Sequential Search Model Research Articles

Estimation of Sequential Search Models

We propose a new likelihood-based estimation method for the sequential search model. By allowing search costs to be heterogeneous across consumers and products, we can directly compute the joint probability of the search sequence and the purchase decision when consumers are searching for the idiosyncratic preference shocks in their utility functions. Under this procedure, one recursively makes random draws for each dimension that requires numerical integration to simulate the probabilities associated with the purchase decision and the search sequence under the sequential search algorithm. We then present details from an extensive simulation study that compares the proposed approach with existing estimation methods recently used for sequential search model estimation, viz., the kernel-smoothed frequency simulator (KSFS) and the crude frequency simulator (CFS). In the empirical application, we apply the proposed method to the Expedia dataset from Kaggle which has previously been analyzed using the KSFS estimator and the assumption of homogeneous search costs. We demonstrate that the proposed method has a better predictive performance associated with differences in the estimated effects of various drivers of clicks and purchases, and highlight the importance of the heterogeneous search costs assumption even when KSFS is used to estimate the sequential search model. Lastly, from a managerial perspective, we show that sorting products by their expected utilities can enhance consumer welfare and increase the number of transactions.

Consumer Search Costs and Preferences on the Internet

We conduct an empirical analysis of consumer preferences and search costs on an Internet platform. Using data from a major French platform (PriceMinister), we show descriptive evidence of substantial price dispersion among adverts for the same product, of consumers often not choosing the cheapest advert and sometimes choosing an advert dominated in price and non-price characteristics by another available advert. We consider a sequential search model where consumers sample adverts in an endogenous order based on their preferences and search costs. We show that the optimal search-and-purchase strategy can be characterized by a set of inequalities which can feasibly be tested on transaction and advert data. This allows us to estimate, for each transaction, a set of preference and search cost parameter values, thus allowing for flexible consumer heterogeneity in preferences and search costs. The estimated model can then describe a wide range of consumer search and purchase behaviours. We find that the model can explain almost all transactions in the data and requires non-zero preferences and search costs for at least 50% and 22% (respectively) of observations. We also find evidence of heterogeneous and sometimes substantial search costs.

Competition in Designing Pandora's Boxes

We revisit the classic sequential-search model by Weitzman (1979) in which an agent is presented with a number of boxes containing uncertain prizes, from which he selects one prize after sequentially opening the boxes and learning the prize contained within. In our model, each box is owned by an independent and ex-ante identical designer, whose objective is to get the agent to select the prize of his box. Each designer persuades the agent to pick his prize by designing the prize distribution of his box, subject to the constraints that (i) the expected value of the distribution is a constant, and (ii) the size of prize realizations is bounded. We fully characterize all symmetric equilibria, and show that they have a simple linear structure. Moreover, we find that a decrease in the agent's search cost mitigates competition, thus benefitting the designers. Furthermore, when competition is mild, all symmetric equilibria are in mixed strategies. By interpreting prize distributions as firms' product-design choices, this finding suggests that equilibrium dispersion in product designs can arise in a sequential-search setting with ex-ante identical firms and consumers.

Two-Stage Pandora's Box for Product Ranking

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.

Asymmetric sequential search under incomplete information

AbstractWe study a multistage sequential search model with n agents who compete for one job. The agents arrive sequentially, each one in a different stage. The agents' abilities, which are private information, are derived from heterogeneous distribution functions. In each stage, the designer chooses an ability threshold. If an agent has a higher ability than the threshold in the stage in which he arrives, he gets the job and the search is over. The agent's ability is not revealed when he wins the job and the designer has only an estimation of this ability according to the threshold placed by him. We analyze the optimal ability thresholds imposed by the designer who wishes to maximize the ability estimation of the agent who gets the job net of the search cost. We also investigate the relation between the optimal ability thresholds as well as the optimal order of agents in all stages according to the agents' distributions of abilities.

Sequential Search with a Price Freeze Option - Theory and Experimental Evidence

We study the economics of price freeze options (PFOs), by introducing them into a model of sequential search. The model makes a number of predictions, which we test in a laboratory experiment. The experiment varies (1) whether freezing is possible or not, (2) the cost of freezing, and (3) the length of the time horizon. We consider both settings in which prior offers cannot be recalled, and those in which recall is imperfect. We find that the observed treatment effects are consistent with the predictions of our model, though on average searches are terminated earlier than predicted. Interestingly, the extent of undersearching is magnified by the presence of an affordable PFO.

