We study the power and limits of optimal dynamic pricing in combinatorial markets; i.e., dynamic pricing that leads to optimal social welfare. Previous work by Cohen-Addad et al. [EC'16] demonstrated the existence of optimal dynamic prices for unit-demand buyers, and showed a market with coverage valuations that admits no such prices. However, finding the frontier of markets (i.e., valuation functions) that admit optimal dynamic prices remains an open problem. In this work we establish positive and negative results that narrow the existing gap.
On the positive side, we provide tools for handling markets beyond unit-demand valuations. In particular, we characterize all optimal allocations in multi-demand markets. This characterization allows us to partition the items into equivalence classes according to the role they play in achieving optimality. Using these tools, we provide a poly-time optimal dynamic pricing algorithm for up to $3$ multi-demand buyers.
On the negative side, we establish a maximal domain theorem, showing that for every non-gross substitutes valuation, there exist unit-demand valuations such that adding them yields a market that does not admit an optimal dynamic pricing. This result is the dynamic pricing equivalent of the seminal maximal domain theorem by Gul and Stacchetti [JET'99] for Walrasian equilibrium. Yang [JET'17] discovered an error in their original proof, and established a different, incomparable version of their maximal domain theorem. En route to our maximal domain theorem for optimal dynamic pricing, we provide the first complete proof of the original theorem by Gul and Stacchetti.
We study fairness in the context of feature-based price discrimination in monopoly markets. We propose a new notion of individual fairness, namely, α-fairness, which guarantees that individuals with similar features face similar prices. First, we study discrete valuation space and give an analytical solution for optimal fair feature-based pricing. We show that the cost of fair pricing is defined as the ratio of expected revenue in an optimal feature-based pricing to the expected revenue in an optimal fair feature-based pricing (CoF) can be arbitrarily large in general. When the revenue functio…
Despite the promising potential of network risk management services (e.g., cyber-insurance) to improve information security, their deployment is relatively scarce, primarily due to such service companies being unable to guarantee profitability. As a novel approach to making cyber-insurance services more viable, we explore a symbiotic relationship between security vendors (e.g., Symantec) capable of price differentiating their clients, and cyber-insurance agencies having possession of information related to the security investments of their clients. The goal of this relationship is to (i) allow…
We study a model of congestible resources, where pricing and scheduling are intertwined. Motivated by the problem of pricing cloud instances, we model a cloud computing service as linked $GI/GI/\cdot$ queuing systems where the provider chooses to offer a fixed pricing service, a dynamic market based service, or a hybrid of both, where jobs can be preempted in the market-based service. Users (jobs), who are heterogeneous in both the value they place on service and their cost for waiting, then choose between the services offered. Combining insights from auction theory with queuing theory we are …
We study market mechanisms for allocating divisible goods to competing agents with quasilinear utilities. For \emph{linear} pricing (i.e., the cost of a good is proportional to the quantity purchased), the First Welfare Theorem states that Walrasian equilibria maximize the sum of agent valuations. This ensures efficiency, but can lead to extreme inequality across individuals. Many real-world markets -- especially for water -- use \emph{convex} pricing instead, often known as increasing block tariffs (IBTs). IBTs are thought to promote equality, but there is a dearth of theoretical support for …
Big data has been emerging as a new approach in utilizing large datasets to optimize complex system operations. Big data is fueled with Internet-of-Things (IoT) services that generate immense sensory data from numerous sensors and devices. While most current research focus of big data is on machine learning and resource management design, the economic modeling and analysis have been largely overlooked. This paper thus investigates the big data market model and optimal pricing scheme. We first study the utility of data from the data science perspective, i.e., using the machine learning methods.…
Transportation Network Companies employ dynamic pricing methods at periods of peak travel to incentivise driver participation and balance supply and demand for rides. Surge pricing multipliers are commonly used and are applied following demand and estimates of customer and driver trip valuations. Combinatorial double auctions have been identified as a suitable alternative, as they can achieve maximum social welfare in the allocation by relying on customers and drivers stating their valuations. A shortcoming of current models, however, is that they fail to account for the effects of trip detour…
