Reference Price Effects Research Articles

Two-tier price membership mechanism design based on user profiles

• The e-commerce platform’s two-tier price membership mechanism design is studied. • We investigate the optimal two-tier price membership mechanism. • Discuss two-tier price membership considering consumer behaviors. • The two-tier price membership mechanism can achieve a triple-win situation. E-commerce platforms have pioneered many innovative business models based on their strong big data capabilities and consumer profile technology. This paper studies the design of the two-tier price membership mechanism in e-commerce platforms, i.e., the price discrimination in membership fees for different consumer groups. We analyze this mechanism considering and not considering certain consumer behaviors, respectively. We surprisingly find that the entry thresholds of the two-tier price mechanism in four different scenarios coincide at the critical point of whether consumers will buy the membership. The entry threshold provided by the platform distinguishes high-value consumers. When not considering the reference price effect, the two-tier price mechanism will degenerate into a uniform-price mechanism. The high membership fee only acts as a reference price for high-value consumers. Finally, we discuss social welfare and show that a triple-win scenario can occur among the platform, members, and merchants when the cross-buying effect is strong enough.

Optimal product line design with reference price effects

A reference price is the price expectation of consumers for a product. When considering whether to buy a product, consumers usually compare its price with the reference price, which leads to psychological gain-loss utility affecting the consumers’ willingness to pay for the product. In this paper, we incorporate a reference price into the product line design problem and investigate the strategic implications of reference price effects for both the firm and consumers. We first study the optimal quality-price bundle design problem of a monopolistic firm and investigate the impact of reference price effects on the optimal quality and price decision when the number of products in the line is given. We show that as the importance of price comparison increases, the optimal range of qualities in the product line narrows. Specifically, the lowest quality in the product line is distorted upward, while the quality gap between adjacent products narrows. In particular, when consumers attach great importance to price comparison, the reference price effects may cause the firm to abandon discrimination among consumers and instead offer just a single product. We also investigate the optimal product variety setting problem considering a fixed setup cost incurred for each product in the choice set. Our numerical studies using synthetic and real-world data demonstrate that the demand model with reference price has better goodness of fit and prediction accuracy. The impact of neglecting reference price in the product line design problem is significant, potentially leading to substantial profit loss. Finally, we extend our work through general discussions of the model and through the dynamic pricing problem incorporating temporal reference price effects.

Wholesale-price vs cost-sharing contracts in a green supply chain with reference price effect under different power structures

PurposeThis research aims to examine which cooperative contract (wholesale-price contract or cost-sharing contract) can more effectively upgrade the green degree of product and promote demand when considering consumer reference price effect under different power structures.Design/methodology/approachThis research investigates a dyadic green supply chain composed of one manufacturer and one retailer. Four Stackelberg game models with a cost-sharing contract or a wholesale-price contract are built in retailer-led and manufacturer-led scenarios, respectively. Using backward induction, the optimal green decision under each model is obtained. In addition, the optimal cooperative contract is proposed by comparing these four models.FindingsIt is found that under consumer reference price effect, a cost-sharing contract outperforms a wholesale-price contract in upgrading product greenness and promoting demand. Under any single contract, the retailer-led situation is more conducive to improving product greenness than the manufacturer-led situation. Moreover, consumer reference price effect would reduce the sharing ratio of a cost-sharing contract when the manufacturer dominates, but it could mitigate the problem of double marginalization by reducing wholesale and retail prices under both types of contracts, which would enhance consumer surplus.Originality/valueIt is a new attempt to incorporate consumer reference price effect and power structure into a green supply chain framework and proposes a novel demand function that simultaneously emphasizes consumer reference price effect, consumer environmental awareness and product green attribute. In addition, it provides managerial insights for business managers to choose green cooperative contracts with consumer reference price effect under different power structures.

