Revenue Maximization of Airbnb Marketplace using Search Results
Abstract
Correctly pricing products or services in an online marketplace presents a challenging problem and one of the critical factors for the success of the business. When users are looking to buy an item they typically search for it. Query relevance models are used at this stage to retrieve and rank the items on the search page from most relevant to least relevant. The presented items are naturally “competing” against each other for user purchases. We provide a practical twostage model to price this set of retrieved items for which distributions of their values are learned. The initial output of the pricing strategy is a price vector for the top displayed items in one search event. We later aggregate these results over searches to provide the supplier with the optimal price for each item. We applied our solution to largescale search data obtained from Airbnb Experiences marketplace. Offline evaluation results show that our strategy improves upon baseline pricing strategies on key metrics by at least +% in terms of booking regret and +% in terms of revenue potential.
Marketplace Pricing; Optimal Pricing; Revenue Maximization
1 Introduction
Online marketplace are used every day by millions of users worldwide to find and buy the right product or a service. Examples of online marketplaces include ecommerce sites where customers can buy products and travel sites where customers can book places to stay while they travel. The one important problem which all online marketplaces have in common is how to determine the right price for a product or a service. Depending on the type of marketplace, the price is usually set by the suppliers or the sellers. However, the marketplace typically has additional demand data and signals it could use to determine the right price of a product, i.e. its value. The marketplace can use it to provide services to suppliers such as price recommendations or even automatic price optimization where the price is changed dynamically to maximize suppliers revenue while exploiting the characteristics of the demand. On the other hand, the marketplace also leverages the signals about the inferred product value when surfacing products to buyers who are searching, i.e. in product recommendation and search ranking algorithms. The biggest challenge and the main topic of this paper is how to accurately determine the right price for a product.
Existing work on determining the best item price are typically considering items independently [25], thus ignoring the multiple choice context user has when searching for an item. In the search setting, the user interacts with an algorithm that ranks the items to be shown to the user and the most relevant and most appealing results are shown first. Consequently, the top items receive substantial buyer attention and hence are a major contributor to purchases made in the marketplace. They are also in constant competition among each other and this needs to be taken into consideration when building the price inference model.
In this paper we propose a practical solution for determining the item prices that maximizes marketplace revenue based on search result data and the historical engagement with items that appeared in search. As already discussed, the search ranking algorithm aims at showing the most relevant items given the query parameters and ranking them in order of purchase probability. The set of shown results varies depending on entered query, keywords, filters used, etc. The items that rank higher receive substantially more attention than items that rank lower, and hence those items significantly contribute to whole marketplace revenue. Therefore, when aiming to increase marketplace and seller revenue it is essential to optimize and properly price the highly rank items.
To determine the optimal price for an item, we consider a case in which there is only one buyer and many items, where each item is displayed alongside other items in search results. The item cooccurs in search with a different items every time, depending on the search query and therefore our predicted price for this item changes from search to search. For each item, their optimal price is a random variable depending on value distributions of codisplayed items. The final price for a given item is determined based on all the searches it appeared in and all the predicted prices it had in those searches, i.e. it is based on the distribution of predicted prices in all search results.
We applied our price prediction model on Airbnb Experiences marketplace dataset. Airbnb Experiences are handcrafted activities designed and led by expert hosts that offer a unique taste of local scene and culture. The Experiences marketplace covers more than 1,000 destinations worldwide, including unique places like Easter Island, Tasmania, and Iceland. As the marketplace grew, datadriven host and guest recommendations became very important factors for the continued growth and success of the marketplace. One of the important aspects of hosting an experience is how to price it. Hosts determine the initial price of the activity they offer but they often change it afterwards to adapt to demand trends and competition. However, since hosts do not have a detailed overview of the demand, seasonality and the competition, they are not able to determine the optimal datadriven price themselves. For this reason Airbnb offers hosts price recommendations that are based on the uptodate demand, seasonality and competition.
We used 6 months of anonymized search data from Airbnb Experiences marketplace to test our new pricing strategy, which aims to maximize revenue for the marketplace. We conducted comprehensive offline experiments to test the performance of the proposed strategy and demonstrated that it outperforms existing stateoftheart pricing strategy based on several relevant metrics.
