Sequential Search Model Research Articles

Bayesian Nonparametric Sequential Search

Sequential search models are popular in marketing for studying consumer search behavior. Current search models use parametric assumptions regarding different aspects of the models, such as random shocks, search costs, and consumer preferences. These assumptions can be restrictive. The authors develop a novel Bayesian nonparametric framework for sequential search to flexibly model unknown distributions. They also develop Markov chain Monte Carlo methods for inferring the model unknowns. The authors conduct simulation studies to demonstrate that currently popular parametric search models can yield incorrect estimates and inferences when the data-generating process deviates from their assumptions. In contrast, the proposed model accurately recovers these quantities for various data-generating processes. The methodology is then applied to online search and purchase data from a Japanese retailer. The results show that several heterogeneity distributions have complex patterns, such as multimodality and skewness, that are not captured by a parametric benchmark model. The authors also estimate the monetary value of search costs, the price elasticities, and a counterfactual profit gain under a personalized couponing strategy and find substantial differences in the results from the two models.

Optimal Prototyping with Noisy Measurements

Problem definition: Prototyping and testing are an integral part of almost any new product development process, helping firms navigate the inherent uncertainties of creating new products. Recent developments in rapid prototyping, including technologies that enable cheaper low-fidelity tests, have opened up the possibilities for firms in reconfiguring their product development processes. Firms can, by choosing the level of evaluation fidelity, alter the traditional cost-quality trade-offs inherent in sequential prototyping. Methodology/results: The current article formulates a general model of sequential search where firms can proceed by obtaining noisy low-fidelity evaluations of their prototypes. Our results demonstrate that the imperfect fidelity of evaluations alters the firm’s optimal experimentation, with the starkest difference being that it may make it optimal for the firm to select and launch a prototype that did not yield the best evaluation. In addition, our analysis of optimal measurement technology reveals that the focal firm should demand the most precise measurements when their ex-ante uncertainty is moderate (not too high or low). We also consider extensions analyzing how the optimal choice of evaluation fidelity is affected by the number of available prototypes, by operational flexibility (to dynamically change measurement technology), and by the ability to outsource evaluations to an experimentation platform. Managerial implications: We develop managerial insights for how the optimal choice of fidelity and the optimal length of the evaluation cycle should be planned depending on the evaluation costs and the firm’s ex-ante uncertainty. The resulting framework offers guidance to product and software development firms to successfully leverage imperfect fidelity experiments. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.1133 .

On the impact of co-optimizing station locations, trip assignment, and charging schedules for electric buses

As many public transportation systems around the world transition to electric buses, the planning and operation of fleets can be improved via tailored decision-support tools. In this work, we study the impact of jointly locating charging facilities, assigning electric buses to trips, and determining when and where to charge the buses. We propose a mixed integer linear program that co-optimizes planning and operational decisions jointly and an iterated local search heuristic to solve large-scale instances. Herein, we use a concurrent scheduler algorithm to generate an initial feasible solution, which serves as a starting point for our iterated local search algorithm. In the sequential case, we first optimize trip assignments and charging locations. Charging schedules are then determined after fixing the optimal decisions from the first level. The joint model, on the other hand, integrates charge scheduling within the local search procedure. The solution quality of the joint and sequential iterated local search models are compared for multiple real-world bus transit networks. Our results demonstrate that joint models can help further improve operating costs by 14.1% and lower total costs by about 4.1% on average compared with sequential models. In addition, energy consumption costs and contracted power capacity costs have been reduced significantly due to our integrated planning approach.

Simulated maximum likelihood estimation of the sequential search model

AbstractWe propose a new approach to simulate the likelihood of the sequential search model. By allowing search costs to be heterogeneous across consumers and products, we directly compute the joint probability of the search and purchase decisions when consumers are searching for the idiosyncratic preference shocks in their utility functions. Under the assumptions of Weitzman’s sequential search algorithm, the proposed procedure recursively makes random draws for each quantity that requires numerical integration while enforcing the conditions stipulated by the algorithm. In an extensive simulation study, we compare the proposed method with existing likelihood simulators that have recently been used to estimate the sequential search model. The proposed method attributes the uncertainty in the search order to the consumer-product-level distribution of search costs and the uncertainty in the purchase decision to the distribution of match values across consumers and products. This results in more precise estimation and an improvement in prediction accuracy. We also show that the proposed method allows for different assumptions on the search cost distribution and that it recovers consumers’ relative preferences even if the utility function and/or the search cost distribution is mis-specified. We then apply our approach to online search data from Expedia for field-data validation. From a substantive perspective, we find that search costs and “position” effects affect products in the lower part of the product listing page more than they do those in the upper part of the page.