Deep reinforcement learning approach for solving joint pricing and inventory problem with reference price effects

Reference prices, developed by consumers who frequently buy their desired products or services and form psychological price expectations as a benchmark, have significant impacts on customers’ purchase behaviors and firms’ operational strategies. Therefore, to determine an appropriate pricing and ordering strategy to maximize the total discounted revenues of a retailer, we consider joint pricing and inventory management system under reference price effects in an infinite horizon. Such a system involves uncertain market turbulence and customers’ sensitivities to gains and losses (loss-averse, gain-seeking and loss-neutral). We aggregate those factors into a general value function model with only a few realistic constraints on the variables and structure parameters. A deep reinforcement learning approach based on Double Deep Q-Networks with a target network (TN-DDQN) algorithm is proposed and forms the core of the expert decision system. Two ground truth algorithms (value iteration and real-demand-response policy) and two classical RL algorithms (Double Q-learning and Q-learning) are compared with the TN-DDQN algorithm in discrete and continuous state spaces respectively. Through a sequence of experiments, we find that the retailer should not ignore the impact of current prices on future demand, and a myopic policy will cause the retailer’s profits to decrease through reference price effects. Moreover, we also find that if customers have high abilities to remember previous prices, the retailer must bring sales prices down and raise the order-up-to level accordingly. Our system with the TN-DDQN algorithm provides a new way to handle complicated behavioral science and operation problems, which can be applied in a broader field.

Reference Price Effects in Vacation Rental Markets

Reference Price Effects in Vacation Rental Markets

Equilibrium decisions on pricing and innovation that impact reference price dynamics

<p style='text-indent:20px;'>Previous studies have confirmed that reference prices play an essential role in consumer purchasing decisions, and some researchers have suggested that reference prices are positively influenced by innovation. Therefore, we construct an interactive effect of innovation and reference price to study their combined impact on supply chain decisions. We model a supply chain, where a manufacturer determines the innovation level and the wholesale price while the retailer controls the retail price, as a dynamic Stackelberg game. We show that the interactive effect causes the steady-state wholesale and retail prices to increase, thus motivating the manufacturer to increase innovation investment. We see that the retail price and the level of innovation increase in reference price effect whereas they decrease in consumer memory. The centralized firm has a higher steady-state innovation level and innovation/price ratio and lower steady-state retail price compared to the decentralized supply chain. Consumers also benefit from the interactive effect as well as from centralization. Finally, we use numerical analysis to demonstrate our results and offer some managerial implications.</p>

Dynamic Pricing in the Presence of Social Externalities and Reference-Price Effect

Dynamic Pricing in the Presence of Social Externalities and Reference-Price Effect

Reference Price Effects in First-price Private-value Auctions

External reference points, such as outside options or budget constraints, are common in bidding environments. We experimentally investigate the impact of external reference points for bidding in first-price auctions with independent private values. We find that the presence of a reference point distorts bidding behaviour. There are “reference price effects” consistent with a preference for certainty and anchoring bias. To establish robustness, we conduct a second experiment that controls for bidders’ first-order beliefs. After controlling for beliefs, the reference price effect dominates. We observe that the imposition of a ceiling on the opponent’s maximum bid set at the upper bound of the risk-neutral Nash equilibrium support is strong enough to reverse the well-documented pattern of overbidding in first-price auctions and indeed to induce significant underbidding. The findings inform on the implications of auction formats that involve reference points, and specifically buy-it-now price options that are common in internet auction listings.

Estimating expectations-based reference-price effects in the used-car retail market

Estimating expectations-based reference-price effects in the used-car retail market

Two-period pricing strategy in a supply chain with intertemporal and horizontal reference price effects

In practice, before purchasing products, customers would compare the current price with past observed prices (referred to as the intertemporal reference price effect) and retail prices of other sellers (referred to as the horizontal reference price effect). This study considers a two-period supply chain with one manufacturer who sells a product through two competing retailers. We assume that the manufacturer acts as the Stackelberg game leader, and both retailers act as followers. The manufacturer can quote the same or different wholesale prices for the two retailers, whereas both retailers can employ a pre-announced or responsive pricing strategy. We study the impact of intertemporal and horizontal reference price effects on the selection of pricing formats. Our results show that both retailers and manufacturers can benefit from intertemporal effects. However, the horizontal effect hurts the retailer’s profit, but still improves that of the manufacturer. In equilibrium, the manufacturer sets different wholesale prices to retailers who would employ the pre-announced pricing strategy. Finally, we find that the intertemporal reference price effect plays a key role in the pricing strategy equilibrium of the manufacturer and retailers. Our results complement the dynamic pricing strategy literature and provide new managerial implications for supply chain management. Highlights Pricing format selection problems with IRPE and HRPE are investigated. IRPE hurts the payoff of both retailers but improves the manufacturer. In equilibrium, the manufacturer prefers the strategy “DP”. IRPE plays an important role in pricing format selecting than HRPE.