2 Related work
Machine learning empowered pricing strategy has drawn remarkable attention in data science area, where the availability of large data enables the forecast of demand of products or other target quantities. There has been a rapid development in demand estimation using machine leaning [1]. However, the generalization of these demand learning approaches to Airbnb marketplace is rather challenging. In [25], the authors discussed several challenges of deriving an accurate demand estimation for Airbnb Homes, which are also applicable to Airbnb Experiences. For example, similarly to how the price of a specific Airbnb Home rarely changes for different days in the calendar year, the price of a specific Airbnb Experience hosted on different days is mostly the same or varies in small ranges, which makes the price extrapolation very difficult. In addition, experiences that belong to different categories are quite different, e.g. surfing vs. cooking class, which jeopardizes the generalization of the demand estimation from one category to another. Most pricing problems are applications of revenue management theory [21, 11], which has been an active topic in academic research and relates closely to dynamic pricing [26, 22, 8, 12, 14, 24, 13, 23]. Another branch focuses more on static pricing (see [18] for a survey). However, most studies either assume a known demand function, or addresses the demand uncertainty through learning methods with limited practical applicability. Recently, [17] considers a static pricing strategy for multiproducts with substitution. Their work consists of a modeling stage to predict the demand given price and other features, and a second optimization step to find optimal price that maximize the profit function.
Airbnb, as a growing community marketplace, gains considerable attention from academic research, ranging from its impact on traditional hotel industry [27] to the analysis of its pricing strategies [19, 10]. The problem of our interest is optimal itempricing, which fits into the general framework of the optimal multidimensional deterministic mechanism design. The optimal mechanism design is a fundamental problem in economics and has attracted substantial attention in the theory of computation community. The major focus of existing literature in computer science is to study the computational efficiency of the mechanism [6, 7, 2, 15, 3, 4]. Among various problem formulations, we found the pricing scenario on Airbnb Platform is closely related to the Bayesian Unitdemand ItemPricing Problem [6], which studies the revenuemaximizing pricing strategy against a single unitdemand consumer of whom the valuation for all items are known by the seller. In addition, the consumer will select the item with the maximum value and price difference . In solving this multidimensional mechanism, [6] and [7] obtain polynomialtime constant factor approximations to the optimal revenue. Later [5] proposes a nearoptimal polynomialtime approximation through algorithm reduction techniques such as probability and domain discretization. Our problem formulation follows that of [5], with an explicit characterization on the distributions of consumer’s valuations (Normal distribution). When trying to implement their proposed algorithm, we realized that there was a practicality issue that hinders its realworld application. To address this issue, we build a machine learning model to learn the value distributions, and then resort to numerical algorithms to efficiently solve the problem.
3 Problem Definition
In this section we give an overview of the problems we are interested in solving in order to find the best price for an item. Our first goal is to find the right price for each item appearing in the top search results such that we can maximize the revenue of the suppliers. In other words, in user’s single search for items, we restricted our self to the top N ranked items on the page, . For each item we assume a value distribution is given. This value distribution needs to be learned by us as well. We then want to find a price vector that will allow the suppliers to maximize the total revenue potential in that specific search. At last we will aggregate these pricing vectors over time in order to suggest the best item price to the item supplier.
Formally, our pricing problem follows the scenario described in [5]. Suppose there is a single seller, with products to sell, and one consumer who is unitdemand, i.e., the consumer is interested in purchasing at most one product. The seller has access to the distributions of the consumer’s valuations on products . Specifically, we assume that are mutually independent random variables drawn from a set of known distributions . The consumer is assumed to purchase the product with the largest value and price gap. Then, given a price vector , the expected revenue of the seller is defined as
(1) 
This problem formulation can be naturally applied to the Airbnb Experiences Marketplace. On Airbnb Experiences platform, there are thousands of travelers searching for experiences every day. For each search initialized by a user, our platform recommends top experiences based on a machine learning algorithm that takes as input various user features, query information and experiences features and outputs a probability of booking. Finally, the experiences are ranked based on the predicted booking probabilities and shown to the user in that order.
