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To disclose or to conceal? Comparison of different disclosure policies in queues with loss-averse customers
Abstract
In many service industries, information disclosure about the product can alleviate customers' loss aversion induced by uncertain product valuation. In this paper, we consider a single-server queueing system in which the manager who privately learns the valuation information discloses the valuation information strategically to loss-averse customers. We investigate the impact of the customers' loss aversion on the system's equilibrium arrival rate and the manager's optimal disclosure policy. We find that loss aversion restrains customers from joining the queue. Surprisingly, we find that there is no one disclosure policy that always prevails over other disclosure policies. Specifically, the full disclosure policy is optimal only when the valuation is large and the degree of loss aversion is moderate. The full non-disclosure policy is optimal when the degree of loss aversion is too large or too small, or the valuation is small. The threshold disclosure policy is optimal when the valuation and the degree of loss aversion are moderate. Furthermore, under the threshold disclosure policy, the increasing degree of loss aversion makes managers be more reluctant to disclose the valuation.
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In this paper, we incorporate loss preference into an M/M/1 queueing with a threshold disclosure policy and analyze its impact on the customers' queueing strategies and the queueing system's idle stationary probability. In the queueing system, customers are strategic and divided into two groups: the informed and the uninformed. Informed customers are assumed to be fully rational, whereas uninformed customers are assumed to have loss preference. Uninformed customers with loss preference are categorized into two types according to their asymmetry perceptions, which anchor on the difference between gain and loss: loss neutrality and loss aversion. We firstly determine customers' equilibrium decisions, and then derive the idle stationary probability at equilibrium. We find that loss preference reduces the customers' joining probability, and results in a higher idle stationary probability. Furthermore, we find that for the uninformed customers with stronger loss aversion, the system manager should lower the threshold of disclosure to maintain a stable demand of uninformed customers. In addition, in the case of mixed-strategy at equilibrium, with the increase of the threshold of disclosure, the idle stationary probability increases for an underloaded queue. However, for an overloaded queue, the idle stationary probability decreases with increasing the threshold of disclosure.
We investigate a server's best queue disclosure strategy in a single-server service system with an uncertain quality level (which is assumed to be binary). We consider this problem from the perspective of a Bayesian persuasion game. The server first commits to a possibly mixed strategy stating the probability that the queue length will be revealed to customers upon their arrival given a realized quality level. The service quality level is then realized, and the server's corresponding queue-disclosure action is observed by customers, who then update their beliefs regarding service quality and decide whether or not to join the service system. We reformulate the server's decision problem as looking for the best Bayes-plausible distribution of posterior beliefs regarding service quality. We demonstrate that the maximal expected effective arrival rate, as a function of the prior belief, can be graphed as the upper envelope of all convex combinations of any two arbitrary points on the two effective arrival rate functions of the revealed and concealed queues. We show that when the market size is sufficiently small (large), the server always conceals (reveals) the queue, regardless of the realized service quality. Numerically, we find that in a medium-sized market, the server's optimal commitment strategy is often hybrid or mixed, that is, randomizing queue concealment and revelation. We also extend our analysis to a situation in which the server aims to maximize social welfare. We show that under certain conditions, it is always beneficial for the welfare-maximizing social planner to randomize queue concealment and revelation, regardless of the market size.
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We study the problem of strategic choice of arrival time to a single-server queue with opening and closing times when there is uncertainty regarding service speed. A Poisson population of customers choose their arrival time with the goal of minimizing their expected waiting times and are served on a first-come first-served basis. There are two types of customers that differ in their beliefs regarding the service-time distribution. The inconsistent beliefs may arise from randomness in the server state along with noisy signals that customers observe. Customers are aware of the two types of populations with differing beliefs. We characterize the Nash equilibrium dynamics for exponentially distributed service times and show how they substantially differ from the model with homogeneous customers. We further provide an explicit solution for a fluid approximation of the game. For general service-time distributions we provide an algorithm for computing the equilibrium in a discrete-time setting. We find that in equilibrium customers with different beliefs arrive during different (and often disjoint) time intervals. Numerical analysis further shows that the mean waiting time increases with the coefficient of variation of the service time. Furthermore, we present a learning agent-based model (ABM) in which customers make joining decisions based solely on their signals and past experience. We numerically compare the long-term average outcome of the ABM with that of the equilibrium and find that the arrival distributions are quite close if we assume (for the equilibrium solution) that customers are fully rational and have knowledge of the system parameters, while they may greatly differ if customers have limited information or computing abilities.
Understanding the impact of the queue length information on the behavior of customers is nowadays a hot topic for strategic queueing problems. Particularly, it is important to understand how this information impacts the equilibrium behavior and therefore global performance metrics in order to give some recommendations to service providers for optimizing their objective. Recent works are focused on information policies in order to optimize the provider’s profit. In this work, the aim is to maximize the expected social welfare. It is intuitive that the expected social welfare is higher when more information is available to new customers. In some circumstances, and particularly when the queue is overloaded, providing the information up to a particular level of occupancy yields a better expected social welfare compared to always providing queue length information to new customers. This counterintuitive result comes mainly from the strategic behavior of customers at equilibrium when queue length information is not available. After proving that there exists such an optimal information disclosure policy (IDP) for arbitrary arrival and service rates, we go further and study the expected social welfare for the overloaded context in which the arrival rate equals the service rate. Finally, numerical illustrations corroborate our contributions, and moreover, they show that an admission control policy can be also proposed, combined with an IDP, in order to optimize the expected social welfare of the system.