Dynamic pricing with reference price effects in integrated online and offline retailing

Omnichannel retailing is of growing importance. Yet, retailers lack knowledge about how to set prices overtime in their different channels, that is, in-store and online, which gives rise to a dual-channel pricing problem. The retailing issue is even more salient when consumers are prone to a psychological element, that is, when a reference price exerts influence. This article fills the gap by offering an analytical model of intertemporal price setting for dual channel pricing problem. We present an optimal control framework of dynamic pricing when (1) consumer behaviour is prone to a reference price and (2) the online channel is subject to the last-mile delivery cost. Analytical results, which hold for a general (nonlinear) reference-dependent demand formulation, inform about the relationships between the store and online prices over time and also about the market power of the retailer in each channel. Numerical results describe the features of three different phases of the planning horizon. The managerial recommendations show how a retailer sets differentiated dynamic pricing policies when offline and online channels are integrated. Such recommendations pave the way to more profitable omnichannel management.

Consumer's Green Preference, Reference Price Effect and Supply Chain Green Innovation

Consumer's Green Preference, Reference Price Effect and Supply Chain Green Innovation

Understanding the distributional impacts of health insurance reform: Evidence from a consumer cost-sharing program.

We examine the heterogeneous effects of reference pricing, a health insurance reform introduced by the California Public Employees' Retirement System (CalPERS), on the distribution of spending by patients and insurers. Using medical claims data for CalPERS and a comparison group not subject to reference pricing, we use the changes-in-changes approach to estimate the quantile treatment effects of the program across different medical procedures. We find that the quantile treatment effects vary across the patient spending distributions, with a range of positive and negative estimates of the QTE, depending on the medical procedure considered. However, across all procedures, the insurer's spending distributions tend to shift left, with the largest reductions occurring in the right-tail of the spending distributions. These effects are not captured by mean estimates but have important policy implications.

On Examining The Influence of Marquee Sellers in B2B Secondary Market Platforms for IT Products

While digital platforms have become mainstream, there still remain some unanswered questions pertaining to managing platform ecosystems. One such unexplored question pertains to the effect of marquee sellers on the platform – marquee sellers arguably attract other sellers and buyers to the platform, thereby enhancing the platform’s value. In this paper, we study how adding a marquee seller to a B2B secondary market platform for IT products affects other sellers, in terms of the prices they obtain for comparable products. Using proprietary data on B2B secondary market auctions obtained from a platform provider, we show that the entry of a marquee seller has a positive effect on the prices obtained by other sellers on the platform, reflecting a reference price effect. We further show that this positive effect on final prices is moderated by the extent to which bidders are active on multiple seller sites on the same platform, and the extent to which bidders participate in the marquee seller site. We explain these effects using theory in multi-homing and involvement, in terms of how reference prices are set. Our work extends the platforms literature by considering the specific influence of a marquee seller on other sellers, thereby informing platform owners on the implications of the advice to add more marquee sellers to platforms. We also contribute to the literature on secondary markets for durable, used IT products, which are instrumental in reducing e-waste and mitigating the environmental damage done by electronic products in landfills.

Differential game model of cooperative advertising in a supply chain with deteriorating items, competing retailers and reference price effects

ABSTRACT The phenomenon of cooperative advertising in the market has always been widespread. Considering a supply chain consisting of one manufacturer and multiple retailers with competitive relationships, we explore advertising strategies for deteriorating items when market demand is affected by reference price. By establishing a differential game model, the equilibrium advertising strategies and supply chain profits under different situations are analysed from a long-term and dynamic perspective under decentralised and centralised control, and the trajectories of goodwill and reference prices over time are presented. The conclusions derived provide implications for managers to design optimal advertising strategies.

Strategic Analysis of the Pricing Mechanisms in an Online Book Supply Chain in the Presence of Reference Price Effects

(1) Background: A binding recommended retail price has been used in several markets in a variety of forms, and the book market is a typical example. Publishers sell books to online retailers at a unit wholesale discount computed on the cover price. Retailers are then allowed to set the retail price. Therefore, if consumers regard the cover prices as reference points, then they may be more likely to purchase books if retail prices are lower than the cover prices. (2) Methods: We develop a Stackelberg game model for a book supply chain to investigates how reference price effects affect retailers and publisher’s pricing strategies. (3) Results: The results show that retailers will sell printed books at a discount only when the publisher’s wholesale discount rate is not high. Further, as the intensity of the reference price effects increases, (a) the lower boundary of the wholesale discount rate rises, (b) publishers’ profits increase and (c) retailers’ profits increase relative to the level of consumers’ e-books acceptance. (4) Conclusions: This result is related to the fact that the online retailer, such as Amazon and JD.com, like to invoke reference price effects in consumers’ minds by highlighting the printed book’s discount rate.