Our goal is to find a nearoptimal price vector that maximizes the expected revenue. In literature, a natural approach is to discretize the domain of price and then search for the optimum in the discretized domain. However, the running time of resulting algorithms is exponential in the number of products [6, 16]. [5] develops a nearoptimal polynomialtime algorithm for this problem, whose running time is polynomial in with and being the approximation error. Nevertheless, even for moderate , the resulting running time would still be very long. This severe tradeoff between computational efficiency and approximation accuracy makes it impractical for us to use. In Section 4.2, we introduce how we adapt the formulation (4.2) to Airbnb Experiences marketplace to solve it efficiently.
Traditional revenue maximization pricing strategies usually optimize for the expected revenue defined by
(2) 
where is the probability of the product being booked at price . In common marketplaces, is often predicted using product features, prices, and spatial and temporal data [1]. Clearly, an accurate estimation of is critical to the success of (2), which is in general difficult for Airbnb Experiences marketplace. More importantly, formulation (1) allows competition and substitution effects in demand as it replaces individual booking probability with a winning probability. During a particular search, one of the driving factors of whether or not an experience will be booked is its relative competitiveness over the other codisplayed experiences, which is not wellcaptured by .
4 Model
In this work, we propose a twostage pricing model for supply revenue maximization using search events data. An accurate model for item values in the first phase and an efficient optimization in the second phase are the two key components of our pricing strategy. In the first stage, we use a regression model to predict the booked price for each experience. The booked price is used as the value surrogate of an experience from the view of our experiences guests. In the second stage, we construct a supply revenue optimization problem on the basis of value model to find the optimal price in terms of revenue maximization for each search. To circumvent the inherent challenge of the exponential solution space and the inefficiency of existing discretization and approximation techniques [5], we apply numerical optimization algorithms to achieve practicality and scalability.
4.1 Value models
Our first problem to solve is to find the inherent value of each item. We rely on the marketplace feedback at this stage, using the purchase event as confirmation of value for the booked experience. Specifically, whether to book an experience at a specific price or not is a decision made by our customers, and thus the booking event represents customer’s validation of the price set by the seller. This is common practice for picking ground truth when modeling a marketplace, because it is a meeting point of demand and supply. We model the booked price using a variety of demand, supply and item relevant features. More formally we do a regression with the following loss function:
(3) 
where is the booked price, is the regularization factor, is the number of bookings in the training set, is the parameter to learn, and is a set of features which describe the booked experience as well as the overall demand and market conditions.
Category  item category 
Host language  # languages spoken by the host 
Reviews  # of reviews 
AVG Review  Average Review score 
Photo Quality  The picture quality of the item 
Conversion Rate  Conversion rate of the item in search 
Demand Score  an index of demand for an item 
Table 1 reports a subset of the features we considered during value learning phase.
In order to find a value distribution for each item, we make an assumption that for each experience, the value follows a normal distribution , where is output from our value model and is estimated by looking at values of the experience in the past month. The optimization for the objective function outputs price vectors that are in the same scale as input values, so using booked price ensures the price suggestion will land in a reasonable range of market prices. We use XGBoost [9] to train the value model.
The output of the first phase is a predicted booking price for every experience. We use this prediction as the mean of a value distribution for experiences in the second optimization stage.
4.2 Revenue Maximization Pricing Strategy
So far we have proposed a method that is able to learn a value distribution for each item. In the next stage of our solution we aim at determining an optimal price for each item considering their search context and other items that appear alongside them in the search results. Our proposed pricing strategy considers that these set of items are "competing" among each other, and its objective is to maximize the suppliers revenue. We proceed by computing the optimal price for each search event individually, and then aggregating the computed prices to output a single price suggestion for each item.
More formally, for each search, we maximize the following objective function:
(4) 
where is a searchspecific value multiplier capturing information about user’s preference in this search. For example, it could be the ranking score from the search ranking model. In general, if an item has a higher ranking score in a search, then its value in that search should also be amplified. This winning probability takes into account the fact that in addition to user preferences, price is an important determining factor during purchase. To compute the optimal price for each search, we rewrite the winning probability explicitly as a function of the distribution function of values. We assume that the values for experiences in the same search are mutually independent variables drawn from , as described previously. To reduce the computation load, we constrain the search space to bounded sets:

Truncate the value distributions from to a bounded range . In implementation, this means that for each value distribution, we shift all probability mass above to the point and all probability mass below to the point . Choice of and will be given in Theorem 1.