Sequential Search with Refinement: Model and Application with Click-Stream Data

We propose a structural model of consumer sequential search under uncertainty about attribute levels of products. Our identification of the search model relies on exclusion restriction variables that separate consumer utility and search cost. Because such exclusion restrictions are often available in online click-stream data, the identification and corresponding estimation strategy is generalizable for many online shopping websites where such data can be easily collected. Furthermore, one important feature of online search technology is that it gives consumers the ability to refine search results using tools such as sorting and filtering based on product attributes. The proposed model can integrate consumers’ decisions of search and refinement. The model is instantiated using consumer click-stream data of online hotel bookings provided by a travel website. The results show that refinement tools have significant effects on consumer behavior and market structure. We find that the refinement tools encourage 33% more searches and enhance the utility of purchased products by 17%. Most websites by default rank search results according to their popularity, quality, or relevance to consumers (e.g., Google). When consumers are unaware of such default ranking rules, they may engage in disproportionately more searches using refinement tools. Consequently, overall consumer surplus may deteriorate when total search cost outweighs the enhanced utility. In contrast, if the website simply informs consumers that the default ranking already reflects product popularity, quality, or relevance, consumers search less and their surplus improves. We also find that refinement tools lead to a less concentrated market structure. This paper was accepted by J. Miguel Villas-Boas, marketing.

TV Channel Search and Commercial Breaks

This study investigates time lapses that interrupt product consumption. Preeminent examples are commercial breaks during television or radio programming. The authors suggest that breaks facilitate consumers’ search for alternatives. Specifically, when there is so much uncertainty that consumers are unclear about utility levels of different products, they engage in costly search to resolve the uncertainty. For TV programming, breaks lower the opportunity cost of search, allowing the consumer to sample alternative channels without further interrupting the viewing experience on the current channel. Using data from the Chinese TV market, the authors estimate a sequential search model to study consumer TV channel choice behavior. The data contain a quasi-natural experiment due to a Chinese government policy change on commercial breaks. The natural experiment creates exogenous variations in the data that enable the empirical identification of heterogeneous consumer preference and search cost. The data patterns support the idea that viewers search for alternatives during commercial breaks. Drawing on the estimates, the authors investigate how the timing of breaks affects TV channels’ viewership, offering insights about how to strategically adjust the timing of breaks.

Price-Matching Guarantees with Endogenous Consumer Search

Price-matching guarantees (PMGs) are offered in a wide array of product categories in retail markets. PMGs offer consumers the assurance that, should they find a lower price elsewhere within a specified period after purchase the retailer will match that price and refund the price difference. The goal of this study is to explain the following stylized facts: (1) many retailers that operate both online and offline implement PMG offline but not online; (2) the practices of PMG vary considerably across retail categories; and (3) some retailers launch specialized websites that automatically check competitors’ prices for consumers after purchase. To this end, we build a sequential search model that endogenizes consumers’ pre- and postpurchase search decisions. We find that PMG expands retail demand but intensifies price competition on two dimensions. PMG drives retailers to offer deeper promotions because it increases the overall extent of consumer search, which we call the primary competition-intensifying effect. We also find a new secondary competition-intensifying effect, which results from endogenous consumer search. As deeper promotions incentivize consumers to continue price search, retailers are forced to lower the “regular” price to deter consumers from searching. The strength of the secondary competition-intensifying effect increases with the ratio of product valuation to search cost, which explains the variation in PMG practices online versus offline and across retail categories. We show that an asymmetric equilibrium exists such that one retailer offers PMG while the other does not. In this equilibrium, the PMG retailer may benefit from launching a price check website to facilitate consumers’ postpurchase search. This paper was accepted by J. Miguel Villas-Boas, marketing.

A search model of costly product returns

This paper analyses a market in which consumers buy horizontally differentiated products without knowing their exact valuations. By paying return costs, the consumers may return less-preferred items and obtain refunds. The consumers shop sequentially and their shopping strategy is similar to the search strategy of a consumer in a sequential costly search model. Thus, the pricing strategies of firms are identical to those in a price-directed sequential search model. Price competition is more intense, and the symmetric equilibrium price is lower when returns are costlier. As a result, consumer surplus is increasing in the return cost.

