model in which the decision of a buyer to buy the product is influenced by friends that own the product and the price at which the product is offered. The influence model we analyze is quite general, naturally extending both the Linear Threshold model and the Independent Cascade model, while also incorporating price information. We consider sales proceeding in a cascading manner through the network, i.e. a buyer is offered the product via recommendations from its neighbors who own the product. In this setting, the seller influences events by offering a cashback to recommenders and by setting prices (via coupons or discounts) for each buyer in the social network. Finding a seller strategy which maximizes the expected revenue in this setting turns out to be NP-hard. However, we propose a seller strategy that generates revenue guaranteed to be within a constant factor of the optimal strategy in a wide variety of models. The strategy is based on an influence-and-exploit idea, and it consists of finding the right trade-off at each time step between: generating revenue from the current user versus offering the product for free and using the influence generated from this sale later in the process. We also show how local search can be used to improve the performance of this technique in practice. We consider the problem of designing budget feasible mechanisms for a dealer, who aims to maximize revenue by buying items from a seller market and selling them to a buyer market that consists of unit-demand buyers. Different from the related literature, the dealer's value'' for a set of items that he purchased from the seller market is not directly given as a number but it is defined to be the maximum revenue the dealer can obtain from selling the items to the buyers. We aim to design mechanisms that are dominant-strategy truthful for the sellers to report their costs and envy-free for the buyers to purchase their most preferred items (given their prices) in the final outcome, such that the total payment to the sellers does not exceed the dealer's budget and the dealer's revenue is (approximately) maximized. First, to understand the structure of the optimal mechanisms, we show that the maximum (envy-free) revenue obtainable by the dealer as a function of the set of purchased items is monotone and subadditive. Thus, existing results on subadditive optimization problems are potentially applicable in solving the mechanism design problem for the dealer. However, a crucial assumption adopted by all previous studies on subadditive functions is that the mechanism or algorithm has access to the value oracle and or the demand oracle. In the dealer's problem, instead, we show that (1) the demand oracle can be efficiently simulated by the value oracle and (2) both have efficient O(log n)-approximation algorithms, where n is the number of buyers. This is particularly interesting given the literature, since, in general, the demand oracle can always efficiently simulate the value oracle, and there are cases where the demand oracle is strictly more powerful. Our results show that, for the dealer's problem, the two oracles are as powerful as each other. Finally, using the results above, we provide a polynomial-time budget feasible mechanism for the dealer that doesn't use any oracle and provides an O((log2n)(log2m))-approximation of the optimal revenue, where m is the number of sellers. Most of existing e-commerce recommender systems aim to recommend the right product to a user, based on whether the user is likely to purchase or like a product. On the other hand, the effectiveness of recommendations also depends on the time of the recommendation. Let us take a user who just purchased a laptop as an example. She may purchase a replacement battery in 2 years (assuming that the laptop's original battery often fails to work around that time) and purchase a new laptop in another 2 years. In this case, it is not a good idea to recommend a new laptop or a replacement battery right after the user purchased the new laptop. It could hurt the user's satisfaction of the recommender system if she receives a potentially right product recommendation at the wrong time. We argue that a system should not only recommend the most relevant item, but also recommend at the right time. This paper studies the new problem: how to recommend the right product at the right time? We adapt the proportional hazards modeling approach in survival analysis to the recommendation research field and propose a new opportunity model to explicitly incorporate time in an e-commerce recommender system. The new model estimates the joint probability of a user making a follow-up purchase of a particular product at a particular time. This joint purchase probability can be leveraged by recommender systems in various scenarios, including the zero-query pull-based recommendation scenario (e.g. recommendation on an e-commerce web site) and a proactive push-based promotion scenario (e.g. email or text message based marketing). We evaluate the opportunity modeling approach with multiple metrics. Experimental results on a data collected by a real-world e-commerce website(shop.com) show that it can predict a user's follow-up purchase behavior at a particular time with descent accuracy. In addition, the opportunity model significantly improves the conversion rate in pull-based systems and the user satisfaction utility in push-based systems. We consider the problem of devising incentive strategies for viral marketing of a product. In particular, we assume that the seller can influence penetration of the product by offering two incentive programs: a) direct incentives to potential buyers (influence) and b) referral rewards for customers who influence potential buyers to make the purchase (exploit connections). The problem is to determine the optimal timing of these programs over a finite time horizon. In contrast to algorithmic perspective popular in the literature, we take a mean-field approach and formulate the problem as a continuous-time deterministic optimal control problem. We show that the optimal strategy for the seller has a simple structure and can take both forms, namely, influence-and-exploit and exploit-and-influence. We also show that in some cases it may optimal for the seller to deploy incentive programs mostly for low degree nodes. We support our theoretical results through numerical studies and provide practical insights by analyzing various scenarios.