Restrict the price vector to a bounded set , and consequently this reduces the search space from to bounded rectangles . This also ensures that price output from the algorithm will fall into a reasonable region.
These constraints on input and output variables incur loss on the revenue, and we will bound this loss in section 4.3. After domain truncation, we can rewrite the winning probability of th item as:
(5)  
where and are the distribution function and probability density function of the th experience’s value distribution, respectively. In our experiments, (5) is evaluated numerically by discretizing the value support. The objective function can be rewritten as
(6) 
For top experiences from each search event , we calculate optimal price vector . Since the expected revenue is a function of winning probabilities, which depend on the codisplayed experiences, the optimal price of the same experience is a random variable depending on the underlying value distributions of all top experiences in the search. For the experience , we aggregate prices obtained from all search events where it appeared as one of the top results by taking the average, i.e., , where is the set of experiences that were ranked on top for the th search event, and is the number of search events where the experience were ranked on top.
4.3 Theoretical results
In this part, we study the revenue loss due to the restriction and truncation performed on the price and value distribution support, respectively. We first restate the Lemma 24 and Lemma 27 in [5], which present results on the restriction of price vector.
Lemma 1.
Suppose that the values of items are independently distributed on , and for any price vector , construct a new price vector as follows: , , and otherwise . Then the expected revenue and from two price vectors and satisfy .
Lemma 2.
, for any price vector , define as follows, let , if , and otherwise . Then the expected revenues and from these two price vectors satisfy .
By Lemma 1 and Lemma 2, we can see that when values of items are independently distributed on , then for any price vector , if we transform it to another price vector , , then the expected revenue and from these two price vectors and satisfy .
Next we show that we can truncate the support of value distributions to bounded range without hurting much revenue.
Theorem 1.
Given a collection of random variables , where , if we truncate their distributions to a bounded range , where and with being the quantile of distributions of ^{1}^{1}1In our experiments, is often set as .. For any price vector , , , where and are the revenues when the consumer’s values are distributed before and after truncation respectively.
Proof.
For a set of random variables that are distributed as , define a new set of random variables as
(7) 
An important fact is that for any given price , and are different only when for some , which reduces to the event that . To see this, if , , then , and thus . If such that , and thus , then the price of item is higher than values and , so the item will not be purchased for both cases. Since the maximum price is , we have the following bound for ,
(8)  
∎
5 Experiments
In this section we aim to evaluate the effectiveness of the proposed solution using two search data sets, which are based on real users and not expert users. We use a timebased holdout of the search event data as a test set, for comparison purposes. We proceed by describing our data set, experimental framework, metrics used for evaluation purposes and parameter tuning. We conclude by discussing the results.
5.1 Data set
Our data set is composed of search result data from Airbnb Experiences marketplace. As we mentioned in the introduction, this marketplace allows users to search for unique activities to do while travelling. A typical experience takes 2 hours on average. Experience Hosts can offer these activities to several travellers at the same time, and they can offer the same activity multiple times per day. We sampled a set of anonymized searches which occurred between 1st of January and 31st of May . We kept only searches in which the user actually purchased an experience. For each search we collected detailed information on displayed experiences, including the ranking position for all experiences in that search. In Figure 1 we show the ranking position of the experience that ends up being booked by the customer. As it can be observed, most of the booked experiences were ranking high on the search page. Therefore, we can conclude that the top ranking positions is where the biggest competition for bookings is happening.
In addition to experience ranking information we collect a variety of other experience attributes that are used for feature engineering purpose, as described in Section 4. Table 2 reports few more statistics of our data set
Number of search events  
Number of distinct experiences  
Number of search events  Data set 2 (training)  
Number of search events  Data set 2 (test)  
Number of search events  Data set 1 (training)  
Number of search events  Data set 1 (test) 
A large portion of our training set is used for training the value model, which was described in Section 4.1. We use a small portion of the training set to train our pricing strategy which determines an optimal price for each experience. We consider two scenarios. In the first scenario we train our pricing strategy using the first days of April and we use the last week of April as our test set, referred to as Data set . In the second scenario we train our pricing strategy on the first days of May and use the last week of May as a test set, referred to as Data set .