WeStore or AppStore: How Customers Shop Differently in Mobile Apps vs. Social Commerce

In the dynamic e-commerce environment, social commerce has emerged as a revolutionary force, transforming how consumers interact and transact online. This paper investigates the differences in customers’ search and purchase patterns between a prominent online retailer’s burgeoning social commerce channel, the WeChat mini-program, and its native mobile app. We analyze the customers’ entire journey through a sequential search model that encapsulates decisions from channel selection to product search, search termination, and the final purchase. This study contributes to the search model literature by being the first to estimate both fixed and marginal search costs in a sequential search model in an omnichannel retail environment. We calculate fixed search costs, marginal search costs, and preferences for each channel, revealing differences in customers’ behaviors across channels. Our analysis shows that customers’ fixed search costs are higher, but marginal costs are lower on WeChat channel compared to the App channel. Also, customer characteristics like historical spending levels and search timing influence their search costs. From these insights, we suggest strategies tailored to each channel capitalizing on the differences in customers’ search costs. The first strategy encourages search initiation by lowering fixed search costs through peer-to-peer link sharing in the WeChat channel. The second strategy aims to minimize marginal search costs using search-triggering coupons in the App channel. Implementing these strategies significantly boosts conversion rates and profits for the online retailer. This research is one of the first to explore the differences between traditional retail channels and emerging social commerce channels.

Worker selectivity and fiscal externalities from unemployment insurance

A robust prediction of job search models is that unemployment insurance (UI) makes workers more selective about which jobs they accept, thereby raising average accepted wages and thus generating a positive fiscal externality. We provide a sufficient-statistics formula for evaluating the size of this selectivity effect and argue theoretically that it is likely to be small. In a standard sequential search model, the effect of UI on wages is linked to its effect on the job-finding hazard; the slope of the relationship between these elasticities depends on a small number of estimable statistics, key among them observed worker flows. Plausible calibrations of the model imply that the magnitude of the wage elasticity is small relative to the job-finding elasticity. Although ignoring the wage effect of UI would over-estimate its fiscal cost and under-estimate its welfare benefit, the model-implied formula predicts the magnitude of this bias to be small.

Integrated sequential fuzzy logic search models for simulating wastewater treatment plants missing influent parameters

AbstractAiming at achieving optimum operations of wastewater treatment plant (WWTP) processes, it is essential to develop accurate predictive models for expected influent pollutant loads. To overcome limited timespan data and model complexity, this study is devoted to propose an integration of inputs' sequential search with the adaptive neuro‐fuzzy inference system (ANFIS) for reducing the modelling complexity. The input data included nine influent parameters measured bi‐weekly for 12 years at a WWTP, South Africa (SA). The sequential search process was used for input optimization to select the most representative inputs in modelling four parameters. The obtained results indicated a strong correlation with R2 and NSE above 0.85 for the four targeted influent parameters. After validating the developed models using different criteria, the missing records were predicted throughout the study period. The integration of sequential search input optimization and ANFIS modelling was able to provide a high performance in modelling WWTP datasets.

Escaping search when buying

This paper studies a duopoly with horizontally differentiated products and costly sequential consumer search. Prices are posted and search costs must be paid to observe the match values of goods. Consumers choose both in what order to inspect the products and whether to inspect the goods before purchasing. When the expected match value is relatively high, consumers always consider the cheaper product first. However if the expected match value is low, then consumers may check the more expensive product first. The fact that a consumer may buy a product without inspection softens price competition. As a result, the comparative statics of prices and surplus division with respect to search costs is different from that of a sequential search model with observable prices.

Product Ranking on Online Platforms

On online platforms, consumers face an abundance of options that are displayed in the form of a position ranking. Only products placed in the first few positions are readily accessible to the consumer, and she needs to exert effort to access more options. For such platforms, we develop a two-stage sequential search model where, in the first stage, the consumer sequentially screens positions to observe the preference weight of the products placed in them and forms a consideration set. In the second stage, she observes the additional idiosyncratic utility that she can derive from each product and chooses the highest-utility product within her consideration set. For this model, we first characterize the optimal sequential search policy of a welfare-maximizing consumer. We then study how platforms with different objectives should rank products. We focus on two objectives: (i) maximizing the platform’s market share and (ii) maximizing the consumer’s welfare. Somewhat surprisingly, we show that ranking products in decreasing order of their preference weights does not necessarily maximize market share or consumer welfare. Such a ranking may shorten the consumer’s consideration set due to the externality effect of high-positioned products on low-positioned ones, leading to insufficient screening. We then show that both problems—maximizing market share and maximizing consumer welfare—are NP-complete. We develop novel near-optimal polynomial-time ranking algorithms for each objective. Further, we show that, even though ranking products in decreasing order of their preference weights is suboptimal, such a ranking enjoys strong performance guarantees for both objectives. We complement our theoretical developments with numerical studies using synthetic data, in which we show (1) that heuristic versions of our algorithms that do not rely on model primitives perform well and (2) that our model can be effectively estimated using a maximum likelihood estimator. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Consumer Online Search with Partially Revealed Information