This paper studies an emerging business model of line-sitting in which customers seeking service can hire others (line-sitters) to wait in line on behalf of them. We develop a queueing-game-theoretic model that captures the interaction among customers, the line-sitting firm, and the service provider to examine the impact of line-sitting on the service provider’s revenue and customer welfare. We also contrast line-sitting with the well-known priority purchasing scheme, as both allow customers to pay extra to skip the wait. Our main results are as follows. First, we find that both accommodating line-sitting and selling priority can bring in extra revenue for the service provider, although by different means—selling priority increases revenue mainly by allowing the service provider to practice price discrimination that extracts more customer surplus, whereas line-sitting does so through demand expansion, attracting customers who would not otherwise join. Second, the priority purchasing scheme tends to make the customer population worse off, whereas line-sitting can be a win–win proposition for both the service provider and the customers. Nevertheless, having the additional option of hiring line-sitters does not always benefit customers as a whole because the demand expansion effect also induces negative congestion externalities. Finally, despite the fact that the service provider collects the priority payment as revenue but not the line-sitting payment, which accrues to the third-party line-sitting firm, we demonstrate that, somewhat surprisingly, accommodating line-sitting can raise more revenue for the service provider than directly selling priority.
This paper was accepted by Charles Corbett, operations management.
Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. Moreover, the use of unbounded utility to model risk attitudes fails to explain some decision-making paradoxes. In contrast, this paper deals with the utility maximization of the newsvendor using a class of bounded utility functions to study the effect of loss aversion on the newsvendor certainty equivalents and risk premiums. New formulas are introduced to find the utility-optimal order quantity of the normal distribution. The results show that when an exponential loss aversion exists, the classical newsvendor optimal quantity serves as a lower bound when the overage costs are high and as an upper bound when the underage costs are high. In addition, we show that high loss aversion entails higher risk premiums. Similar conclusion holds when the overage/underage costs increase. Higher standard deviations, on the other hand, mean lower utility-optimal quantities and higher risk premiums. The presented formulas are advantageous in finding the optimal order quantities and risk premiums of a stochastic short-shelf life inventory when the loss is a key factor in the decision-making process.
How would the growing prevalence of real-time delay information affect a service system? We consider a single-server queueing system where customers arrive according to a Poisson process and the service time follows an exponential distribution. There are two streams of customers, one informed about real-time delay and the other uninformed. The customers’ uninformed behavior may be due to information ignorance or rational behavior in the presence of an information fee. We characterize the equilibrium behavior of customers with information heterogeneity and investigate how the presence of a larger fraction of informed customers affects the system performance measures, i.e., throughput and social welfare. We show that the effects of growing information prevalence on system performance measures are determined by the equilibrium joining behavior of uninformed customers. Perhaps surprisingly, we find that throughput and social welfare can be unimodal in the fraction of informed customers. In other words, some amount of information heterogeneity in the population can lead to more efficient outcomes, in terms of the system throughput or social welfare, than information homogeneity. For example, under a very mild condition, throughput in a system with an offered load of 1 will always suffer if there are more than 58% of informed customers in the population. Moreover, it is shown that for an overloaded system with offered load sufficiently higher than 1, social welfare always reaches its maximum when some fraction of customers is uninformed of the congestion level in real time.
The online appendix is available at https://doi.org/10.1287/mnsc.2017.2747 .
This paper was accepted by Gad Allon, operations management.
The uniform pricing puzzle for vertically differentiated media and entertainment products (movies, books,
music, mobile apps, etc.) is that a firm with market power sells high- and low-quality products at the same
price even though quality is perfectly observable and price adjustments are not costly. We resolve this puzzle
by assuming that consumers have an uncertain taste for quality and accounting for consumer loss aversion in
monetary and consumption utilities. The novelty of our approach is that the so-called reference transaction
is endogenously set as part of a "personal equilibrium" and is based only on past purchases of same-quality
products.
What are the impacts of information prevalence on a service system? We study a single-server queueing system where customers arrive according to a Poisson process and service takes an exponential time. There are two streams of customers, one informed about real-time delay and one uninformed. We characterize the equilibrium behavior of customers who may balk in such a system and investigate how a marginal increase in information possession (i.e., a larger fraction of informed customers) would affect the system in terms of performance measures such as throughput, service accessibility, individual welfare, and social welfare. We show that the impacts of information prevalence on system performance measures are determined by the equilibrium joining behavior of uninformed customers. Perhaps surprisingly, we find that throughput and social welfare can be unimodal in the fraction of informed customers. In other words, some amount of information ignorance in the population can lead to strictly more efficient outcomes, in terms of the system throughput or social welfare, than information homogeneity. For example, for a critically loaded system (i.e., the implied utilization is 1) in which informed customers have a joining threshold no less than 2, throughput would always suffer if there are more than 58% of informed customers in the population. When a general system has an implied utilization sufficiently higher than 1, there is always a critical level in (0,1) on the fraction of informed customers beyond which social welfare suffers.