5.2 Experimental Framework
For each day in training set, we have a set of searches, where each search contains many experiences displayed to the user. In order to find the optimal price for each search, we need to have the value distribution of each experience that appeared in that search. We therefore train a value model (VALUE) using all the information available one day before the user search ^{2}^{2}2Note that this corresponds to the realworld scenario where the machine learning models are retrained everyday, and used for inference purpose during the next day.. For each search, we assume that the value follows a normal distribution centered at our predicted score for each experience. The scores are predicted using the machine learning model that was trained using past booked prices as labels, and listing attributes as features. It should be noted that no price related attributes were included as features for this model, and thus our predicted value is independent of the actual price of experiences. In order to find the value distribution for each experience and , we use a sample standard deviation of values over days as an estimator of the .
When training the pricing strategy, we restrict ourselves to the top experiences that appear on the search page in each search.
For each experience shown in a particular search, we use our pricing strategy to compute a price vector. Since the predicted price is searchspecific, i.e., experience optimal price depends on the codisplayed experiences, we restrict our attention to the experiences that appeared frequently in the top search positions and combine the obtained prices from different searches for each experience by a simple average.
The revenue maximization (REV_MAX) strategy which was described in Section 4.2 is applied to each search to determine the optimal price for each experience from top positions. The algorithm used to carry out the optimization is LBFGSB [20, 28]. LBFGSB is a limitedmemory quasiNewton method for simple boxconstrained optimization problem. In experiments, to reduce computational complexity, we may further restrict price search space of experience to a smaller range, e.g., where and are estimated by the output from value model. At the end of this process, every experience has its actual price, and a suggested price. In cases where we are not able to provide any suggestion, e.g. experience were never ranked at top in searches, we use the predicted value from VALUE model as the suggested price. In the next section we describe how we use the suggested price and the actual price together with booking information to build a set of metrics for evaluation purpose.
5.3 Metrics
In this section we introduce a set of metrics used in our offline evaluation. Most of our metrics are inspired by previous work on Airbnb dynamic pricing [25] and were adapted to our searchbased methodology. The main assumption is that if an experience is booked after a particular search then the suggested price should have been same or higher than the booked price, otherwise we have “regret", and if it was not booked, it would be better to suggest a lower price.
Let be a generic experience, and be a set of searches, where is a search containing experiences, denotes an experience which got booked during search , denotes the price of experience in search and denotes the suggested price for experience during the test search^{3}^{3}3Note that our suggestion for experience is fixed for the whole test set., we can define our metrics in the following way:

Booking Regret (BR), defined as,
(9) where we first compute the regret of each search as the relative difference between the booked experience price and the suggested price for that experience, and then we get the median over all searches. The intuition is that a good price suggestion method should not suggest a price that is lower than booked price, which hurts the revenue of suppliers. Thus a lower booking regret is an indicator of a better price suggestion strategy. On the other hand, the lower the suggested price, the higher the regret w.r.t. the price that the experience was booked for;

Weighted Booking Regret (), is defined as,
(10) Since booking regret captures the revenue loss w.r.t. the booked price but not the absolute loss of the suppliers, we define to measure the absolute revenue loss;

Price Decrease Recall (PDR), is defined as,
(11) where in the numerator we are considering the experiences that were not booked, and had a lower price suggested than their original price, and the denominator includes all the experiences that were not booked over all searches. The intuition here is that if the experience was not booked, and the price suggestion was higher than the actual price then we have a miss, otherwise we have a hit. Higher PDR is a possible indication of a better price suggestion. However PDR has limitations in the presence of competition, e.g. a properly priced experience may still not get booked when it cooccurs with experiences that are more competitive. Another point is that not all nonbooked experiences during one search have to be sold for the best outcome. To overcome these limitations and have some insights on what each strategy is thinking when it lowers a price, we further defined PDR_HP (high revenue potential) and PDR_LP (low revenue potential), where we compute PDR for the two subsets of nonbooked experiences. In the first case (PDR_HP) we consider only experiences that have a value above the upper quartile of all experiences values, and a conversion rate that is below the lower quartile, despite receiving many impressions. In the second case (PDR_LP) we consider experiences that have a value below the lower quartile, and high conversion rate (above the upper quartile). A good pricing strategy should have PDR_HP that is higher than PDR_LP, indicating it is targeting the high revenue potential experiences.

