Static Pricing Research Articles

Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements

Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements

Dynamic pricing and inventory model for perishable products with reference price and reference quality

Reference price (quality) is a benchmark point used by consumers to make price (quality) judgements. Combining reference price and reference quality with dynamic pricing and inventory management, this paper applies differential equations theory to construct a optimal control model for perishable products when the quality of products declines exponentially. The demand of products depends on price, quality, reference price and reference quality, among which reference price and reference quality are influenced by consumers’ past memory. The aim is to maximize the retailer’s profit during the period. The conclusions are as follows. Firstly, a optimal dynamic pricing and inventory model for perishable products with reference price and reference quality is constructed, and the model is extended to dual decision variables, stochastic demand, time-dependent effects, competitive and infinite planing horizon setups. Secondly, through the Pontryagin maximum principle, the analytical expression of the optimal dynamic price is derived. Thirdly, a linear search method to solve the optimal static price is proposed. Finally, the sensitivity of the main parameters is analyzed and the corresponding management enlightenments are given. By comparison of dynamic and static pricing, we find that dynamic pricing can achieve more profits and take a shorter selling period. In addition, for the sales problem of perishable products affected by both reference price and reference quality, retailers should adopt skimming pricing strategy (the optimal price decreases with time). Furthermore, to obtain more profit, retails should strive to increase the sensitivity coefficients of two types of reference, and the reference quality memory coefficient, while to decrease the reference price memory coefficient.

The Art of Balancing Price and Plug: Developing a Theoretical Model for Dynamic Pricing in the Electric Vehicle Market

This study presents a novel approach to understanding the complex dynamics of the electric vehicle (EV) market through the lens of differential game theory. We developed a comprehensive model that captures the strategic interactions between EV manufacturers and charging network operators, while incorporating the effects of consumer behavior, market uncertainties, and reference price effects. Using differential game theory, we examined the impact of reference price effects and the charging network’s influence on pricing strategies, focusing on three distinct approaches: basic pricing, static pricing considering reference price effects, and dynamic pricing strategies. Our model offers new insights into consumer behavior and price expectations in the rapidly evolving EV market. The key findings reveal that under static or dynamic pricing strategies, the optimal pricing for EV manufacturers is positively correlated with the initial reference price. When the initial reference price is high (low), the optimal pricing strategy resembles skimming pricing (penetration pricing). As the effort level of charging network operators increases and their influence on consumers’ purchase decisions grows stronger, EV manufacturers tend to set higher prices. Notably, while dynamic pricing strategies can optimize EV manufacturers’ profits, the profits of charging network operators may decrease compared with static pricing strategies. This integrated approach significantly contributes to the field by bridging gaps among market dynamics, pricing strategies, and the infrastructure’s development in the context of electric mobility, providing a comprehensive framework for understanding and optimizing the EV ecosystem. Ultimately, this study advances sustainable business models that balance profitability, consumer behavior, and the infrastructure’s growth in the rapidly evolving EV market.

Utilizing Static Pricing to Boost Room Revenue in Archipelago International Indonesia Hotels Group

Purpose: This research examines the implementation of static rates to increase room revenue at Archipelago International Indonesia Hotels Group. While the majority of Archipelago International management considers that dynamic rates are more effective at increasing room revenue, the impact of global economic events such as the Covid-19 pandemic, wars, and earthquakes (force majeure) has been underestimated. Static rates can be used to respond to economic downturns induced by these occurrences, which reduce demand. Research methods: This research uses qualitative research methodologies to assess current practices and offer ideal static rate models. It is supported by three concepts and theories: static rates, room revenue, and hotel management. This research also uses tourism economy and revenue management as theoretical foundations. Results and discussion: The findings highlight suboptimal implementation challenges and propose two models at Archipelago International Indonesia Hotels Group: (1) Static Rates Stand Alone: managed by the channel manager for a minimum two-night stay, beneficial for remote or pre-opening hotels, during low occupancy or economic downturns; and (2) Bundle Packages: combining room rates with other services to increase revenue and promote additional facilities. Implication: These models provide consistent pricing, improved forecasting, and increased brand awareness. Implementing these models can help Archipelago International optimize its revenue plans and financial performance.