Mobile data demand is increasing tremendously in wireless social networks, and thus an efficient pricing scheme for social-enabled services is urgently needed. Though static pricing is dominant in the actual data market, price intuitively ought to be dynamically changed to yield greater revenue. The critical question is how to design the optimal dynamic pricing scheme, with prospects for maximizing the expected long-term revenue. In this paper, we study the sequential dynamic pricing scheme of a monopoly mobile network operator in the social data market. In the market, the operator, i.e., the …
In settings where full incentive-compatibility is not available, such as core-constraint combinatorial auctions and budget-balanced combinatorial exchanges, we may wish to design mechanisms that are as incentive-compatible as possible. This paper offers a new characterization of approximate incentive-compatibility by casting the pricing problem as a meta-game between the center and the participating agents. Through a suitable set of simplifications, we describe the equilibrium of this game as a variational problem. We use this to characterize the space of optimal prices, enabling closed-form s…
We study large markets with a single seller which can produce many types of goods, and many multi-minded buyers. The seller chooses posted prices for its many items, and the buyers purchase bundles to maximize their utility. For this setting, we consider the following questions: What fraction of the optimum social welfare does a revenue maximizing solution achieve? Are there pricing mechanisms which achieve both good revenue and good welfare simultaneously? To address these questions, we give efficient pricing schemes which are guaranteed to result in both good revenue and welfare, as long as …
We analyze the computational complexity of market maker pricing algorithms for combinatorial prediction markets. We focus on Hanson's popular logarithmic market scoring rule market maker (LMSR). Our goal is to implicitly maintain correct LMSR prices across an exponentially large outcome space. We examine both permutation combinatorics, where outcomes are permutations of objects, and Boolean combinatorics, where outcomes are combinations of binary events. We look at three restrictive languages that limit what traders can bet on. Even with severely limited languages, we find that LMSR pricing is…
We show that a competitive equilibrium always exists in combinatorial auctions with anonymous graphical valuations and pricing, using discrete geometry. This is an intuitive and easy-to-construct class of valuations that can model both complementarity and substitutes, and to our knowledge, it is the first class besides gross substitutes that have guaranteed competitive equilibrium. We prove through counter-examples that our result is tight, and we give explicit algorithms for constructive competitive pricing vectors. We also give extensions to multi-unit combinatorial auctions (also known as p…
University of Electronic Science and Technology of China（电子科技大学）；The University of Auckland（奥克兰大学）
A data marketplace is an online venue that brings data owners, data brokers, and data consumers together and facilitates commoditisation of data amongst them. Data pricing, as a key function of a data marketplace, demands quantifying the monetary value of data. A considerable number of studies on data pricing can be found in literature. This paper attempts to comprehensively review the state-of-the-art on existing data pricing studies to provide a general understanding of this emerging research area. Our key contribution lies in a new taxonomy of data pricing studies that unifies different att…
This paper analyzes two pricing schemes commonly used in WiFi markets: the flat-rate and the usage-based pricing. The flat-rate pricing encourages the maximum usage, while the usage-based pricing can flexibly attract more users especially those with low valuations in mobile Internet access. First, we use theoretical analysis to compare the two schemes and show that for a single provider in a market, as long as the WiFi capacity is abundant, the flat-rate pricing leads to more revenue. Second, we study how a global provider (e.g., Skype) collaborates with this monopolist in each local market to…
Following the work of Babaioff et al, we consider the pricing game with strategic vendors and a single buyer, modeling a scenario in which multiple competing vendors have very good knowledge of a buyer, as is common in online markets. We add to this model the realistic assumption that the buyer has a fixed budget and does not have unlimited funds. When the buyer's valuation function is additive, we are able to completely characterize the different possible pure Nash Equilibria (PNE) and in particular obtain a necessary and sufficient condition for uniqueness. Furthermore, we characterize the m…
We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor gu…
