Revenue Maximization Problem Research Articles

Inequity aversion pricing over social networks: Approximation algorithms and hardness results

We study a revenue maximization problem in the context of social networks. Namely, we generalize a model introduced by Alon, Mansour, and Tennenholtz [2] that captures inequity aversion, i.e., it captures the fact that prices offered to neighboring nodes should not differ significantly. We first provide approximation algorithms for a natural class of instances, where the total revenue is the sum of single-value revenue functions. Our results improve on the current state of the art, especially when the number of distinct prices is small. This applies, for instance, to settings where the seller will only consider a fixed number of discount types or special offers. To complement our positive results, we resolve one of the open questions posed in [2] by establishing APX-hardness for the problem. Surprisingly, we further show that the problem is NP-complete even when the price differences are allowed to be large, or even when the number of allowed distinct prices is as small as three. Finally, we study extensions of the model regarding the demand type of the clients.

Data-Driven Caching With Users’ Content Preference Privacy in Information-Centric Networks

Information-centric networking (ICN) as an emerging networking paradigm has recently gained significant attention, due to the improvement of content delivery efficiency. The built-in network storage for caching is a key component in ICN to provide low latency service and reduce high backhaul traffic by caching popular content. However, users' content preference contains individual sensitive characteristics which is distinguishable from others. Therefore, in this work, we propose a data-driven caching revenue maximization problem with the considerations of users' local differential privacy. Specifically, we employ dBitFlip, a local differential privacy (LDP) mechanism, to locally add differential private noise to the users' preference content information. We leverage data-driven approach to predict the content popularity based on the reference distribution constructed by the reported noisy preference content data from users, mathematically present the distance between the noisy reference distribution and the true distribution by the tolerance level, and prove the relationship among the tolerance level, differential privacy budget and the confidence level. We provide feasible solutions to the proposed revenue maximization problem, and conduct simulations to show the effectiveness of the proposed scheme.

An Approximation Algorithm for Sharing-Aware Virtual Machine Revenue Maximization

Cloud providers face the challenge of efficiently managing their infrastructure through minimizing resource consumption while allocating service requests such that their revenue is maximized. Solutions addressing this challenge should consider the sharing of memory pages among virtual machines (VMs) and the available capacity of each type of requested resources. We provide such solution by designing a greedy approximation algorithm for solving the sharing-aware virtual machine revenue maximization ( $\mathsf{SAVMRM}$ SAVMRM ) problem. The $\mathsf{SAVMRM}$ SAVMRM problem requires determining the set of VMs that can be instantiated on a given server such that the revenue derived from hosting the VMs is maximized. In addition, we model the $\mathsf{SAVMRM}$ SAVMRM problem as a multilinear binary program and optimally solve it, while accounting for page sharing and multiple resource constraints. We determine and analyze the approximability properties of our proposed greedy algorithm and evaluate it by performing extensive experiments using Google cluster workload traces. The experimental results show that under various scenarios, our proposed algorithm generates higher revenue than other VM allocation algorithms while achieving significant reduction of allocated memory.

Data-Driven Spectrum Trading with Secondary Users’ Differential Privacy Preservation

Spectrum trading benefits both secondary users (SUs) and primary users (PUs), while it poses great challenges to maximize PUs' revenue, since SUs' demands are uncertain and individual SU's traffic portfolio contains private information. In this paper, we propose a data-driven spectrum trading scheme which maximizes PUs' revenue and preserves SUs' demand differential privacy. Briefly, we introduce a novel network architecture consisting of the primary service provider (PSP), the secondary service provider (SSP) and the secondary traffic estimator and database (STED). Under the proposed architecture, PSP aggregates available spectrum from PUs, and sells the spectrum to SSP at fixed wholesale price, directly to SUs at spot price, or both. The PSP has to accurately estimate SUs' demands. To estimate SUs' demand, the STED exploits data-driven approach to choose sampled SUs to construct the reference distribution of SUs' demands, and utilizes reference distribution to estimate the demand distribution of all SUs. Moreover, the STED adds noises to preserve the demand differential privacy of sampled SUs before it answers the demand estimation queries from the PSP. With the estimated SUs' demand, we formulate the revenue maximization problem into a risk-averse optimization, develop feasible solutions, and verify its effectiveness through both theoretical proof and simulations.