Revenue Potential (REV_POTENT), is defined as,
(12) where it considers all nonbooked experiences for which we suggested a price that is lower than the actual price, and we want to approximately obtain what would have been the revenue gain if they were booked, due to the adoption of the suggested price. ^{4}^{4}4We adjusted the demand by an elasticity of demand of , that is an increase of for a price drop of . indicates a demand index, which is the probability of an experience getting booked. This will be described in more detail in the next section, where we learned this probability for a comparison with other strategies.

Recall (RECALL), is defined as the percentage of experiences for which the model was able to suggest a price.
5.4 Comparisons
In this section we describe the baselines and related work we used in our offline experiments for comparison to our proposed solution. The Customized Regression Model (CRM) proposed in [25] for determining an optimal price for Airbnb Home rental is the main related work in our comparisons. The CRM method consists of two components: a booking probability model and a pricing strategy layer. The booking probability model is constructed to estimate the demand for a future night at specific prices. The authors recognize the difficulty in using the estimated demand directly in (2) to maximize the revenue, and therefore construct a second strategy layer that maps the booking probability to a price suggestion. We implemented the CRM booking probability model [25] using the same set of features used in our value model (Table 1), plus a pivot price. In contrast to Airbnb Home marketplace where only a single guest can book a single listing night, in the Airbnb Experience marketplace multiple guests can book the same Experience on the same day. Therefore, we needed to adapt the implementation of CRM booking probability model to account for the difference by considering experiences which had at least a single booking as positives and ones which had zero bookings as negatives.
The second component of CRM requires to learn a demand index function , which takes the booking probability as input. To learn , the CRM strategy model adopts a customized loss function, and learns a for each experience. However, our data set has less price dynamics, and thus it was not ideal to learn at the experience level. Therefore, we aggregated the experiences at the market and category level and learned one for each market and category. When CRM is not able to suggest any price, we used the actual price as suggested one.
Baselines. To better monitor the behavior of the set of metrics, we also compare with two baseline pricing strategies. The first strategy prices all products at zero (ZERO), and the second strategy (AVG) uses the average booked price observed in the training set as a suggested price.
6 Results
position  Experience Title  VALUE  REV_MAX  price  CRM 

A Potter’s Wheel in Brooklyn  
Sailing Tour of New York and Brooklyn  
Rooftop yoga, massage and snacks  
New NYC’s #1 Rooftop Parties Tour  
Hasidic Brooklyn  
Play & cuddle with cats and kittens  
Brooklyn Bridge photoshoot  
The Upper West Side Bookstore Crawl  
Chinatown and Little Italy Tour  
See 30+ Top New York Sights Fun Guide  
Taste of NYC Helicopter Tour 
In this section we present the experimental results which compare our proposed methodology to the baselines and related work. Table 3 reports an example of top results appearing during one search event, with the title of the experience, the actual price shown to the user, and the ranking position. We report the results of the VALUE model for each experience as well as REV_MAX and CRM suggested price for that experience. We can observe that different pricing strategies priced the experiences quite differently. In this example, the booked experience was ranked at position , and both VALUE model and REV_MAX strategy increased its calendar price, while CRM reduced its price. Compared to VALUE, if a nonbooked experience has a relatively high predicted value (e.g. helicopter tour), then the REV_MAX strategy tends to decrease its predicted value to improve its bookings, as this experience has a higher revenue potential.
Figure 2 plots the distribution of suggested prices from different strategies. We can observe that REV_MAX strategy has similar distribution to value model, both of them are more centralized and have lighter tails than the CRM and actual price. CRM has the trend to shift the prices to the left, which may increase bookings at the cost of worse booking regret and booking values.