Dynamic pricing schemes were introduced as an alternative to posted-price mechanisms. In contrast to static models, the dynamic setting allows to update the prices between buyer-arrivals based on the remaining sets of items and buyers, and so it is capable of maximizing social welfare without the need for a central coordinator. In this paper, we study the existence of optimal dynamic pricing schemes in combinatorial markets. In particular, we concentrate on multi-demand valuations, a natural extension of unit-demand valuations. The proposed approach is based on computing an optimal dual soluti…
In a crowdsourcing market, a requester is looking to form a team of workers to perform a complex task that requires a variety of skills. Candidate workers advertise their certified skills and bid prices for their participation. We design four incentive mechanisms for selecting workers to form a valid team (that can complete the task) and determining each individual worker's payment. We examine profitability, individual rationality, computational efficiency, and truthfulness for each of the four mechanisms. Our analysis shows that TruTeam, one of the four mechanisms, is superior to the others, …
In this paper, we study the problem of maximizing social welfare in combinatorial markets through pricing schemes. We consider the existence of prices that are capable to achieve optimal social welfare without a central tie-breaking coordinator. In the case of two buyers with rank valuations, we give polynomial-time algorithms that always find such prices when one of the matroids is a simple partition matroid or both matroids are strongly base orderable. This result partially answers a question raised by Düetting and Végh in 2017. We further formalize a weighted variant of the conjecture of Dü…
Locational marginal pricing (LMP) is a widely employed method for pricing electricity in the wholesale electricity market. Although it is well known that the LMP mechanism is vulnerable to market manipulation, there is little literature providing a systematic analysis of this phenomenon. In the first part of this paper, we investigate the economic dispatch outcomes of the LMP mechanism with strategic agents. We show via counterexamples, that contrary to popular belief, a Nash equilibrium may not exist. And when it exists, the price of anarchy may be arbitrarily large. We then provide two suffi…
Most sales applications are characterized by competition and limited demand information. For successful pricing strategies, frequent price adjustments as well as anticipation of market dynamics are crucial. Both effects are challenging as competitive markets are complex and computations of optimized pricing adjustments can be time-consuming. We analyze stochastic dynamic pricing models under oligopoly competition for the sale of perishable goods. To circumvent the curse of dimensionality, we propose a heuristic approach to efficiently compute price adjustments. To demonstrate our strategy's ap…
A personal data market is a platform including three participants: data owners (individuals), data buyers and market maker. Data owners who provide personal data are compensated according to their privacy loss. Data buyers can submit a query and pay for the result according to their desired accuracy. Market maker coordinates between data owner and buyer. This framework has been previously studied based on differential privacy. However, the previous study assumes data owners can accept any level of privacy loss and data buyers can conduct the transaction without regard to the financial budget. …
Shanghai Jiao Tong University（上海交通大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）
The society's insatiable appetites for personal data are driving the emergency of data markets, allowing data consumers to launch customized queries over the datasets collected by a data broker from data owners. In this paper, we study how the data broker can maximize her cumulative revenue by posting reasonable prices for sequential queries. We thus propose a contextual dynamic pricing mechanism with the reserve price constraint, which features the properties of ellipsoid for efficient online optimization, and can support linear and non-linear market value models with uncertainty. In particul…
Pricing decisions are often made when market information is still poor. In turn, existing theoretical models often reason about the response of optimal prices to changing market characteristics without exploiting all available information about the demand distribution. Our aim is to develop a theory for the optimization and systematic comparison of prices between different instances of the same market under various forms of knowledge about the corresponding demand distributions. We revisit the classic problem of monopoly pricing under demand uncertainty in a vertical market with an upstream su…
Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements
Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）；Department of Management Science and Engineering, Stanford University（斯坦福大学管理科学与工程学院）