An Approximation Scheme for Data Monetization

The unprecedented rate at which data is being generated has led to the growth of data markets where valuable datasets are bought and sold. A salient feature of this market is that a data-buyer (agent) is endowed with multi-dimensional private information, namely her ``ideal'' record that she values the most and how her valuation for a given record changes as its distance from her ideal record changes. Consequently, the revenue-maximization problem faced by a data-seller (principal), who serves multiple buyers, is a multi-dimensional mechanism-design problem, which is well-recognized as being difficult to solve. Our main result in this paper is an approximation scheme that guarantees a revenue within as close a positive amount from the optimal revenue as desired. The scheme generates a posted-price menu consisting of a set of item-price pairs -- each entry in the menu consists of an item, i.e., a set of records from the dataset, and the price corresponding to that item. As a tradeoff, the length of the menu resulting from the scheme increases as the desired guarantee gets closer to zero. For convenience in practice, data-sellers may want the ability to limit the length of the menu used by the scheme. To facilitate this, we extend our analysis to obtain a general approximation guarantee corresponding to a menu of any given length. We also demonstrate how the seller can exploit buyers' preferences to generate intuitive and useful rules of thumb for an effective practical implementation of the scheme.

Dynamic Pricing for Smart Mobile Edge Computing: A Reinforcement Learning Approach

This letter studies the revenue maximization problem for the mobile edge computing (MEC) system, where an access point (AP) is equipped with an MEC server, providing job offloading service for multiple resource-hungry users and charging users a service fee for it. Usually, the information about users' personal demand is unknown and users' job arrival rate is time-varying, which make pricing highly challenging. As such, we develop a policy gradient (PG)-based reinforcement learning (RL) algorithm. In specific, a deep neural network (DNN) is adopted as the policy network to design price policy, and a baseline neural network (BNN) is used to reduce the inherent high variance of the gradient obtained using PG. The proposed PG-based algorithm enables continuous pricing, thus constituting an advancement over the conventional Q-learning algorithm that has provided only discrete action space. Simulation results show that our proposed method converges to the optimal revenue performance, while the Q-learning algorithm suffers 44% revenue loss.

Revenue Maximization for Content-Oriented Wireless Caching Networks (CWCNs) With Repair and Recommendation Considerations

To maintain reliability of content-oriented wireless caching networks (CWCNs), repair mechanism is of necessity to be considered due to the natural that storage entities are individually unreliable and thus subject to failure on account of hardware error, network congestion or software updating. Meanwhile, recommendation is tunable for edge caching performance improvement. In this paper, we study the revenue maximization problem for CWCNs with both repair and recommendation considerations. The formulated problem is an integer non-convex and non-linear problem, and thus is difficult to be solved. The difficulties are intrinsically derived from the implicit weighted sum costs (WSCs) as regards storage and repair of each content and the coupling among the Boolean variables. For the sake of analytical tractability, a two-step methodology is developed. Specifically, we first explore the optimal storage and repair amount among the content providers to minimize the WSCs in terms of successfully fixing any occurred data corruption for the stored contents. Thereof, an explicit instance is provided to show how the contents can be coded, stored and then repaired in our network given that an error occurs. Based on the obtained storage and repair amount vectors, we solve the resultant joint caching and recommendation decision making problem (DMP). To be more specific, we decouple the DMP into a pair of subproblems, namely a cache placement and a recommendation optimization subproblems. For each subproblem, a globally optimal and a time-efficient suboptimal solutions are developed, respectively. Later, a versatile iterative paradigm is devised to do the decision making jointly. The convergence performance and the complexity analysis of the proposed algorithms are rigorously analyzed. Numerical results confirm the convergence performance of our iterative algorithms and illustrate their revenue improvements compared to various baseline schemes.

