Dynamic pricing and learning: Historical origins, current research, and new directions

Boer, den Arnoud

doi:10.1016/j.sorms.2015.03.001

Cited by 307 publications

(87 citation statements)

References 292 publications

(154 reference statements)

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“…Dynamic pricing is a common practice where sellers adjust prices for products or services based on current demand. Developed initially by the airline industry with yield management, dynamic pricing is now a wide-spread phenomenon (Den Boer, 2015). Recent technological evolutions concerning real-time access to demand-related data (big data), real-time data processing, pricing algorithm automatization (allowing for real-time computation of optimal prices), and new technologies to implement frequent price changes (smart labels) contribute to dynamic pricing diffusion in the retailing industry.…”

Section: Introductionmentioning

confidence: 99%

Dynamic pricing for inventories with reference price effects

Chenavaz

Paraschiv

2018

Economics

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This article presents a dynamic pricing model of a retailer selling an inventory, accounting for consumer behavior. The authors propose an optimal control model, maximizing the intertemporal profit with consumers sensitive to the selling price and to a reference price. The optimal dynamic pricing policy is solved with Pontryagin's maximum principle with a structural (general) demand function. The authors obtain an original pricing rule, which explicitly accounts for the impact of price and inventory on future profits. The dynamics of price do not have to imitate the dynamics of the reference price. Instead, the dynamics of price are tied to opposing effects linked to this reference price. The authors also discuss managerial implications with regards to behavioral pricing policies. JEL C61 D03 D40 M21 M37

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Section: Introductionmentioning

confidence: 99%

Dynamic pricing for inventories with reference price effects

Chenavaz

Paraschiv

2018

Economics

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“…The literature on dynamic pricing with demand learning can be broadly divided into two categories: parametric and nonparametric models. (See den Boer [16] for a recent overview of the field.) In the parametric model, it is assumed that the firms know the functional form of the underlying demand function (e.g., linear, logit, etc.).…”

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confidence: 99%

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

2014

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We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the firm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a specific functional form. We propose a family of pricing heuristics that successfully balance the tradeoff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is affected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.3 revenue loss? It turns out that it is possible: If we use Stochastic Approximation algorithms (i.e., Kiefer-Wolfowitz and Robbins-Monro, see Broadie et al. [10]) during the exploitation phase instead of another bisection search, then the resulting revenue loss is exactly Θ( √ θ). Thus, we have provided an "optimal" nonparametric pricing heuristic for the setting of a single-product problem with inventory constraint. (In the case where the firms know the functional form of the demand function, i.e., parametric model, the Ω( √ θ) lower bound has been repeatedly shown to be tight. For example, in the setting without inventory constraints, Keskin and Zeevi [27], den Boer and Zwart [19], and Broder and Rusmevichientong [11], each proposes a parametric pricing heuristic that guarantees a revenue loss of the order of O( √ θ) . As for the setting with inventory constraints, recently Chen et al. [13] propose a heuristic that exactly matches this lower bound. Their result holds for a general parametric model with an arbitrary set of inventory constraints. Thus, they have resolved the parametric dynamic pricing problem with inventory constraints.)

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“…One of the areas where OLC in MAS has a tremendous potential is dynamic pricing . In fact, given the increasing amount of available data and the speed at which markets operate, feedback control is starting to play an increasingly important role in the setting of dynamic pricing.…”

Section: Conclusion Open Questions and Challengesmentioning

confidence: 99%

Hybrid online learning control in networked multiagent systems: A survey

Poveda

Benosman

Teel

2018

Adaptive Control & Signal

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This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous-time dynamical systems and discrete-time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning-based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous-time dynamical systems and discrete-time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems. KEYWORDSadaptive control, hybrid dynamical systems, learning, multiagent systems, networked systems 228One of the fields where control systems with learning and adaptation have recently seen increased attention is in the area of networked multiagent systems (MAS), 16,17 which are systems comprised of multiple interacting subsystems, each subsystem having individual dynamics and computational capabilities as well as limited sensing, communication, and actuation. Depending on the structure of the underlying communication graph between the agents of the system, MAS can be centralized or decentralized. In a centralized MAS, there exists one central agent which has access to the state information of all other agents and which is able to compute the control action for all agents of the system. On the other hand, in a decentralized or distributed MAS, agents individually compute their own control signals, which are shared with a subset of the other agents characterized by a communication graph. Figure 1 illustrates three MASs with different communication graphs. Centralized MASs are typically not scalable, and they present the disadvantage of having a single point of failure that could potentially shut down the complete system. 16 Decentralized and distributed systems, on the other hand, are scalable and more robust, and in nonstationary environments, they allow for adaptation and self-organization of the system. 18 Recent technological advances in communication and computation have made MAS ubiquitous, and today, they can be found in several engineering systems such as in power generation and distribution systems, 19-21 teams of ...

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Dynamic pricing and learning: Historical origins, current research, and new directions

Cited by 307 publications

References 292 publications

Dynamic pricing for inventories with reference price effects

Dynamic pricing for inventories with reference price effects

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

Hybrid online learning control in networked multiagent systems: A survey

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