Surge Pricing and Its Spatial Supply Response

Using Prices to Spatially Match Supply and Demand 

Ride-hailing platforms have brought forward a new business model, along with a host of new operational challenges. Among them lies spatial frictions: supply (drivers) and demand (customers) are dispersed across a geographical area. This spatial dispersion introduces missed opportunities leading to lower consumer surplus, lower driver surplus and lower profits for the platforms.  These frictions are further exacerbated by the fact that drivers are typically independent agents, who can choose where to operate within their cities---the current norm at many platforms, including Uber, Lyft and Didi.  While this operating model has its advantages, such as offering drivers more control, it also implies that drivers cannot be directed to where the platform believes they are needed, unless they are properly incentivized to do so. In “Surge Pricing and Its Spatial Supply Response” (Management Science 2021), Omar Besbes, Francisco Castro and Ilan Lobel explore the general problem of spatial pricing: how should a platform optimally price to maximize revenues while appropriately incentivizing drivers to potentially reposition across the city.

As an example, consider a situation in which there is a demand surge in parts of the city while most drivers are located elsewhere in the city. A natural response would be for the platform to raise prices (and driver wages) in those locations. Such a price increase would have two effects. The first effect is a demand-side one: some fraction of the riders at the locations with excess demand would exit the system rather than pay a higher fare. The second effect is a supply-side one: drivers throughout the city may find the locations with high prices more attractive than the ones where they are currently located and may decide to relocate. While the demand effect is a local effect, and thus easier to manage, the supply effect is global in nature, and might, for example, create a deficit of drivers at some locations that were originally well-supplied. In other words, prices set in one region of a city impact demand and supply in this region, but also potentially impact supply globally. Therefore, prices must be optimized jointly, rather than set independently for different locations.

The paper by Besbes, Castro and Lobel analyzes the optimization of spatial pricing policies when supply units are strategic. The authors develop a two-dimensional spatial framework in which a platform selects prices for different locations, and drivers respond by choosing where to relocate, in equilibrium, based on prices, travel costs and driver congestion levels. Through this model, the authors uncover how changes in prices in one location propagate to other regions of a city and what are the implications for the platform’s pricing problem.

In technical terms, analyzing the spatial pricing problem is intricate as the problem turns out to be an optimal transport problem (deciding how to reallocate drivers throughout a city), but with a target distribution that is itself endogenous. That is, while in classical optimal transport theory the origin and final distributions are given, in the spatial pricing problem the final distribution of drivers across locations is not given and must be optimized. The authors show that both prices and the final distribution of drivers can, ultimately, be found by solving a collection of capacitated knapsack problems. Given this, the equilibrium flow (relocation) of drivers corresponds to the solution of an optimal transport problem. 

Managerial Implications

Most ride-hailing platforms divide cities into small regions (e.g., hexagons) over which supply and demand conditions are aggregated. In its original form, surge pricing algorithms would optimize the conditions within each small region in isolation. The first important message of the paper is that such myopic or hyper-local pricing can lead to poor performance. The problem is that while optimizing locally can improve local performance, it ignores the spatial externalities caused by driver relocation. The paper argues that it is crucial for the platform to consider a global optimization that accounts for how incentives propagate across the city. By properly pricing a set of regions synchronously the platform cannot only boost revenues in those regions but also incentivize the proper repositioning of drivers towards other, more profitable, locations.  

The authors establish that the optimal spatial pricing can be found using a form of spatial decomposition into regions where driver movements occur, which they call “attraction regions.”. This provides a semi-local description of optimal pricing policies, with no drivers being encouraged to move between different attraction regions. Within these attraction regions, the platform designs its spatial pricing policy to attract drivers toward more profitable locations. The attraction regions cannot be managed completely independently, though. The platform still needs to ensure that drivers that are at a border between two attraction regions are properly incentivized not to move between regions. With the appropriate coupling of the regions, the platform can construct an optimal global spatial policy.

A striking result from the paper is that the optimal pricing policy may not only induce movement towards the more profitable regions for the platform such as concert venues or airports but potentially also away from those regions.  Consider, for example, a concert venue where there is a big need for drivers. If the platform merely raises prices in the venue area, it might not attract enough drivers. To attract enough drivers to the venue, the platform also needs to make other places in the city less attractive. However, drivers in these disincentivized regions have an option: instead of driving toward the concert, they could drive away from it. To sufficiently incentivize these drivers to drive to where they are needed, the platform is forced to make conditions in those further away regions worse too. This has the surprising effect of incentivizing the repositioning of drivers in the further away region in the opposite direction from the concert venue. What this means is that optimal spatial pricing can behave in fairly counterintuitive ways.

Practitioners in the ride-hailing industry have relied heavily on localized pricing policies. The main reason for this is that these policies are not only simple to understand but also are straightforward to implement. The paper by Besbes, Castro and Lobel advocates for the development of network pricing policies that account simultaneously for city-wide supply demand imbalances and drivers’ incentives. The results in this paper highlight that a global pricing policy can generate significantly better performance than a heuristic that would simply respond locally to demand variations. In other words, anticipating the global supply response and taking advantage of the full flexibility of spatial pricing are key to improving performance.

Read the full article at: https://doi.org/10.1287/mnsc.2020.3622.

Reference

Besbes O, Castro F, Lobel I (2021). Surge Pricing and Its Spatial Supply Response. Management Science 67(3):1350-1367.

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