Strategic bidding of distributed energy resources in coupled local and central markets

This paper explores a revenue maximization problem for distributed energy resources in a local day-ahead and balancing market. The local market creates opportunities for competition among distributed energy resources, however it may also lead to exercising market power. In the day-ahead market, the strategic revenue maximization of the distributed energy resources is modelled through a bi-level optimization. The upper-level in the bi-level optimization is from the strategic distributed energy resource’s perspective and the lower-level problem is from the local market operator’s perspective. The balancing market (where there is perfect competition) is modelled by the shrinking rolling horizon approach. A wind farm with a storage system is considered as a case study of a strategic distributed energy resource to evaluate its profitability within the proposed revenue maximization problem. The revenue of the wind farm in the local market is compared with the one in a (business-as-usual) centralized market where it cannot exercise market power. Sensitivity analysis regarding the effect of changing the distribution system parameters e.g. the branch resistances and the loads, on the revenue of the wind farm and its bidding behaviour is performed. Moreover, the role of the storage system on the revenue of the wind farm is studied. Results show that an overloaded or weak distribution system will positively influence the strategic position of the wind farm. Finally, it is shown that depending on the existence of market power, a storage system can bring extra revenues for the wind farm, by hedging against its uncertain output. • Formulation of a bi-level shrinking horizon bidding strategy for DERs in local markets. • Application of the bidding strategy problem to a combined wind and storage system. • A comparison between DER revenue in the local market versus the centralized market. • Study of distribution network parameters on DER’s ability to exercise market power. • Paper shows the application of market power in the local market.

A k-Hop Collaborate Game Model: Adaptive Strategy to Maximize Total Revenue

In Online Social Networks (OSNs), interpersonal communication and information sharing are happening all the time, and it is real-time. When a user initiates an activity in OSNs, immediately, he/she will have a certain influence in his/her friendship circle naturally, some users in the initiator's friendship circle will be attracted to participate in this activity. Based on such a fact, we design a k-hop Collaborate Game Model, which means that an activity initiated by a user can only influence those users whose distance are within k-hop from this initiator in OSNs. Besides, we introduce the problem of Revenue Maximization under k-hop Collaborate Game (RMKCG), which identifies a limited number of initiators in order to obtain revenue as much as possible. Collaborate Game Model describes in detail how to quantify revenue and the logic behind it. We do not know how many followers would be generated from an activity in advance, thus, we need to adopt an adaptive strategy, where the decision who is the next potential initiator depends on the results of past decisions. Adaptive RMKCG problem can be considered as a new stochastic optimization problem, and we prove it is NP-hard, adaptive monotone, but not adaptive submodular. But in some special cases, it is adaptive submodular and an adaptive greedy strategy can obtain a $(1-1/e)$-approximation by adaptive submodularity theory. Due to the complexity of our model, it is hard to compute the marginal gain for each candidate user, then, we propose a convenient and efficient computational method. The effectiveness and correctness of our algorithms are validated by heavy simulation on real-world social networks eventually.

The Market for Surprises: Selling Substitute Goods Through Lotteries

Abstract In this paper, we solve the revenue maximization problem of a multi-product monopolist when the products are substitutes. We consider a Hotelling model with two horizontally differentiated goods located at the endpoints of the segment. Consumers are located uniformly on the segment; their valuations for each good are equal to the base consumption value minus distance costs. When the base consumption value is high, the seller maximizes her expected profit by offering a menu of base and opaque goods. In particular, a single half-half lottery over base goods is optimal under concave and linear costs. When base consumption value is low, only base goods are sold. Finally, when base consumption value is intermediate, the optimal mechanism may entail the offering of lotteries with the positive probability of no delivery. Our findings can explain the emergence of opaque goods sales (e.g., hotel bookings without a complete description of the hotel through hotwire.com or priceline.com) as the outcome of the industry’s search for the optimal selling scheme.

Revenue maximization in optical router nodes

In this paper, a few models for optical router nodes are considered. The stations (ports) of such a node try to transmit packets. Successful transmission of a packet of type j at station i gives a profit γij, but there is also a positive probability that such a packet is dropped, causing a penalty θij. Consider one fixed cycle (frame), in which each station is assigned some visit time. The goal is to choose the visit times in such a way that the revenue is maximized. In our first model there is only one wavelength, and we take the finiteness of buffers into account. The revenue maximization problem is shown to be separable concave, thus allowing application of a very efficient algorithm. In our second model we allow multiple wavelengths. We aim to maximize the revenue by optimally assigning stations to wavelengths and, for each wavelength, by optimally choosing the visit times of the allocated stations within the cycle. This gives rise to a mixed integer linear programming problem (MILP) which is NP-hard. To solve this problem fast and efficiently we provide a three-step heuristic. It consists of (i) solving a separable concave optimization problem, then (ii) allocating the stations to wavelengths using a simple bin packing algorithm, and finally (iii) solving another set of separable concave optimization problems. We present numerical results to investigate the effectiveness of the heuristic and the advantages of having multiple wavelengths. Finally, some model variants are briefly discussed.