Information about sellers' past behavior in the market for lemons

This paper studies the role of time-on-the-market information in dynamic trading environments under adverse selection. I consider a sequential search model in which (informed) sellers receive price offers from (uninformed) buyers and analyze both the case in which buyers receive no information about sellers' trading histories and the case in which buyers observe sellers' time-on-the-market. I analyze how the observability of time-on-the-market influences agents' trading behavior and investigate its welfare implications in both the single-seller environment and the stationary market environment.

Price Search and Periodic Price Discounts

This paper empirically investigates the interplay between buyer search behavior and firm pricing strategy in a commodity market where many firms compete in price to sell homogeneous products. We use the heterogeneity in buyer search cost to rationalize why a firm offers periodic price discounts and enjoys a high profit in such a market. An estimation method is proposed to recover the nonparametric distribution of buyer search cost from the price and transaction volume data. With both data, we show that the search cost distribution can be estimated nonparametrically in a sequential search model, and estimation results from a nonsequential search model are robust to the assumption on the maximum number of searches. We also show that the commonly observed high-low pricing strategy can be an optimal strategy for firms when buyers search for price information sequentially. As an empirical application, we use the proposed method to estimate the two search models using data on a commodity product sold by a firm in a business-to-business market. The models predict a high profit margin for the firm, which is consistent with the data, but the sequential search model fits with the observed price distributions and supply costs better than the nonsequential search model. The online appendix is available at https://doi.org/10.1287/mnsc.2016.2641 . This paper was accepted by Matthew Shum, marketing.

Simulating the Mutual Sequential Mate Search Model Under Non-Homogenous Preferences

This paper extends the Todd and Miller's (1999) mutual sequential mate search model with homogenous preferences to the case of non-homogenous preferences. Our simulations show that the size of heterogeneity in the preferences affects the performance rankings -as well as the absolute success levels- of the mate search heuristics in the model with respect to both mating likelihood and mating stability.

Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry

We study the identification of the search method consumers use when resolving uncertainty in the prices of alternatives. We show that the search method—simultaneous or sequential—is identified with data on consumers’ consideration sets (but not the sequence of searches), prices for the considered alternatives and marketwide price distributions. We show that identification comes from differences in the patterns of actual prices in consumers’ consideration sets across search methods. We also provide a new estimation approach for the sequential search model that uses such data. Using data on consumer shopping behavior in the U.S. auto insurance industry that contain information on consideration sets and choices, we find that the pattern of actual prices in consumers’ consideration sets is consistent with consumers searching simultaneously. Via counterfactuals we show that the consideration set and purchase market shares of the largest insurance companies are overpredicted under the incorrect assumption of sequential search. As the search method affects consumers’ consideration sets, which in turn influence brand choices, understanding the nature of consumer search and its implications for consideration and choice is important from a managerial perspective. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mksc.2016.0995 .

Informality as a stepping stone: A search-theoretical assessment of informal sector and government policy

This paper develops a model of sequential job search to understand the factors determining the effect of tax and enforcement policies on the size (i.e., employment share) of informal sector. The focus is on the role of informal sector as a stepping stone to formal jobs. I argue that the stepping-stone role of informal jobs is an important concept determining how strongly government policies affect the size of informal sector. I measure the extent of the stepping-stone role with the intensity of skill accumulation in the informal sector. If informal jobs help workers acquire skills, gain expertise, and build professional networks for boosting the chances to switch to a formal job, then the size of informal sector is less sensitive to government policy. In this case, the option value of a job in informal sector will be high and a worker with an informal job will not rush to switch to a formal job when a policy encouraging formal employment is in effect. If, on the other hand, informal sector does not provide satisfactory training opportunities, then the size of informal sector becomes more sensitive to government policy. Calibrating the model to the Brazilian data, I perform numerical exercises confirming that the effect of government policy on the size of informal sector is a decreasing function of the intensity of skill acquisition in the informal sector.