Uncertain random optimal control model for deteriorating inventory with the finite horizon

This paper examines a deteriorating inventory model with combined pricing and production during a limited selling time in an uncertain random setting. Demand is influenced by market size and price, which are portrayed in terms of random variables. The uncertainty factors affecting the inventory are represented by multiple Liu processes. Inventories deteriorate by a certain percentage and back-orders for inventories are permitted. This study aims to determine the optimal level of production rate and pricing that maximizes the producer’s total expected profit through the application of uncertain random optimal control theory, which is based on uncertain theory and probability theory. Numerical examples are used to compare joint pricing dynamic production model with dynamic production model under an optimal static price, highlighting the benefits of implementing joint pricing dynamic production model. Furthermore, it is evident that an increase in deterioration rate results in decreased on-hand inventory, yet higher production rate and price. It should also be noted that different levels of probability expectation of demand can have an impact on production inventory problem.

Updated‐generation product introduction decisions under trade‐in programs and different pricing strategies

AbstractManufacturers introduce updated‐generation products to meet intensified competition under trade‐in programs. Based on this phenomenon, we built a two‐period game‐theoretic model, in which the manufacturer sells the old‐generation product during both periods and considers whether to introduce the updated‐generation product in the second period. We find that under a static pricing strategy, if the costs of both products are low, the updated‐generation product's entry increases the old‐generation product's retail price. The manufacturer cannot benefit from introducing the updated‐generation product if the updated‐generation product's cost is high. Under a dynamic pricing strategy, the updated‐generation product entry benefits both the manufacturer and the consumer.

Can Generalized Cost-Effectiveness Analysis Leverage Meaningful Use of Novel Value Elements in Pharmacoeconomics to Inform Medicare Drug Price Negotiation?

ObjectivesDecision makers considering using cost-effectiveness analysis (CEA) to inform health-technology assessment must contend with documented and controversial shortfalls of CEA, including its assumption of disease severity independence and static pricing. ISPOR has recently introduced novel value elements besides direct healthcare cost and effectiveness for the patient, and these should be captured in CEA. Although novel value elements advance our understanding of “what” should be measured (value of hope, severity of disease, health equity, etc), there is limited direction on “how” to measure them in conventional CEA. Furthermore, with Medicare empowered to set drug prices under the Inflation Reduction Act, it is not clear what role CEA might have on where prices are set, given objections to the quality-adjusted life year in conventional approaches. MethodsWe critically reviewed the evidence for expanding conventional CEA methods to a more generalized approach of generalized CEA (GCEA). ResultsGCEA accounts for methods that address objections to the quality-adjusted life year and incorporate novel value elements. Although GCEA offers advantages, it also requires further research to develop “off-the-shelf” resources to help inform, for example, maximum fair price in the context of Medicare drug price negotiation. ConclusionsShould a shift toward GCEA reveal that the societal value of novel medicines exceeds their market-based costs, which will raise the key question of what market failure Medicare negotiation is meant to solve, if any, and therefore what the appropriate role of such negotiation might be to maximize the value society might garner from the development of novel medicines.

Trend-Chasing Versus Minimalism: Selling Fewer, Better Products to Fashion-Sensitive Customers

Fashion sellers are sometimes critiqued for selling low durability products, resulting in waste. Blame is also directed at consumers, who purchase new fashions despite having accumulated a closet full of prior fashions. The “slow fashion” movement encourages sellers to produce higher durable products, thus supporting less frequent purchases by consumers. Using an infinite-time model and considering strategic consumer behavior, including their ability to accumulate a “closet” of varieties over time, we analyze the seller’s profit-maximizing price and product-durability decisions. We initially assume a static price but later analyze the potential profit gains from dynamic pricing. When analyzing a heterogeneous consumer market, we initially allow customers to vary (distributed uniformly) in their sensitivity to fashion. Subsequently, we explore alternative distributions for consumers’ fashion sensitivity and the correlation between their fashion sensitivities and product valuations. Using this framework, we show how the seller’s optimal price and durability decisions yield distinct shopping segments, which we refer to as the minimalist versus trend-chasers. We find that if the degree of fashion uncertainty is moderate, the seller’s optimal choice of product durability will support the emergence of both behaviors. As the variety uncertainty expands, if the seller’s costs are sufficiently low, it will support a throwaway culture via disposable products. Otherwise, given high costs, the seller optimally targets a slow fashion-type outcome, with consumers targeting reuse (with durability) rather than variety. Our findings shed light on consumers’ optimal purchasing behaviors in relation to both market parameters and the firm’s pricing and durability decisions.