RECALL  BR  BR_w  PDR  REV_POTENT  

REV_MAX  
VALUE  
CRM  
ZERO  
AVG  # 
Table 4 report results for New York’s Airbnb Experiences market. Results suggest that our new pricing strategy is able to make suggestions for most of experiences in test set (> 99%). Compared to CRM model, REV_MAX strategy decreases BR and BR_w by and , respectively. REV_MAX strategy also has a higher revenue potential than CRM. Compared with VALUE model, REV_MAX improves BR and BR_w by and , respectively. Since there is a tradeoff between BR and PDR, REV_MAX decreases PDR of VALUE model. In terms of revenue maximization, we attach more importance to lower BR and BR_w than to a higher PDR. The baseline strategies, ZERO and AVG, perform very well in some metrics but fail for the others, which demonstrates a tradeoff among these metrics and the importance of evaluating using the set of metrics in its entirety. In terms of PDR, CRM has higher PDR than REV_MAX.
PDR  PDR_HP  PDR_LP  PDR_HP/PDR_LP  

REV_MAX  
VALUE  
CRM  
ZERO  
AVG 
To overcome the limitation of PDR as described in Section 5.3, in Table 5 we report the result for New York market with the ratio between PDR_HP and PDR_LP (PDR_HP/PDR_LP). A higher ratio indicates a better pricing strategy. We can see that REV_MAX outperforms CRM and baselines. CRM has a higher overall PDR, yet there is no big difference between PDR_HP and PDR_LP; In contrast, REV_MAX and VALUE have much higher PDR_HP than PDR_LP, and consequently result in a better PDR_HP than CRM. This implies that non booked experiences which have large room for improvement in terms of revenue contribution have had a lower price suggested, and thus by decreasing the price to improve their bookings, they have a high potential to boost the revenue.
We conducted experiments in top Airbnb Experience markets and summarized the averaged results in Table 6^{5}^{5}5For confidentiality we removed the recall of the AVG strategy.. For Data set 1, result suggests that our new pricing strategy improves BR by and BR_w by of VALUE model, at a cost of decreasing the overall PDR by . Compared with CRM, REV_MAX lowers the BR and BR_w by and , respectively. To investigate PDR, we report the ratio between PDR_HP and PDR_LP for our data sets in Table 7. We can observe that though CRM has a higher overall PDR, REV_MAX strategy and VALUE are able to target more accurately the experiences that have a large revenue potential, i.e., larger PDR_HP compared to PDR_LP, and thus both have a higher PDR_HP/PDR_LP than that of CRM. In terms of revenue potential, our new strategy has comparable performance with the value model, and both outperform other strategies. The comparison results for Data set 2 are similar.
RECALL  BR  BR_w  PDR  REV_POTENT  
Data set  
REV_MAX  
VALUE  
CRM  
ZERO  
AVG  #  
Data set  
REV_MAX  
VALUE  
CRM  
ZERO  
AVG  #  # 
PDR  PDR_HP  PDR_LP  PDR_HP/PDR_LP  
Data set  
REV_MAX  
VALUE  
CRM  
ZERO  
AVG  
Data set  
REV_MAX 
0.49  0.59  0.37  1.59 
VALUE  0.52  0.70  0.41  1.68 
CRM  0.66  0.63  0.57  1.10 
ZERO  1.00  1.00  0.99  1.00 
AVG  0.24  0.21  0.23  0.92 
7 Conclusions and future work
In this paper, we propose a new pricing strategy that aims to maximize revenue for Airbnb Experiences Marketplace using search results. We started from a simple idea that when users are looking for items in a marketplace they typically search for it. The top ranked items shown to the user are therefore "competing" with each other for purchases.
We found that the algorithmic solution proposed in previous work [5] is not applicable to the realworld scenario. We proposed a practical solution to maximize the revenue for a unitdemand, single seller, multidimensional pricing problem in the context of search. Our unique input to the algorithm is a learned distribution of value for each item, and the set of top ranking items on search page. We then aggregate the best price for items found during search events and come up with the best price for each item. To reduce computation complexity of the proposed solution, we restrict the price space as well as the support of value distributions, and establish a theoretical bound on the revenue loss incurred by such restrictions. We conducted comprehensive offline evaluations to demonstrate the performance of the proposed strategy. Results using two realworld search data sets show that our pricing strategy outperforms related work. For future work, we would like to find more effective ways to aggregate optimal prices obtained from different search results, try different value models, and extend the work to other contexts. We also plan to conduct online experiments to further demonstrate the effectiveness of our pricing model.
References
 [1] (2015) Demand estimation with machine learning and model combination. Technical report National Bureau of Economic Research. Cited by: §2, §3.