In the operations research literature, the queue joining probability is monotonic decreasing in the queue length; the longer the queue, the fewer consumers join. Recent academic and empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. We provide a simple explanation for these nonmonotonic queue-joining strategies by relaxing the informational assumptions in Naor’s model. Instead of imposing that the expected service time and service value are common knowledge, we assume that they are unknown to consumers, but positively correlated. Under such informational assumptions, the posterior expected waiting cost and service value increase in the observed queue length. As a consequence, we show that queue-joining equilibria may emerge for which the joining probability increases locally in the queue length. We refer to these as “sputtering equilibria”. We discuss when and why such sputtering equilibria exist for discrete as well as continuously distributed priors on the expected service time (with positively correlated service value).
Kluwer Academic Publishers Boston/Dordrecht/London To the memory of my parents, Sara and
We study the properties of a profit-maximizing monopolist's optimal price distribution when selling to a loss-averse consumer, where (following Kőszegi and Rabin (2006)) we assume that the consumer's reference point is her recent rational expectations about the purchase. If it is close to costless for the consumer to observe the realized price of the product, then – in a pattern consistent with several recently documented facts regarding supermarket pricing – the monopolist chooses low and variable “sale” prices with some probability and a high and sticky “regular” price with the complementary probability. Realizing that she will buy at the sale prices and hence that she will purchase with positive probability, the consumer chooses to avoid the painful uncertainty in whether she will get the product by buying also at the regular price. If it is more costly for the consumer to observe the realized price, then – in a pattern consistent with the pricing behavior of some other retailers (e.g. movie theaters) – the monopolist chooses a sticky price and holds no sales. In this case, a sale is less tempting and hence less effective in generating an expectation to purchase with positive probability. We also show that ex-ante competition for loyal consumers leads to sticky pricing while ex-post competition leads to marginal-cost pricing, and discuss several other extensions of the model.
This paper proposes a model of cab drivers' labor supply, building on Henry S. Farber's (2005, 2008) empirical analyses and Botond Koszegi and Matthew Rabin's (2006; henceforth "KR") theory of reference-dependent preferences. Following KR, our model has targets for hours as well as income, determined by proxied rational expectations. Our model, estimated with Farber's data, reconciles his finding that stopping probabilities are significantly related to hours but not income with Colin Camerer et al.'s (1997) negative "wage" elasticity of hours; and avoids Farber's criticism that estimates of drivers' income targets are too unstable to yield a useful model of labor supply. (JEL J22, J31, L92)
This study investigates reference-dependent choice with a stochastic, state-dependent reference point. The optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) if the reference point is selected fully endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. We develop a choice model in which adjustment costs can cause stickiness relative to an initial, exogenous reference point. Using historical U.S. investment benchmark data, we show that this model is consistent with diversification across bonds and stocks for a wide range of evaluation horizons, despite the historically high-risk premium of stocks compared to bonds. This paper was accepted by Peter Wakker, decision analysis.
Information about delays can enhance service quality in many industries. Delay information can take many forms, with difierent degrees of precision. Difierent levels of information have difierent efiects on customers and so on the overall system. To explore these efiects, we consider a queue with balking under three levels of delay information: no information, partial information (the system occupancy) and full information (the exact waiting time). We assume Poisson arrivals, independent, exponential service times, and a single server. Customers decide whether to stay or balk based on their expected waiting costs, conditional on the information provided. We show how to compute the key performance measures in the three systems, obtaining closed-form solutions for special cases. We then compare the three systems. We identify some important cases where more accurate delay information improves performance. In other cases, however, information can actually hurt the provider or the customers.
This study investigates reference-dependent choice with a stochastic, state-dependent reference point. The optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) if the reference point is selected fully endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. We develop a choice model in which adjustment costs can cause stickiness relative to an initial, exogenous reference point. Using historical U.S. investment benchmark data, we show that this model is consistent with diversification across bonds and stocks for a wide range of evaluation horizons, despite the historically high-risk premium of stocks compared to bonds.
This paper was accepted by Peter Wakker, decision analysis.
This paper reconsiders whether cabdrivers' labor supply decisions reflect reference-dependent preferences. Following Botond Koszegi and Matthew Rabin (2006), we construct a model with targets for hours as well as income, both determined by rational expectations. Estimating using Henry S. Farber's (2005, 2008) data, we show that the reference-dependent model can reconcile his 2005 finding that drivers' stopping probabilities are significantly related to hours but not income with the negative wage elasticity of hours found by Colin Camerer et al. (1997) and Farber (2005, 2008). The model yields sensible estimates that avoid Farber's (2008) criticism that drivers' income targets are too unstable to allow a useful reference-dependent model of labor supply.