Dynamic pricing: Definition, implications for managers, and future research directions

Dynamic pricing has evolved with technology from earlier price negotiations. To maximize revenue and provide specialized shopping experiences, businesses today use algorithms and data analysis to adapt prices. We define dynamic pricing as price changes that are prompted by changes or differences in four key underlying market demand drivers: (1) People (i.e., individual consumers or consumer segments), (2) Product configurations, (3) Periods (i.e., time), and (4) Places (i.e., locations). The transition from static pricing (uniform prices) to dynamic pricing (changing prices) is evident from different examples, such as online retailers personalizing offers based on customer behavior, and algorithms using facial recognition for personalized pricing in physical stores.Fueled by AI and machine learning algorithms, dynamic pricing is transforming industries from transportation to e-commerce, optimizing revenue and enhancing customer experiences. While it offers benefits like personalization, challenges include ethical concerns, cost of implementation, and customer dissatisfaction. Effective data organization and AI expertise are crucial, but potential pitfalls and regulatory oversight must also be considered. This paper examines the multidimensional application of dynamic pricing, highlights the adaptability and efficiency of dynamic pricing in forming profitable pricing strategies and maximizing revenue, and calls for continued research on the topic to balance revenue, customer satisfaction, and ethics.

Static Pricing for Multi-unit Prophet Inequalities

Characterizing the Efficiency of Static Pricing Schemes as a Function of the Supply The problem of selling a supply of k units to a stream of customers constitutes one of the cornerstones in revenue management. Static pricing schemes (that output the same price to all customers) are commonly used because of their simplicity and their many desirable properties; they are anonymous, nonadaptive, and order oblivious. Although the efficiency of those schemes should improve as the supply k increases, prior work has only focused either on algorithms that aim for a constant approximation that is independent of k or on the setting where k becomes really large. In contrast, this paper characterizes the efficiency of static pricing schemes as a function of the supply. Our approach stems from identifying a “sweet spot” between selling enough items and obtaining enough utility from customers with high valuations. Subsequent work shows that our pricing scheme is the optimal static pricing for every value of k.

Self-Preferencing

When markets at successive or complementary stages are imperfectly competitive, firms that operate at multiple stages typically have a strong incentive to purchase from, sell to, or otherwise coordinate with its own operations at adjacent stations compared with those of individual firms. But, to the extent that such self-preferencing eliminates double marginalization that would occur under vertical separation or otherwise facilitates coordination that is difficult to accomplish between firms, competition rules that discourage self-preferencing, such as restrictions on vertical mergers or integration, can harm consumers. In 2020, the United States Department of Justice and Federal Trade Commission issue revised vertical merger guidelines that promised enforcement that more nearly resembles how they review horizontal mergers – that is, by predicting effects on static pricing incentives. But the economics of how vertical mergers on pricing incentives is more complicated than the economics of how horizontal mergers affect pricing incentives. If U.S. enforcement is based on a consumer welfare standard, the U.S. agencies will struggle to find a robust methodology for distinguishing anticompetitive from procompetitive vertical mergers. Self-preferencing has also played a key role in allegations of anticompetitive behavior in technologically advancing industries. A review of past allegations of anticompetitive product innovation against IBM, Microsoft, and Google reveals the challenges in designing rules that limit self-preferencing without acting as a drag on innovation.