 [2] (2010) Budget constrained auctions with heterogeneous items. In Proceedings of the fortysecond ACM symposium on Theory of computing, pp. 379–388. Cited by: §2.
 [3] (2012) An algorithmic characterization of multidimensional mechanisms. In Proceedings of the fortyfourth annual ACM symposium on Theory of computing, pp. 459–478. Cited by: §2.
 [4] (2012) Optimal multidimensional mechanism design: reducing revenue to welfare maximization. In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pp. 130–139. Cited by: §2.
 [5] (2015) Extreme value theorems for optimal multidimensional pricing. Games and Economic Behavior 92, pp. 266–305. Cited by: §2, §3, §3, §4.3, §4, §7.
 [6] (2007) Algorithmic pricing via virtual valuations. In Proceedings of the 8th ACM conference on Electronic commerce, pp. 243–251. Cited by: §2, §3.
 [7] (2010) Multiparameter mechanism design and sequential posted pricing. In Proceedings of the fortysecond ACM symposium on Theory of computing, pp. 311–320. Cited by: §2.
 [8] (2015) Recent developments in dynamic pricing research: multiple products, competition, and limited demand information. Production and Operations Management 24 (5), pp. 704–731. Cited by: §2.
 [9] (2016) Xgboost: a scalable tree boosting system. In Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining, pp. 785–794. Cited by: §4.1.
 [10] (2017) Consumer valuation of airbnb listings: a hedonic pricing approach. International journal of contemporary hospitality management 29 (9), pp. 2405–2424. Cited by: §2.
 [11] (2007) An overview of research on revenue management: current issues and future research. International journal of revenue management 1 (1), pp. 97–128. Cited by: §2.
 [12] (2015) Dynamic pricing and learning: historical origins, current research, and new directions. Surveys in operations research and management science 20 (1), pp. 1–18. Cited by: §2.
 [13] (2011) Demand learning and dynamic pricing under competition in a statespace framework. IEEE Transactions on Engineering Management 59 (2), pp. 240–249. Cited by: §2.
 [14] (2009) Dynamic pricing and inventory control of substitute products. Manufacturing & Service Operations Management 11 (2), pp. 317–339. Cited by: §2.
 [15] (2017) Approximate revenue maximization with multiple items. Journal of Economic Theory 172, pp. 313–347. Cited by: §2.
 [16] (2005) Nearoptimal pricing in nearlinear time. In Workshop on Algorithms and Data Structures, pp. 422–431. Cited by: §3.
 [17] (2017) Optimization beyond prediction: prescriptive price optimization. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1833–1841. Cited by: §2.
 [18] (2014) Demand models for the static retail price optimization problema revenue management perspective. In 4th Student Conference on Operational Research, Cited by: §2.
 [19] (2018) Pricing strategies on airbnb: are multiunit hosts revenue pros?. International Journal of Hospitality Management. Cited by: §2.
 [20] (1989) On the limited memory bfgs method for large scale optimization. Mathematical programming 45 (13), pp. 503–528. Cited by: §5.2.
 [21] (2005) Pricing and revenue optimization. Stanford University Press. Cited by: §2.
 [22] (2006) The theory and practice of revenue management. Vol. 68, Springer Science & Business Media. Cited by: §2.
 [23] (2009) Dynamic pricing and revenue management process in internet retailing under uncertainty: an integrated real options approach. Omega 37 (2), pp. 471–481. Cited by: §2.
 [24] (2017) Robust quadratic programming for price optimization.. In IJCAI, pp. 4648–4654. Cited by: §2.
 [25] (2018) Customized regression model for airbnb dynamic pricing. In Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 932–940. Cited by: §1, §2, §5.3, §5.4.
 [26] (2010) Revenue management: a practical pricing perspective. Springer. Cited by: §2.
 [27] (2017) The rise of the sharing economy: estimating the impact of airbnb on the hotel industry. Journal of marketing research 54 (5), pp. 687–705. Cited by: §2.
 [28] (1997) Algorithm 778: lbfgsb: fortran subroutines for largescale boundconstrained optimization. ACM Transactions on Mathematical Software (TOMS) 23 (4), pp. 550–560. Cited by: §5.2.