Price Uncertainty and Market Power in Retail Gasoline: The Role of Price Signs on an Italian Highway

We investigate the effect of consumers' price uncertainty and search costs on gasoline price levels. The introduction of a mandatory price disclosure policy on the Italian highway enables us to observe market prices when (a) consumers have no price information; and (b) some information about the prices of competing stations is available to consumers. To characterize the observed pricing outcomes in the marketplace we then propose a model of consumers' sequential search and purchase of gasoline and combine it with a model of gas station pricing. Using data on actual prices and traffic patterns on a particular segment of the highway, we obtain estimates for consumer search costs and other model parameters. Via a counterfactual analysis, we then predict the levels of prices that would prevail in a scenario where consumers have full price knowledge. We also use our model and estimates to measure the stations' market power as a consequence of consumers' lack of price information. We find that when consumers do not have price information, gas stations are able to charge 35.8% more, in terms of higher price-cost margins, than when prices are known. We provide welfare implications of the current mandatory disclosure policy, and quantify the additional benefit of making price information available to all consumers.

Ex-Ante Preference in a Consumer Search Market

Consumers usually have ex-ante preferences over differentiated products before they spend significant time searching for the ones that fit their tastes best. To understand how ex-ante preferences influence a search market, I construct a sequential search model in a Hotelling setting where consumers search for match values with transparent price information available from the Internet. I show that, in response to a change in the search cost, firms choose their pricing strategies depending on the shape of the ex-ante preference distribution. Consumers as a whole can become worse off when the search cost decreases as they may need to pay higher prices. The model is extended to show that firms always have incentives to disclose prices.

Price Search and Periodic Price Discounts

This paper empirically investigates the interplay between buyer search behavior and firm pricing strategy in a commodity market where many firms price compete to sell homogeneous products. We use the heterogeneity in buyers’ search costs to explain why a firm offers periodic price discounts and enjoys a high profit. An estimation method is proposed to recover the non-parametric distribution of the search costs from the price and transaction volume data. With both data, we show that the search cost distribution can be estimated non-parametrically in a sequential search model, and estimation results from a non-sequential search model are robust to the assumption of the maximum number of searches. We also show the commonly observed high-low pricing strategy can be an optimal strategy for firms when buyers search prices sequentially. As an empirical application, we use the proposed method to estimate the search models using data on a commodity product sold by a firm in a B-to-B market. The models predict a high profit margin for the firm that is consistent with the data, but the sequential search model fits with the observed price distributions and supply costs better than the non-sequential search model.

Price-Matching Guarantee with Endogeneized Consumer Search

Price-matching guarantees (PMGs) are offered in a wide array of product categories in retail markets. PMGs offer consumers the assurance that, should they find a lower price elsewhere within a specified period after purchase, the retailer will match that price and refund the price difference. The goal of this study is to explain the following stylized facts: (1) many retailers that operate both online and offline implement PMG offline but not online; (2) the practices of PMG vary considerably across retail categories; and (3) some retailers launch specialized websites that automatically check competitors’ prices for consumers after purchase. To this end, we build a sequential search model that endogenizes consumers’ pre- and post-purchase search decisions. We find that PMG expands retail demand but intensifies price competition on two dimensions. PMG drives retailers to offer deeper promotions because it increases the overall extent of consumer search, which we call the primary competition-intensifying effect. We also find a new secondary competition-intensifying effect, which results from endogenous consumer search. As deeper promotions incentivize consumers to continue price search, retailers are forced to lower the “regular” price to deter consumers from searching. The strength of the secondary competition-intensifying effect increases with the ratio of product valuation to search cost, which explains the variation in PMG practices online vs. offline and across retail categories. We show that an asymmetric equilibrium exists such that one retailer offers PMG while the other does not. In this equilibrium the PMG retailer may benefit from launching a price check website to facilitate consumers’ post-purchase search.

Accounting for age in marital search decisions

Spouse quality, measured by educational attainment, varies significantly with the age at which an individual marries, peaking in the mid-twenties then declining through the early-forties. Interestingly, this decline is much sharper for women than men, meaning women increasingly marry less educated men as they age. Moreover, quality has worsened for educated women over several decades, while it has improved for men. Using a non-stationary sequential search model, we identify and quantify the search frictions that generate these age-dependent marriage outcomes. We find that single-life utility is typically the dominant friction, though college women in the 1950 and 1970 cohorts are affected even more by deteriorating suitor quality. Regardless of educational status, individual choice (as opposed to pure luck) is pivotal in explaining marriage market outcomes earlier in life.