Dynamic Pricing Provides Robust Equilibria in Stochastic Ridesharing Networks

Using prices induced by dual variables of a centralized optimization problem induces welfare-optimal equilibria among strategic drivers. We reveal a stark deficiency of such static pricing algorithms: it is possible for them to induce additional equilibria with arbitrarily low social welfare. Moreover, small perturbations to the marketplace, such as those caused by idiosyncratic randomness or model misspecification, can cause the welfare-optimal equilibrium to be Pareto-dominated (in terms of driver utility) by suboptimal equilibria. We show that dynamic pricing solves this problem. We describe a dynamic pricing algorithm that resolves the centralized optimization problem in each time period and show that it satisfies a new equilibrium robustness property, which guarantees that every induced (approximate) equilibrium is (approximately) welfare optimal. We also propose a novel two-level model of ridesharing networks with strategic drivers and spatiotemporal dynamics that lets us retain macroscopic uncertainty, such as correlated shocks caused by weather or other public events, when analyzing a large market limit in which idiosyncratic sources of uncertainty vanish. Funding: J. M. Cashore was supported by an NSERC PGS D Fellowship. P. Frazier was supported by AFOSR [Grant FA9550-19-1-0283]. É. Tardos was supported by AFOSR [Grant FA9550-19-1-0183] and [NSF Grants CCF-1408673 and CCF-1563714]. Supplemental Material: The online companion is available at https://doi.org/10.1287/moor.2022.0163 .

Reinforcement Learning for Dynamic Pricing of Shared-Use Autonomous Mobility Systems Considering Heterogeneous Users: Model Development and Scenario Testing

A key aspect of the success of shared-use autonomous mobility systems will be the ability to price rides in real time. As these services become more prevalent, it becomes of high importance to detect shifts in behavior to quickly optimize the system and ensure system efficiency and economic viability. Therefore, (1) pricing algorithms should be able to price rides according to complex underlying demand functions with heterogeneous customers and (2) the algorithm should be able detect nonstationary behavior (e.g., changing customers’ willingness to pay) from its previously learnt decisions and alter its pricing mechanism accordingly. We formulate a dynamic pricing and learning problem as a Markov decision process and subsequently solve it through a reinforcement learning (RL) algorithm, with heterogeneous customers accepting the trip characteristics (price, expected wait time) probabilistically. Insights from a fixed fleet operation of an autonomous private ridesourcing system in Chicago are presented. Given our formulation of the demand model, the algorithm learns in 25 days, increasing revenue by 90% and decreasing customer wait times by 90% compared to day 5. After gathering insights from the RL algorithm and applying optimal static pricing (i.e., a constant specific surge multiplier), we find that RL can achieve near 90% optimality in revenue. The RL algorithm, nevertheless, proves to be robust. Two scenarios are tested where a sudden shock occurs or customers slowly change their willingness to pay, illustrating that RL can quickly adapt its parameters to the situation.

Impacts of differentiated services and competition on the pricing strategies of ride‐hailing platforms

AbstractDifferentiated services and competition have made the operation of ride‐hailing platforms (i.e., Uber and Didi) more complex. Timely optimizing their pricing strategies will be conducive to the profitability of the platform enterprises. This paper considers the differentiation in service level of two ride‐hailing brands and the Bertrand price competition between platforms, and we propose dynamic, differentiated, and static pricing strategies based on the market demand fluctuation. The optimal prices in each case are derived, and the impacts of the Bertrand competition and differentiated services on the platform's optimal pricing strategies are analyzed. Our results show that competition between platforms will change the impact of the demand fluctuation on the optimal decisions of the platform. Additionally, we find that the optimal prices of two ride‐hailing brands all increase with the coefficient of service differentiation, but the optimal price of the brand with higher service level is increased faster. The numerical studies indicate that if one of the two platforms gives priority to offering differentiated services, the profit loss caused by competition can be attenuated to a great extent.

Defining Biometrics With Privacy and Benefits: A Research Agenda

This conceptual paper defines and gives examples of biometrics, explains how biometric tracking is currently used (e.g. to predict IQ), and presents innovative future uses of biometric tracking (e.g. to customize the price of products in real time). Specifically, this paper outlines a novel biometric pricing technology (BPT) which uses facial tracking to set the price of products using a new participatory dynamic pricing (vs. static pricing) system. Based on the privacy paradox, this paper addresses the acceptance, concerns and usage of a new emerging technology by consumers and its potential applications. To explore this, we develop a typology of perceived benefits and perceived privacy to predict consumer reactions to biometric technology. In addition, we present a research agenda to guide future research on biometric pricing technology. This research agenda offers new insights on how biometric tracking and specifically biometric price setting could be explored from multiple angles, including the consumer experience, technology acceptance, online profiling, governance, public policy, regulation, ethical and future usage-based perspectives.