We modify the Salop (1979) model of price competition with differentiated products by assuming that consumers are loss averse relative to a reference point given by their recent expectations about the purchase. Consumers' sensitivity to losses in money increases the price responsiveness of demand—and hence the intensity of competition—at higher relative to lower market prices, reducing or eliminating price variation both within and between products. When firms face common stochastic costs, in any symmetric equilibrium the markup is strictly decreasing in cost. Even when firms face different cost distributions, we identify conditions under which a focal-price equilibrium (where firms always charge the same "focal" price) exists, and conditions under which any equilibrium is focal. (JEL D11 , D43, D81, L13)
This work is motivated by the practice of add-on services, where an add-on is not valuable unless purchased with a main service. Discrepancies in pricing have been observed in various settings such as restaurants, museums, and attractions regarding whether the add-on should be sold together with the main service, or separately from the main service at an additional charge. While there has been a vast literature on add-on pricing, its application in service-oriented businesses with congestion-prone externalities and delay-sensitive customers is less understood. We develop a queueing model and examine the optimal pricing of add-on services in such systems, and in line with practice, we focus on analyzing two pricing schemes: bundling that charges a single price to sell main and add-on services altogether, and separate selling that charges distinct prices for each service. We establish that in the absence of congestion, separate selling strictly dominates bundling across the board. When there is congestion at the main service but not the add-on, bundling can be more lucrative under a large customer demand. When congestion takes place at both services, separate selling can return to being dominant under a large customer demand. We explain these plots of reversals by illustrating an intricate interplay between pricing, market coverage, and congestion. Collectively, they reveal novel operational advantages of each pricing scheme in exploiting the fundamentals of add-on structures.
In this paper, we study a service provider with opaque price strategy who sells services to loss-averse customers in a congestion-prone facility. The opaque price strategy means that the service provider discloses a price range of services to potential customers through social media. Loss aversion aims to characterize customers' reference-dependent preferences. We analyze a queueing game model with the help of an M/M/1 queueing system and adopt the cutoff structure characterized by reservation price to represent the loss-averse customers' joining decision. Then, we derive the loss-averse customer's reservation price and queueing strategies at equilibrium. In addition, the service provider sets the price to maximize her profit. We obtain some insights into how customers' degree of loss aversion affects the service provider's optimal price. For example, customers with a higher degree of loss aversion on the waiting time and the payment would push the service provider to decrease the optimal price. Customers with a higher degree of loss aversion about the service reward would urge the service provider to increase the optimal price. Furthermore, considering the attachment effect, we obtain the lowest possible expected profit of the service provider.
Problem definition: Customer joining behavior is of major concern for service systems where the service capacity is uncertain. Academic/practical relevance: It remains unclear whether customer inference of uncertain service capacity can lead to follow the crowd (FTC) behavior. Management can release capacity information, but how it affects system performance needs to be understood. Methodology: We use a single-server queue to analyze the joining behavior of customers who infer the actual service capacity based on the queue length upon arrival. We also characterize the impact of capacity information disclosure both analytically and numerically. Results: We find that when other customers’ tendency to join the service increases, a tagged customer can make more accurate inferences of service capacity based on queue length. This inference effect arises together with the congestion effect and can lead to FTC when it outweighs the latter. When multiple equilibria exist, we characterize the conditions under which the inference effect is significant at the aggregate customer level so that the joining equilibrium with a larger joining threshold is Pareto-optimal. Managerial implications: Management needs to be careful in setting the information disclosure policy, as the key problem parameters may affect its impact on system throughput and social welfare in opposite directions.
Funding: L. Yang was supported by the National Natural Science Foundation of China [Grants 71991461 and 71532006]. W. Shang was supported by the Hong Kong Research Grants Council [GRF Project LU 13502219].
Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1139 .
We study the effectiveness of information design in reducing congestion in social services catering to users with varied levels of need. In the absence of price discrimination and centralized admission, the provider relies on sharing information about wait times to improve welfare. We consider a stylized model with heterogeneous users who differ in their private outside options: low-need users have an acceptable outside option to the social service, whereas high-need users have no viable outside option. Upon arrival, a user decides to wait for the service by joining an unobservable first-come-first-serve queue, or leave and seek her outside option. To reduce congestion and improve social outcomes, the service provider seeks to persuade more low-need users to avail their outside option, and thus better serve high-need users. We characterize the Pareto-efficient signaling mechanisms and compare their welfare outcomes against several benchmarks. We show that if either type is the overwhelming majority of the population, then information design does not provide improvement over sharing full information or no information. On the other hand, when the population is sufficiently heterogeneous, information design not only Pareto-dominates full-information and no-information mechanisms, in some regimes it also achieves the same welfare as the “first-best,” that is, the Pareto-efficient centralized admission policy with knowledge of users’ types.
This paper was accepted by Gabriel Weintraub, revenue management and market analytics.