A Building-Material Supply Chain Sustainable Operations under Fairness Concerns and Reference Price Benefits

This paper incorporates fairness concerns and consumer reference price effects into a two-echelon building-material closed-loop supply chain consisting of a manufacturer and a retailer. By establishing four differential game models, we investigate the sustainable operations and cooperation of this supply chain. The four game models are a Nash noncooperative game, Stackelberg game with cost sharing, Stackelberg game with fairness concerns and cost sharing, and centralized decision model. By using dynamic models and optimal control theory, we obtain the two members’ optimal equilibrium strategies in the supply chain. Analytical results show that the consumer reference price effect has a positive impact on the manufacturer’s effort level, retailer’s publicity level, and product brand goodwill, which can improve the supply chain performance. The retailer’s partial commitment to cost sharing can enhance the production enthusiasm of the manufacturer, improve the brand reputation of the product, and enhance the two members’ individual profitability. The distributional fairness concerns of the manufacturer not only prevent the manufacturer and retailer from achieving Pareto improvement but also lead to the decline of the manufacturer’s effort level and profitability. The research conclusions of this paper can provide some insights into the cooperation and sustainable development of the supply chain.

Dynamic game strategies for construction and demolition waste recycling with learning and reference effects

Construction and demolition waste (C&DW) recycling can effectively reduce the environmental impacts caused by the massive amounts of untreated C&DW, and can promote the sustainable development of the construction industry. This study aims to provide relevant insights for the implementation of C&DW recycling, and can be practically used to guide participants' dynamic strategies in the presence of both the reference price effect and cost learning effect. Based on game theory, a static model is developed as a benchmark, including a construction materials manufacturer and a C&DW recycler under a government subsidy. Then, a dual-period dynamic model combining the learning and reference effects is established to broaden the understanding of C&DW recycling management. On this basis, the decisions and revenues of players are compared and analysed, and managerial insights are obtained through numerical analysis. It is found that both the learning and reference effects affect the manufacturer's decisions and revenues, and that the reference effect has a much greater impact on profit than the learning effect. In addition, only the learning effect has a positive influence on the recycler's recycling efforts and profits, thereby promoting C&DW recycling and reducing environmental impacts. Moreover, government subsidies always benefit the environment and recycler, and as the learning ability becomes stronger, the subsidy becomes more efficient in reducing the environmental impacts and improving the recycler's profit. Comparatively, the impact of subsidy on the manufacturer's profits depends on the learning ability. When the learning ability is relatively high, a higher subsidy is detrimental to the manufacturer in the short term but benefits it in the long term.

Optimal pricing in social networks considering reference price effect

We study the optimal monopoly pricing strategies in a social network, in which consumers experience a network effect that is dependent on their neighbors' consumptions and a reference price which is the average price received by their neighbors. We establish a two-stage game model for any social network. Utilizing the backward induction, we derive the equilibrium price by maximizing the monopolist's profit. In addition, we apply this model to the two most commonly used network structures: the star network and the bipartite network. We find that both the network effect and the reference price effect play a critical role in deciding pricing strategies in social networks. Moreover, our numerical results demonstrate that whether to implement discriminatory pricing depends critically on the network structure. This work provides monopoly firms a useful guideline for optimal pricing decisions in social network marketing.

Multiperiod Dynamic Pricing and Inventory Control Decisions for an Omnichannel BOPS Retailer with Reference Price Effects

This paper utilizes the consumers’ reference price in prospect theory to analyze an omnichannel retailer’s multiperiod pricing and inventory management problem in which consumers can cancel their orders before payment and return the products after payment if the products do not meet their expectation. The omnichannel retailer’s optimal equilibrium pricing and ending inventory level are derived under reference price effects by maximizing the discounted total profit over the infinite planning horizon, where the optimal decisions we discussed under two scenarios: loss neutrality and loss aversion. The analysis shows that the convergence of the pricing and ending inventory level toward their equilibrium is from above or below, depending on the relative location of the initial reference price with respect to the unique equilibrium price. Moreover, a set of sensitivity analyses is discussed to characterize the impacts of system parameters on the optimal decisions. This research fills the gap of behavioral operation in the field of omnichannel joint pricing and inventory management.