Contextual Dynamic Pricing with Strategic Buyers

Fair and profitable: How pricing and lead-time quotation policies can help

In “Real-Time Spatial–Intertemporal Pricing and Relocation in a Ride-Hailing Network: Near-Optimal Policies and The Value of Dynamic Pricing,” Chen, Lei, and Jasin consider a dynamic pricing problem faced by a ride-hailing service provider who manages a fixed number of servers and serves price-sensitive customers within a network. Servers serve arriving customers by relocating from the requested origins to destinations within a certain travel time. The authors first propose a static pricing policy based on the optimal solution to a deterministic relaxation of the original stochastic problem. They show that the proposed static policy matches the best possible asymptotic performance of any static policy. The authors further propose a dynamic pricing policy that adaptively changes the prices in a way that reduces the impact of past demand randomness on the balance of future distributions of servers and customers across the network. They show that the dynamic pricing policy achieves significantly better asymptotical performance. The proposed policies and their performance guarantees are further extended to a case where the firm jointly decides the relocation of vacant servers

Management Insights

Optimal pricing and inventory strategies for fashion products under time-dependent interest rate and demand

In a city center that is usually flooded with traffic, finding a parking space is a challenge for most commuters. Searching for parking generates additional urban traffic, increases energy consumption and vehicle emissions, and wastes time. This study examines how parking systems can be used as an effective tool for reducing traffic congestion. It proposes a new, smart approach to parking using real-time dynamic pricing and route guidance in a multi-agent system to better align supply and demand, thereby reducing both congestion and the amount of time spend by drivers searching for parking. To examine the effects of dynamic parking pricing on road traffic, we conducted a multi-agent open-source framework to simulate spatiotemporal distributions of daily individual activity. By extending MATSim, we were able to model parking usage more realistically. We developed several micro-simulation scenarios to evaluate strategy performance for both on-street and off-street parking in the city center of Tunis, Tunisia. The results show that dynamic pricing policies can be used to plan and manage parking areas more efficiently, minimizing the dispersion of parking occupancy lots. Variations in parking prices were shown to increase parking lot vacancies and reduce traffic congestion. Moreover, the system can also generate increased revenue for government and private-sector parking authorities while improving driver satisfaction. Finally, the parking dynamic pricing strategy promises a convenient mobility experience, while increasing efficiency and reducing the negative externalities of urban transportation.

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.

We consider pricing of network resources in a reservation-based quality-of-service architecture. The pricing policy implements a distributed resource allocation to provide guaranteed bounds on packet loss and end-to-end delay for real-time applications. Distributed pricing roles are assigned to each user, each network node, and an arbitrager in between the user and the network. When delay constraints are not binding, we investigate two dynamic pricing algorithms using gradient projection and Newton's method to update prices, and prove their convergence. We analyze the performance of the dynamic pricing policies and show that the gradient algorithm using Newton's method converges more quickly and displays only a few small fluctuations. When delay constraints are binding, we investigate subgradient methods which can provide convergence to some range of the optimal allocation.

Dynamic pricing policy allows the network operator to charge a cost per byte based on the network usage and the traffic load, which can potentially attract greater user consumption and increase operator's revenue. In this paper, we conduct an empirical study on user attitude towards dynamic pricing for wireless data services to examine whether average revenue per user (ARPU) can be effectively enhanced. Using structural equation modelling (SEM) based on 211 datasets collected in the California Bay Area, we reach the following conclusions: 1) consumers agree that current flat–rate wireless data pricing is too high and rigid and can be more flexible; 2) dynamic pricing can increase user satisfaction of the service; 3) dynamic pricing can increase the revenue for operators. Overall, we conclude that dynamic pricing can on one hand provide a better quality of service (QoS) to users and on the other hand achieve greater revenue for the wireless operator.

Problem definition: We consider the dynamic pricing problem of multiple products under (asymmetric) reference effects over an infinite horizon. Unlike existing literature, which is mostly focused on the single-product setting, our multiproduct setting takes into account the cross-product effects among substitutes and incorporates the memory-based reference prices into the multinomial logit (MNL) demand model. Even with the single-product logit demand, the structure of the optimal pricing policy is intractable. Therefore, we focus on the long-run patterns of the optimal pricing policy and also discuss the performance of the myopic pricing policy. Methodology/results: We first provide a comprehensive characterization of the myopic pricing policy, including its solution, long-run convergence behavior, and optimality gap. For the optimal pricing policy, we show an intricate connection between its long-run dynamics and types of reference effects. We demonstrate that the presence of any gain-seeking product renders a long-run constant pricing policy suboptimal. Conversely, the constant policy (or optimal steady state) can exist in both loss-neutral and loss-averse scenarios, where we provide a sufficient condition for such existence and give the analytical expression for the optimal steady state. We further show that when pricing perfect substitutes, the true optimal policy under the multiproduct framework is more likely to yield a long-run cyclic pattern than the policy derived from the single-product framework, a phenomenon that aligns well with the periodic discounts in real-world markets. Managerial implications: This discrepancy in the long-run behaviors between multi- and single-product-based policies highlights the importance of employing the multiproduct framework and addressing the cross-product effects, as sticking to the single-product framework while managing multiple substitutes can misrepresent long-run dynamics and result in suboptimality. In the multiproduct domain, our model suggests that retailers are more likely to benefit from appropriate price variations than maintaining a constant pricing policy. Funding: H. Jiang acknowledges support from the Natural Sciences and Engineering Research Council of Canada [NSERC Discovery Grant RGPIN 2024 05796]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.0801 .