Endogenization of the Reference Point Reduces Loss Aversion
A central idea in behavioral economics is that agents derive utility from gain and losses relative to a certain reference point and that losses loom larger than gains. In “How Endogenization of the Reference Point Affects Loss Aversion: A Study of Portfolio Selection,” He and Strub study the implications of various models of partially endogenous reference points on portfolio selection. In these models, an agent faces a salient exogenous reference point that influences the formation of endogenously determined expectations about the future, through rational expectations, optimal expectations, or mental updating of the reference point. A key finding is that the predictions of these models are identical to a model with an exogenous reference point but a lower degree of loss aversion. This suggests that it is difficult to separately identify an agent’s degree of loss aversion and his or her reference point and may help to explain why experienced and sophisticated agents appear to be less loss averse than expected in some field settings.
Problem definition: We study customer-centric privacy management in service systems. Academic/practical relevance: We explore the consequences of extended control over personal information by customers in such systems. Methodology: We adopt a stylized queueing model to capture a service environment that features a service provider and customers who are strategic in deciding whether to disclose personal information to the service provider—that is, customers’ privacy or information disclosure strategy. A customer’s service request can be one of two types, which affects service time but is unknown when customers commit to a privacy strategy. The service provider can discriminate among customers based on their disclosed information by offering different priorities. Results: Our analysis reveals that, when given control over their personal data, strategic customers do not always choose to withhold them. We find that control over information gives customers a tool they can use to hedge against the service provider’s will, which might not be aligned with the interests of customers. More importantly, we find that under certain conditions, giving customers full control over information (e.g., by introducing a privacy regulation) may not only distort already efficiently operating service system but might also backfire by leading to inferior system performance (i.e., longer average wait time), and it can hurt customers themselves. We demonstrate how a regulator can correct information disclosure inefficiencies through monetary incentives to customers and show that providing such incentives makes economic sense in some scenarios. Finally, the service provider itself can benefit from customers being in control of their personal information by enticing more customers joining the service. Managerial implications: Our findings yield insights into how customers’ individually rational actions concerning information disclosure (e.g., granted by a privacy regulation) can lead to market inefficiencies in the form of longer wait times for services. We provide actionable prescriptions, for both service providers and regulators, that can guide their choices of a privacy and information management approach based on giving customers the option of controlling their personal information.
This paper studies the impact of loss aversion on queue configurations in a doubled‐ended queueing system such as taxi stations. We assume that there exist two types of demands/passengers, namely, short‐haul and long‐haul, with long‐haul demand offering a larger monetary reward for drivers. Loss‐averse drivers decide to either join or balk based on their overall utility. We first consider the passenger‐side system to be a loss system; that is, an arriving passenger balks if there is no taxi waiting for her. We derive the system performance of two queue configurations, i.e., a pooled queue and two dedicated queues. By comparing the total passenger boarding rates, we find that the pooled queue is not always preferable. From the drivers’ perspective, the pooled queue generates a rather stable waiting time and hence mitigates their loss aversion in the waiting time dimension; nevertheless, it creates uncertainty in the reward dimension and thus brings about potential loss. We also compare the two configurations regarding the boarding rate of each type of passengers. We show that dedicated queues can achieve a Pareto improvement; that is, they can generate a higher boarding rate for each type of passenger when drivers are sufficiently loss averse in the reward dimension and not so in the waiting time dimension. Nevertheless, dedicated queues may decrease both passenger boarding rates. We then extend our setting by incorporating passengers’ joining/balking decisions and find that our managerial insights derived from the lost‐demand system still hold.
We explore whether customers are loss averse in time and how delay information may impact such reference-dependent behavior using observational and field experiment data from two call centers of an Israeli bank. We consider settings with no announcements and announcements of different accuracy levels. We face two key challenges: (1) we do not observe the reference points customers use in our data, as any other field studies, and (2) it is difficult to separate the reference-dependent behavior from the potential nonlinear waiting cost of customers. To address these challenges, we develop a dynamic decision model with consumer learning, through which we infer the reference point each customer used during any given call. The reference points may be different across different customers and evolve across different calls of the same customers. We also exclude the alternative explanation by showing that our main reference-dependent models better explain the observed customer abandonment than models where customers have nonlinear waiting cost. Our results indicate that customers are loss averse regardless of the availability or accuracy of the announcements when their waiting time is relatively long (≥ 90s). Although delay announcements do not alter the nature that customers are loss averse, accurate announcements may affect customers’ belief about the offered waiting time and thus, impact the reference points. Through counterfactual studies, we demonstrate that providing delay announcements improves the call center performance given the loss aversion behavior observed in our data. Interestingly, as customers become more loss averse, the value of providing delay announcements decreases.
This paper was accepted by Terry Taylor, operations management.