Modern-day search platforms generally have two layers of information presentation. The outer layer displays the collection of search results with attributes selected by platforms, and consumers click on a product to reveal all its attributes in the inner layer. The information revealed in the outer layer affects the search costs and the probability of finding a match. To address the managerial question of optimal information layout, we create an information complexity measure of the outer layer, namely orderedness entropy, and study the consumer search process for information at the expense of time and cognitive costs. We first conduct online random experiments to show that consumers respond to and actively reduce cognitive cost for which our information complexity measure provides a representation. Then, using a unique and rich panel tracking consumer search behaviors at a large online travel agency (OTA), we specify a novel sequential search model that jointly describes the refinement search and product clicking decisions. We find that cognitive cost is a major component of search cost, while loading time cost has a much smaller share. By varying the information revealed in the outer layer, we propose information layouts that Pareto-improve both revenue and consumer welfare for our OTA. This paper was accepted by Juanjuan Zhang, marketing.

Consumer search with blind buying

This article studies a sequential search model in which consumers can purchase a product without incurring a search cost to inspect the match value, which we call “blind buying”. We show that the optimal search policy is no longer as per Weitzman (1979). When the match value has a symmetric distribution, both consumers and firms are indifferent to the search order, conditional on that blind buying does not take place in the first stage. Blind buying always increases total welfare, and increases market prices and industrial profits if and only if the first-sample search cost is below a threshold value. An increase in the search cost reduces equilibrium prices. Such a result is consistent with existing price-directed search models, but the underlying mechanisms are different. We also show that being prominent can adversely affect a firm if the match value is asymmetrically distributed, which contrasts the literature.

WeStore or AppStore: How we shop differently in Mobile Apps vs. Social Commerce

Social commerce is rapidly growing and attracting new customer segments. This channel is different from traditional retail channels in that it relies on social media platforms for product discovery and purchase. We examine customer behavior and search patterns in an emerging social commerce channel, namely WeChat mini-programs, and in retailers' native apps. We show that customers' fixed and marginal search costs and preferences differ across these two channels. Our research constitutes the first attempt to study customer behavior differences between traditional mobile apps and social media-based channels. Rather than focusing on customers' final purchases, we analyze customers' entire shopping journey using structural search models to quantify their search costs and price sensitivity across the different channels. Previous literature in operations management has estimated traditional discrete choice models to recover customers' cost parameters based on customers' purchase decisions. Instead, we use a sequential search model that characterizes customers’ entire shopping journey. We estimate fixed search costs, marginal search costs, and preferences in each channel and uncover differences in customers' search and purchase behavior across channels. We find that WeChat customers have higher fixed search costs yet smaller marginal search costs compared to App customers. Moreover, customer characteristics such as their user level and time of search impact search costs. Fixed and marginal costs are higher for customers with higher user levels on the WeChat channel. Marginal search costs are higher for customers with higher user levels in the App channel. We propose two channel-specific strategies that leverage customers' search cost differences across channels. The first strategy is to send friend referral discounts to lower fixed search costs in the WeChat channel. The second is to send search-triggering coupons to induce App customers to continue their search. Both strategies can significantly increase conversion rate and profit for online retailer JD.

Informational Cycles in Search Markets

I show that market participants’ equilibrium beliefs can create fluctuations in the volume of trading, even in a stationary environment. I study a sequential search model where buyers face an unknown distribution of offers. Each buyer learns about the distribution by observing whether a randomly chosen buyer traded yesterday. A cyclical equilibrium exists where the informational content of observing a trade fluctuates, which leads to fluctuations in the volume of trading. The cyclical equilibrium is more efficient than steady-state equilibria. The efficiency result holds also if buyers get a signal about past transaction prices or past trading volumes. (JEL D82, D83)

Search Duration

This paper develops and estimates a model of sequential search that accounts for the full set of decisions consumers make while searching (which products to search, search longevity, sequence of purchases, and whether to purchase).

Learning and job search dynamics during the Great Recession

Krueger and Mueller (2011) document that search effort declined with unemployment duration during the Great Recession. I show that variation in past effort explains this decline. Furthermore, job offers increase subsequent effort. These facts are inconsistent with standard models of search. I introduce a model of sequential search in which workers are uncertain about the offer arrival process and learn through search. Evolving beliefs influence search through two competing channels: the opportunity cost of leisure and the option value of unemployment. Estimation of the model indicates that learning provides a strong account of job search dynamics during the Great Recession.