Two‐sided platforms are often coupled with exclusive hardware products that connect two sides of users, the consumers of the hardware product (i.e., buyers) and the application developers (i.e., sellers). The hardware product in the platform business model introduces three important issues that are not yet well understood in the literature of platform pricing: potentially downward‐trending production cost, product quality improvements, and consumers’ strategic behaviors. Using analytical modeling, our study explicitly factors in these issues in analyzing a monopoly platform owner’s two‐sided pricing problem. The platform sequentially introduces and prices quality‐improving hardware products, for which the costliness of quality may decrease. Strategic buyers make purchasing and upgrading decisions, which dynamically determine the buyer‐side network size. Meanwhile, the seller‐side network size is determined endogenously. We find that, an increase in the likelihood or magnitude of the future costliness reduction raises the initial buyer‐side price of the low‐quality product and lowers the seller‐side fee. This strategy, in turn, creates an indirect intertemporal effect that allows the platform to also raise the buyer‐side price(s) of the product(s) sold later. These findings contrast with conventional wisdom and provide an economic explanation for premium introductory pricing of many platform products. Moreover, we find that strengthening the network effect can result in more pronounced increases in the buyer‐side prices.

In this paper, we deal with dynamic pricing strategies for connection-oriented services in wireless systems. Dynamic pricing policies allow the network operator to charge a cost per time unit depending on the network usage. In this way, the users behavior can be regulated and the network management is significantly improved. We model the user demand and the call duration as functions of the service price. By using standard Markovian techniques to represent the system evolution, we devise an optimal linear pricing scheme, which can be easily computed and controlled. When compared with a flat-rate policy, where a constant price for the network services is fixed, the proposed solution is able to provide a better quality of service to the users as well as a greater revenue to the network operator. For example, when eight radio channels are available and the traffic load is equal to 0.8, we obtain a 25% improvement in the network revenue with respect to the flat-rate policy, while the blocking probability is halved.

Through summarizing the previous research about railway passenger fares, this paper proposed a new idea of fare policy portfolio. Considering the various characteristics of fare policy, this paper combined the traditional fare policies to form a pricing policy portfolio, established some mathematic models and also proved the existence of equilibrium price. Combination of market segmentation, market competition and dynamic pricing policy is a suitable railway fare policy portfolio which applies to China railway passenger transport development situation.

Wait Time Based Pricing for Queues with Customer-Chosen Service Times

We consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon. Customers, whose reservation price distribution changes over time, arrive according to a nonhomogeneous Poisson process. We show that at any given time, the optimal price decreases with inventory. We also identify a sufficient condition under which the optimal price decreases over time for a given inventory level. This sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time. In addition to shedding managerial insight, these structural properties enable efficient computation of the optimal policy. Numerical studies are conducted to show the revenue impact of dynamic price policies. Price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price. For the former, our examples show that using optimal dynamic optimal policies achieves 2.4–7.3% revenue improvement over the optimal single price policy. For the latter, the revenue increase can be as high as 100%. These results explain why yield management has become so essential to fashion retailing and travel service industries.

We consider the problem of multi-product dynamic pricing, in a contextual setting, for a seller of differentiated products. In this environment, the customers arrive over time and products are described by high-dimensional feature vectors. Each customer chooses a product according to the widely used Multinomial Logit (MNL) choice model and her utility depends on the product features as well as the prices offered. The seller a-priori does not know the parameters of the choice model but can learn them through interactions with customers. The seller's goal is to design a pricing policy that maximizes her cumulative revenue. This model is motivated by online marketplaces such as Airbnb platform and online advertising. We measure the performance of a pricing policy in terms of regret, which is the expected revenue loss with respect to a clairvoyant policy that knows the parameters of the choice model in advance and always sets the revenue-maximizing prices. We propose a pricing policy, named M3P, that achieves a T-period regret of O(log(Td)(√(T)+d log(T))) under heterogeneous price sensitivity for products with features of dimension d. We also use tools from information theory to prove that no policy can achieve worst-case T-regret better than Ω(√(T)).