Consumers experience a sense of loss when a product’s quality does not match their expectations. To alleviate consumer loss aversion (CLA), firms can disclose information to reduce consumers’ uncertainty about product quality and the resulting psychological loss. In this paper, we investigate the implications of CLA on firm profit, consumer surplus, and social welfare when firms endogenously make quality disclosure decisions. We find that CLA leads symmetric firms to disclose quality more often. Given that CLA weakly reduces consumers’ utility from buying a product and quality disclosure is costly, intuition suggests that CLA is detrimental to firms. We find that this intuition is true only in a monopoly. Surprisingly, CLA makes both firms in a competition better off. Moreover, CLA increases firms’ profit when they invest in quality disclosure instead of money-back guarantees to respond to CLA. We also find that CLA decreases consumer surplus and social welfare. Therefore, educating consumers to improve decision-making skills by deliberating on future outcomes and emotions can benefit firms at the cost of consumers and society. When firms disclose quality sequentially, CLA can discourage the follower from disclosing quality. A strong level of CLA increases the leader’s profit over the follower’s, thereby encouraging firms to be the first mover in quality disclosure.
This paper was accepted by Juanjuan Zhang, marketing.
For experience goods (products or services), given the uncertainty about their actual quality and the growing popularity of social media, potential customers nowadays depend on experiences of peers who have used the goods previously to learn about their quality. In this paper, we study how such customer learning affects a firm's (credible) quality disclosure strategy as well as other relevant decisions. To model such learning, we adopt the anecdotal reasoning framework, which we show to be rational and a special case of the Bayesian framework. There are two main insights that we glean from this study. First, we find that the incorporation of the learning behavior significantly alters the optimal disclosure strategy from its single threshold structure in the extant literature to a multi‐threshold policy. Specifically, firms with high or low quality goods prefer not disclosing quality information in order to utilize the pricing flexibility that such a strategy affords; on the other hand, a medium‐quality firm might disclose its quality level, even though this hinders its pricing flexibility, so that customers are confident about it when purchasing the product. Second, we show that the change in the disclosure strategy impacts the optimal pricing decision, which can be non‐monotone in the quality level. Our results suggest that when disclosure is expensive, high‐quality firms are better off educating potential customers through advertising or social media, rather than disclosing their quality levels. They also suggest to policymakers that mandatory quality disclosure may not be socially optimal as more customers obtain quality information through peer learning. Our findings are robust and hold true under quite general customer valuation distributions, in capacitated settings and even when price can be used as a signal of quality level by firms.
In many systems with limited service capacity, customers must wait in a queue for service. When customers cannot observe the queue, how should a revenue-maximizing service provider convey information about wait times? In “Optimal Signaling Mechanisms in Unobservable Queues,” D. Lingenbrink and K. Iyer study this problem and characterize the structure of the optimal signaling mechanism. To signal optimally, the service provider uses two possible signals, “short” and “long,” to tell customers the queue length is short when below a threshold and long when above it. For the specific case of linear waiting costs, the authors explicitly compute this threshold. Furthermore, they show that for an optimally chosen fixed service price, optimal signaling produces the same expected revenue as a pricing mechanism that sets prices based on the number of customers waiting. This suggests that in settings where one cannot dynamically update prices, signaling can be effective in generating revenue.
Problem definition: We study the following puzzle: why do firms sometimes nurture long wait lines, rather than raising prices (to eliminate these lines)? Academic/practical relevance: In economic theory, prices are studied as a signal of quality, in absence of congestion (wait lines). We study price signaling when customers not only infer quality information from the price, but also from wait lines. Methodology: We developed a stylized model based on queuing and price signaling theory. The firm, privately informed about its quality (high or low), first determines its price. Next, customers arrive according to a Poisson process, observe the price and the wait line upon arrival, and decide whether to purchase. Results: When the proportion of informed consumers is low, to separate on price a high-quality firm must raise its price above the monopoly price. We show that there exist pooling equilibria in which firms instead charge a price lower than the monopoly price. We characterize two pooling equilibria. In both equilibria, a high-quality firm on average has a longer queue than a low-quality one, and long lines signal high quality. In the first one, the price is sufficiently low that short lines in turn signal low quality, so that the queue length almost perfectly reveals the type of the firm. In the second one, the price is in an intermediate range (but remains lower than the monopoly price), and short lines are an imperfect signal of quality. In each of the pooling equilibria, the high-quality firm earns a higher profit than in the separating equilibrium, despite the longer lines. Managerial implications: An empirical implication of our model is that, over time, when more customers become informed about the quality, the price of a new high-quality good should increase and the expected waiting lines should decrease. Our model integrates elements of price signaling in economics and equilibrium queueing in operations research. We hope that our research stimulates further interest in signaling games in service operations environments.
In this chapter, we present theories and applications of reference-dependent preferences. We provide some historical perspective, but also move quickly to the current research frontier, focusing on developments in reference dependence over the last 20 years. We present a number of worked examples to highlight the broad applicability of reference dependence. While our primary focus is gain–loss utility, we also provide a short treatment of probability weighting and its links to reference dependence.