Technical Note—Pricing in On-Demand and One-Way Vehicle-Sharing Networks

In this paper, we introduce a new method for evaluating the performance of static pricing in one-way vehicle-sharing systems. Our approach, based on a well-known recursive relationship, leads to a series of increasingly tight bounds on the performance of the static pricing policy. These bounds are valid for systems with multiple locations, nonzero travel times, and an arbitrary number of vehicles. They also apply to systems where the static pricing policy does not lead to a fully connected network. Our method results in a family of asymptotically optimal static pricing policies that improve upon previous results in the literature. The approach applies to the case of a single location and yields a bound that is at least as tight as the best known bound.

Real-Time Spatial–Intertemporal Pricing and Relocation in a Ride-Hailing Network: Near-Optimal Policies and the Value of Dynamic Pricing

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

Demand management in time-slotted last-mile delivery via dynamic routing with forecast orders

In this paper, we propose a partially time-windowed dynamic routing approach with forecast orders to tackle the dynamic pricing problem of attended home delivery, one of the challenging problems in last-mile logistics. The purpose of forecast orders is to find a cost-effective route map for delivery with forecast orders to guide the delivery system to accept real orders in potentially better time slots for servicing. Initially, we build and optimise virtual routes using forecast orders without time windows. Upon the arrival of real orders, we replace the forecast orders with incoming real orders to help the delivery system estimate the opportunity cost of making the delivery in each time slot. Dynamic pricing is then used to influence the customer’s choices of servicing slots, and based on what the customer selects, the real order replaces the forecast order, and the route map is re-optimised. This strategy leads to better scheduling for the overall route map and more slot availability for incoming customers. Through computational study, we demonstrate the benefit of our approach compared to static pricing and previous dynamic pricing policies, with or without forecast orders. In particular, by employing forecast orders without time windows, we witness a decrease in delivery costs and an increase in the number of accepted orders, leading to higher profits.

Incorporating Dynamic Pricing in Cost-Effectiveness Analysis: Are Known Unknowns Valuable?

Current practice in health technology assessment (HTA) of pharmaceuticals conducts cost-effectiveness analyses (CEAs) based on a static price or the estimated price at market launch. Recent publications suggest incorporating dynamic pricing. To test the feasibility and importance of including dynamic pricing, we compared the standard static approach to four dynamic scenarios by replicating US-based HTA evaluations with dynamic pricing inputs. The four case examples included omalizumab (Xolair®) for the treatment of allergic asthma, elagolix (Orilissa®) for the treatment of endometriosis, ocrelizumab (Ocrevus®) for the treatment of primary progressive multiple sclerosis (PPMS), and dupilumab (Dupixent®) for the treatment of atopic dermatitis (AD). The primary outcome was the relative percentage change in incremental cost-effectiveness ratios (ICERs) per quality-adjusted life-year (QALY) for two dynamic pricing scenarios versus static pricing. Secondary outcomes included the absolute difference in ICERs versus base-case and an assessment of decision uncertainty. Base-case ICERs were $327,000, $102,000, $700,000, and $102,000 for allergic asthma, endometriosis, PPMS, and AD, respectively. Across scenarios and case examples, the range of ICERs versus base-case varied from decreases of 56% to increases of 232%. The absolute difference in ICERs versus base-case ranged from decreases of $120,000 to increases of $758,000. Conclusions on cost effectiveness were altered in 2/16 scenarios across the four case examples. Given the decision context that US payers face, with prices varying over time, findings suggest further research to reduce uncertainty around price trajectories, as well as conducting or updating multiple assessments over the lifecycle of pharmaceutical products.

An exact algorithm for the static pricing problem under discrete mixed logit demand

Price differentiation is a common strategy in many markets. In this paper, we study a static multiproduct price optimization problem with demand given by a discrete mixed multinomial logit model. By considering a mixed logit model that includes customer specific variables and parameters in the utility specification, our pricing problem reflects well the discrete choice models used in practice. To solve this pricing problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a “good” feasible solution and approximate the problem from below. A convex optimization problem is designed using a convexification technique to approximate the optimization problem from above. Then, using a branching method, we tighten the optimality gap. The effectiveness of our algorithm is illustrated on several cases, and compared against solvers and existing state-of-the-art methods in the literature.