Equivalence in Business Models of Informational Intermediary

An intermediary has the technology to provide information about a product to consumers and serves as a platform through which transactions between a monopoly and consumers take place. This paper explores the intermediary's revenue maximization problem across all possible business models. By examining the revenue maximizing solutions under three critical business models, I discover that the market outcomes --- consumers' expected surplus, producer's expected profit and the intermediary's expected revenue --- are equivalent across all business models if and only if the gains from trade are large enough, which provides some insights into, and implications for online selling platforms.

Charging on the Route: An Online Pricing Gateway Congestion Control for ICNs

The Information-Centric Networking (ICN) paradigm has emerged to shift the current host-based network model to a content-oriented one in order to cope with the dominant content-based services in the Internet. Congestion control is a fundamental design concern to support massive content delivery in ICN. While the existing flow-based and hop-by-hop congestion control mechanisms suffer from complexity and compatibility issues, we propose RevMax , a gateway-aware congestion control mechanism based on the architecture of NDN, a well-known ICN platform, to overcome the drawbacks. In the proposed mechanism, the gateway offers a price to each end-user, which urges the user to adjust the request rate according to the price. The optimal pricing policy for the gateway is shown to be formulated as a revenue maximization problem, and an efficient algorithm is proposed to derive the optimal solution. The proposed RevMax mechanism is implemented in NDN and compared to PCON , a state-of-the-art congestion control mechanism for ICNs. Extensive experiments show that RevMax achieves higher throughput, lower network latency, and better fairness in a variety of network scenarios.

Revenue maximization for query pricing

Buying and selling of data online has increased substantially over the last few years. Several frameworks have already been proposed that study query pricing in theory and practice. The key guiding principle in these works is the notion of arbitrage-freeness where the broker can set different prices for different queries made to the dataset, but must ensure that the pricing function does not provide the buyers with opportunities for arbitrage. However, little is known about revenue maximization aspect of query pricing. In this paper, we study the problem faced by a broker selling access to data with the goal of maximizing her revenue. We show that this problem can be formulated as a revenue maximization problem with single-minded buyers and unlimited supply, for which several approximation algorithms are known. We perform an extensive empirical evaluation of the performance of several pricing algorithms for the query pricing problem on real-world instances. In addition to previously known approximation algorithms, we propose several new heuristics and analyze them both theoretically and experimentally. Our experiments show that algorithms with the best theoretical bounds are not necessarily the best empirically. We identify algorithms and heuristics that are both fast and also provide consistently good performance when valuations are drawn from a wide variety of distributions.

Two-Tier Architecture for Spectrum Auction in SDN-Enabled Cloud Radio Access Network

The demand for mobile services is growing aberrantly, which provides both challenges and opportunities for wireless networks. Wireless network virtualization is suggested as a key progression path for enhancing the capacity and resource utilization in the forthcoming fifth-generation mobile networks. In this paper, a software-defined network (SDN) enabled cloud radio access network (C-RAN) framework is proposed for enabling spectrum auction with a two-tier architecture support. In Tier-I, several remote radio heads (RRHs) are introduced to act as the secondary service providers to provide services to its small cell users (SUEs) by exploiting the purchased underutilized or idle resources from the primary service provider in Tier-II. Specifically, in order to maintain quality-of-service requirements of the SUEs, the revenue maximization problem for the RRHs is formulated by considering the user association, band assignment, interference management, and budget allowance. In Tier-II, an SDN-enabled spectrum auction mechanism is proposed for maximizing the social welfare based on the SUEs’ service requirements of all participating RRHs from Tier-I. In this auction mechanism, the bipartite graph is utilized to determine the socially optimal winners and the price charging scheme is proposed inspired by the well-known Vickrey–Clarke–Groves auction method. Simulation results reveal the performance and the benefits of the proposed SDN-enabled spectrum auction mechanism under different scenarios.