We consider a service system in which customers are loss averse toward both price and delay attributes. That is, customers compare these two attributes with their rational expectations of outcomes, with losses being more painful than equal-sized gains are pleasant. We first study customers’ equilibrium queueing strategies. We find that, unlike the traditional case in which loss aversion is not considered, there may exist three equilibrium strategies, one of which is preferred in the sense that customers’ utility is highest at this equilibrium. We then investigate the optimal pricing problem for a monopoly server and find that loss aversion polarizes queues, making long queues even longer and short queues even shorter. Furthermore, loss aversion toward the delay attribute drives the optimal price down, whereas loss aversion toward the price attribute drives it up. We also find that profit- and welfare-maximizing prices are not the same in a monopoly market. Finally, we consider pricing competition in a symmetric duopoly market and find that the conclusions depend on the size of the service capacity relative to the market size. For fast servers, there exists a unique symmetric price equilibrium. Under certain conditions, the effect of loss aversion on waiting time drives the price down, whereas that on the monetary term drives it up. For moderate-speed servers, there also exists a unique symmetric equilibrium. However, the effect of loss aversion on the two attributes works in reverse compared with that in the fast server case. For slow servers, we show that a symmetric equilibrium may not exist, and we numerically find that there may exist two asymmetric equilibria. Interestingly, with loss-averse customers, a firm can obtain a higher profit in a duopoly market than in a monopoly market.
The online appendix is available at https://doi.org/10.1287/opre.2017.1702 .
We find the optimal policy for the information disclosure problem of the M/M/1 queue studied by Simhon et al. (2016). Our optimal disclosure policy is as follows: the service provider informs all customers of the queue length when the queue length is above a specified threshold and does not inform them when the queue length is below the threshold.
Loss aversion can affect support and opposition to Pigovian taxes to reduce externalities. This paper studies road pricing with reference-dependent preferences, modeled by a linear gain-loss utility function. Given this specification, we find that the socially optimal road toll is smaller than the optimal toll in the absence of reference dependence, and it declines in the degree of loss aversion. Loss aversion can also explain the empirical observation that support for road pricing is lower before than after its introduction. We further show that loss aversion may increase or reduce lobbying efforts by driver organizations against the introduction of tolling. It will increase lobbying if a high toll is proposed but drivers initially believe that the probability that it will be introduced is small. Lastly, loss aversion unambiguously reduces lobbying by organizations of non-drivers (representing, for example, environmentalists or public transport users) in favor of the introduction of a toll.
To maximize a firm's profit over a finite planning horizon, we develop a dynamic optimization model by considering loss aversion when making pricing and inventory decisions. We estimate customer demand through a choice model, which incorporates reference price, utility function and customer loss aversion. Our model forms the core of the expert system for decision support. Through a sequence of Bellman equations, we find that the firm's profit is a concave function of price and inventory, and we solve the model optimally. The profit is positively correlated with the reference price, and the price and inventory decisions are non-monotonic functions of loss aversion intensity. Our results shed new light on pricing and inventory management with customer behavior in a multi-period system. Through various theorem developments, we are able to identify the optimal inventory level and the corresponding price. Numerical examples are provided to illustrate and validate the model and to derive managerial insights. To show the potential significance, we demonstrate how a dynamic programming model yields good results with customer loss aversion under realistic customer behavior assumptions. Our system can improve the efficiency of decision making and provide better customer service.
Information about queue length is an important parameter for customers who face the decision whether to join a queue or not. In this paper, we study how optimal information disclosure policies can be used by a service provider of an queue to increase its revenue. Our main contribution is showing that the intuitive policy of informing customers about the current queue length when it is short and hiding this information when it is long is never optimal.
We study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store, and follow the plans in the store. In anticipation of consumers’ purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm’s operational decisions about ordering and contingent pricing and the consumers’ purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers’ beliefs. Under this framework of endogenized reference points, we fully characterize the firm’s optimal inventory and contingent pricing policies. We identify conditions under which the firm’s expected price and profit are increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers’ loss aversion affects the firm’s optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity; and the optimal full price decreases, while the optimal sales frequency increases, in the procurement cost.
This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.
We consider revenue and social optimization in an M/M/1 queue with price and delay sensitive customers, and study the performance of uninformed pricing that does not require any arrival rate information. We formally characterize the optimal uninformed price and its performance relative to pricing with precise arrival rate knowledge. For uniformly distributed customer valuations, under a large set of parameters, we find that uninformed prices can capture more than 99% of the optimal revenue and more than 85% of the optimal social welfare. We further prove that the performance of uninformed prices improves as the customers become more delay sensitive and is always better under revenue optimization compared with social optimization.
We consider an M/M/1 queueing system with impatient consumers who observe the length of the queue before deciding whether to buy the product. The product may have high or low quality, and consumers are heterogeneously informed. The firm chooses a slow or (at a cost) a fast service rate. In equilibrium, informed consumers join the queue if it is below a threshold. The threshold varies with the quality of the good, so an uninformed consumer updates her belief about quality on observing the length of the queue. The strategy of an uninformed consumer has a “hole”: she joins the queue at lengths both below and above the hole, but not at the hole itself. We show that if the prior probability the product has high quality and the proportion of informed consumers are both low, a high-quality firm may select a slower service rate than a low-quality firm. The queue can therefore be a valuable signaling device for a high-quality firm. Strikingly, in some scenarios, the high-quality firm may choose the slow service rate even if the technological cost of speeding up is zero.