Optimal Sequential Search

We introduce a simple new model of sequential search among finitely many options that fits many economic applications. Each payoff is the sum of a random “known factor” and a “hidden factor”, learned at cost. Weitzman (1979) solved the ex post Pandora’s box problem, given known factors. Ours is the ex ante model for estimation, unconditional on known factors, and so resolves major selection effects. 1. Search intensifies over time, as one increasingly exercises the current option, recalls a prior one, or quits. If one recalls, earlier options are recalled more often. 2. We solve a long open question in all search models: which stochastic changes lead one to search longer? Answer: more dispersed payoffs. 3. The stationary search model poorly approximates search with many options: If the known factor density lacks a thin tail (eg. exponential), the recall chance is boundedly positive with vastly many options. 4. Search lasts longer with more options. Hence, if low search frictions increase worker applicant pools of firms, vacancy duration increases.

Voting Rules in Sequential Search by Committees: Theory and Experiments

We propose a committee extension of the individual sequential search model called the “secretary problem,” where collective decisions on when to stop the search are reached via a prespecified voting rule. We offer a game-theoretic analysis of our model and then report two experiments on three-person committees with either uncorrelated or perfectly correlated preferences under three different voting rules followed by a third experiment on single decision makers. Relative to equilibrium predictions, committees with uncorrelated preferences oversearched under minority and majority voting rules but, otherwise, undersearched or approximated equilibrium play. Individually, committee members were often less strategic when their preferences were uncorrelated than when they were perfectly correlated. Collectively, committees’ decisions were more strategic than single decision makers’ only under the unanimity rule, although still not significantly better in terms of the decision makers’ welfare. Finally, across our experiments that involved committee search, the unanimity rule always optimized committee welfare. This paper was accepted by Yan Chen, behavioral economics.

The When and How of Delegated Search

Search models have traditionally been used to describe situations such as the development of new technology, job search, and the search for profitable investment opportunities. We address the problem faced by a firm that must conduct a search and therefore contemplates outsourcing that process. This paper models the firm's problem in a dynamic principal-agent framework while embedding the standard model of sequential search. We identify the conditions under which it is preferable to outsource the process (rather than conducting the search in-house) and describe the optimal contracting mechanism through which to compensate the searching agent. The optimal contract is structured as follows: pay the agent a fixed fee in each period as well as a bonus whenever a suitable alternative is found, where the size of the bonus is defined a priori and decreases over time. This contract has several desirable properties. Namely, it is the result of optimization over the entire contract space, it is both history independent and renegotiation proof, and no variables need to be verifiable by a third party if the time horizon is short enough. Whether or not to outsource a search process reduces to evaluating the principal's trade-of between speed and quality. The age-old aphorism “if you want it done right, do it yourself holds, since in-house search is optimal for a principal who prioritizes quality. Yet in this particular setting, we also establish an addendum: “if you want it done fast, hire someone else to do it.

Testing the Reference-Dependent Model: A Laboratory Search Experiment

Our paper conducts laboratory experiments with the sequential search model to test whether participants engage in search activities in line with theoretical predictions derived from the expected utility model or the reference-dependent model, without assuming any specific formulation rule for a reference point. Our experimental results showed that the participants' search behavior did not align with the reference-dependent model. In addition, the correlation between individual preferences and search behavior reinforced our experimental results; that is, loss aversions were not significantly correlated with search behavior.

The Power of Rankings: Quantifying the Effect of Rankings on Online Consumer Search and Purchase Decisions

Online search intermediaries, such as Amazon or Expedia, use rankings (ordered lists) to present third-party sellers’ products to consumers. These rankings decrease consumer search costs and increase the probability of a match with a seller, ultimately increasing consumer welfare. Constructing relevant rankings requires understanding their causal effect on consumer choices. However, this is challenging because rankings are endogenous: consumers pay more attention to highly ranked products, and intermediaries rank the most relevant products at the top. In this paper, I use the first data set with experimental variation in the ranking from a field experiment at Expedia to make three contributions. First, I identify the causal effect of rankings and show that they affect what consumers search, but conditional on search, do not affect purchases. Second, I quantify the effect of rankings using a sequential search model and find an average position effect of $1.92, which is lower than literature estimates obtained without experimental variation. I also use model predictions, data patterns, and a feature of the data set (opaque offers) to show rankings lower search costs, instead of affecting consumer expectations or utility. Finally, I show a utility-based ranking built on this model’s estimates benefits consumers and the search intermediary. Data and the online appendix are available at https://doi.org/10.1287/mksc.2017.1072 .