Dynamic Pricing with Online Reviews

This paper investigates how the pricing policy of a revenue-maximizing monopolist is influenced by the social learning dynamics of customers that use online reviews to estimate the quality of the product. A salient feature of our problem is that the customers' willingness-to-pay, and hence the demand function, evolves over time in conjunction with the online reviews. The monopolist strives to maximize its total expected revenue over a finite horizon by adjusting prices in response to these dynamics. The revenue maximization problem is studied using two different review models: a quality-based review model, where customers report their experienced quality; and a value-based review model, where reviews internalize both experienced quality as well as the purchase price. To formulate the problem in tractable form, we derive a fluid model which provides a good approximation of the system dynamics when the volume of sales is large. This formulation lends itself to key structural insights into the interactions between optimal pricing policies and review dynamics. In particular, we identify critical time scales and social learning regimes that sharply separate the efficacy of dynamic pricing vis-a-vis fixed-price strategies. Further, we demonstrate the impact of the quality-based and value-based review models on key structural properties of the optimal pricing policies. These structural insights are also elucidated in an illustrative simulation study based on data from an online marketplace.

Price-Based Resource Allocation in Wireless Power Transfer-Enabled Massive MIMO Networks.

This paper considers the price-based resource allocation problem for wireless power transfer (WPT)-enabled massive multiple-input multiple-output (MIMO) networks. The power beacon (PB) can transmit energy to the sensor nodes (SNs) by pricing their harvested energy. Then, the SNs transmit their data to the base station (BS) with large scale antennas by the harvesting energy. The interaction between PB and SNs is modeled as a Stackelberg game. The revenue maximization problem of the PB is transformed into the non-convex optimization problem of the transmit power and the harvesting time of the PB by backward induction. Based on the equivalent convex optimization problem, an optimal resource allocation algorithm is proposed to find the optimal price, energy harvesting time, and power allocation for the PB to maximize its revenue. Finally, simulation results show the effectiveness of the proposed algorithm.

A game-based resource pricing and allocation mechanism for profit maximization in cloud computing

In cloud computing environment, Software as a Service (SaaS) providers offer diverse software services to customers and commonly host their applications and data on the infrastructures supplied by Infrastructure as a Service (IaaS) providers. From the perspective of economics, the basic challenges for both SaaS and IaaS providers are to design resource pricing and allocation policies to maximize their own final revenue. However, IaaS providers seek an optimal price policy of virtual machines to generate more revenue, while SaaS providers want to minimize the cost of using infrastructure resources, and comply with service-level agreement contracts with users at the same time. In this situation, there exists conflict in maximizing revenue of both IaaS and SaaS providers simultaneously. In this paper, we model this revenue maximization problem as the Stackelberg game and analyze the existence and uniqueness of the game equilibrium. Moreover, considering the impact of resource price on users’ willing to access service, we propose a dynamic pricing mechanism to maximize the revenue of both SaaS and IaaS providers. The simulation results demonstrate that, compared to fixed pricing and auction-based pricing mechanisms, the proposed mechanism is superior in the revenue maximization and resource utilization.

Revenue maximization in service systems with heterogeneous customers

In this paper, we consider revenue maximization problems for service systems with heterogeneous customers. To extract meaningful insights, we consider a simplified two queue system where each server charges an admission price to its customers. The customers differ in their cost for unit delay and this customer heterogeneity is modeled as a random variable with distribution F. On arrival, the customers must choose a server that offers the lowest sum of admission price and the expected delay cost.Given the admission prices at the two servers and the explicit knowledge of the distribution F, we first characterize the Wardrop equilibrium routing for the heterogeneous customers. We then consider a monopoly system where both the servers belong to a single operator. For this system we characterize the revenue maximizing program for the monopoly operator and outline its properties. We then consider the duopoly problem where each server competes with the other server to maximize its revenue rate. For the special case when the servers have identical service capacity, we obtain the necessary condition for existence of symmetric Nash equilibrium prices.For the analysis of the monopoly and the duopoly problem, the heterogeneity distribution F is assumed to be explicitly known. However, for most practical scenarios, the functional form of F may not be known to the system operator and in such cases, the revenue maximizing prices cannot be determined. In the last part of the paper, we provide an elementary method to estimate the distribution F. This method relies on suitably varying the admission prices based on the properties of the Wardrop equilibrium. We also illustrate this method with some suitable numerical examples.

Optimal bundles for sponsored search auctions via bracketing scheme

Sponsored search auction has been recently studied and auctioneer’s revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method.We prove that finding a bracketing scheme that maximizes the auctioneer’s revenue is strongly NP-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with K-anonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both NP-hard.