This paper was accepted by Assaf Zeevi, stochastic models and simulation.
Marketers disclose quality information directly to potential consumers using a variety of communication channels. This study investigates how competition may influence duopoly firms' incentive to voluntarily and truthfully reveal quality information. It is shown that firms in competitive markets reveal less information than a monopoly firm does. In addition, sequential disclosure leads to asymmetric equilibrium disclosure behavior: The disclosure leader discloses unambiguously less information than that in the simultaneous disclosure case, whereas the disclosure follower ex ante reveals less (more) private information than both the disclosure leader and that in the simultaneous disclosure case when the disclosure cost is sufficiently low (high). We also examine the firms' equilibrium ex-ante profits and social welfare. It is demonstrated that there may exist a U-shaped relationship between equilibrium monopoly profits (or social welfare under both monopoly and duopoly) and the disclosure cost. Moreover, in comparison to the simultaneous disclosure case, sequential disclosure can lead to increasingly softened competition, improving both firm profitability and social welfare.
Firms normally disclose quality information to consumers using two alternative formats: either directly to consumers or indirectly through downstream retailers. This study investigates optimal disclosure strategies/formats in a channel setting with bilateral monopolies. It shows that retail disclosure leads to more equilibrium information revelation. This is because the manufacturer can, through wholesale price cuts, partially absorb the retailer's effective disclosure cost and thus increase the retailer's incentive for disclosure. The conditions under which a particular disclosure format arises as the manufacturer's optimal choice are also examined. Even though direct disclosure is the ex post dominated option, the manufacturer may benefit from committing ex ante to the direct disclosure format when the cost of disclosure is sufficiently high.
Much experimental evidence indicates that choice depends on the status quo or reference level: changes of reference point often lead to reversals of preference. The authors present a reference-dependent theory of consumer choice, which explains such effects by a deformation of indifference curves about the reference point. The central assumption of the theory is that losses and disadvantages have greater impact on preferences than gains and advantages. Implications of loss aversion for economic behavior are considered. Copyright 1991, the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
We develop a model in which a profit-maximizing monopolist with uncertain cost of production sells to loss-averse, yet rational, consumers. We first introduce (portable) techniques for analyzing the demand of such consumers, and then investigate the monopolist's pricing strategy. Compared to lower possible purchase prices, paying a higher price in the firm's pricing distribution is assessed by consumers as a loss, decreasing demand for the firm's product. We provide conditions under which a firm with continuously distributed marginal cost responds by (locally) eliminating this comparison effect and choosing a discrete price distribution; that is, prices are sticky. Price stickiness is more likely to obtain when the cost distribution has high density, the price responsiveness of demand is low, or consumers are likely to purchase. Whether or not prices are sticky, the monopolist wants to at least mitigate the comparison effect, leading to countercyclical markups. On the other hand, if consumers expect to buy the product, they experience a loss if they end up not consuming it, increasing their willingness to pay for it. Thus, despite the tendency toward price stability, there are also circumstances in which a firm with unchanging cost offers random sales to increase customers' expectation to consume, attracting more demand at higher prices.
We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Copyright 1992 by Kluwer Academic Publishers
We use Koszegi and Rabin's (2006) model of reference-dependent utility, and an extension of it that applies to decisions with delayed consequences, to study preferences over monetary risk. Because our theory equates the reference point with recent probabilistic beliefs about outcomes, it predicts specific ways in which the environment influences attitudes toward modest-scale risk. It replicates "classical" prospect theory—including the prediction of distaste for insuring losses—when exposure to risk is a surprise, but implies first-order risk aversion when a risk, and the possibility of insuring it, are anticipated. A prior expectation to take on risk decreases aversion to both the anticipated and additional risk. For large-scale risk, the model allows for standard "consumption utility" to dominate reference-dependent "gain-loss utility," generating nearly identical risk aversion across situations. (JEL D81)
A queueing model--together with a cost structure--is presented, which envisages the imposition of tolls on newly arriving customers. It is shown that frequently this is a strategy which might lead to the attainment of social optimality.
We develop a model of reference-dependent preferences and loss aversion where “gain-loss utility” is derived from standard
“consumption utility” and the reference point is determined endogenously by the economic environment. We assume that a person's
reference point is her rational expectations held in the recent past about outcomes, which are determined in a personal equilibrium by the requirement that they must be consistent with optimal behavior given expectations. In deterministic environments,
choices maximize consumption utility, but gain-loss utility influences behavior when there is uncertainty. Applying the model
to consumer behavior, we show that willingness to pay for a good is increasing in the expected probability of purchase and
in the expected prices conditional on purchase. In within-day labor-supply decisions, a worker is less likely to continue
work if income earned thus far is unexpectedly high, but more likely to show up as well as continue work if expected income
is high.