The Mathematics Behind Dynamic Pricing Algorithms and its Economic Relevance

Several weeks ago, DJ star Fred Again came to the State Farm Arena for his first-ever show in Atlanta. Several friends and I had nothing planned that night, and so we checked a popular platform, Seatgeek, to check ticket prices. At 10 a.m. the day of, tickets for the floor seats were $100. My friends and I thought, “That’s pretty expensive. Ticket prices will probably go down, though, since there seems to be plenty available right now.” We checked at 12:30 p.m. — $93. Not a significant amount of movement, but something. We checked again at 4 p.m. — $75. “Tickets are still pretty expensive, but $25 off isn’t bad. Going to Fred Again would be a once-in-a-lifetime experience, and I can only imagine prices will continue to go down.” At 9 p.m., before we headed over to the venue, prices were $46. I was starting to think they would practically be handing out tickets for free by the time I arrived. I showed up to the arena at 9:30 p.m., refreshed my Seatgeek page, and read $145.

What my friends and I had tried and failed to do was predict the dynamic pricing algorithms used by Seatgeek. Dynamic pricing is the tool all sorts of platforms use to maximize profits. The basic idea is that prices of a product will vary at different times depending on fluctuating customer demand as well as several other factors to optimize profits (Flipkart Commerce, 2023). Many types of businesses use dynamic pricing models  — airlines, rideshare apps, hotel chains, retailers, etc.

Dynamic pricing has massive economic impacts on both consumers and businesses. Some argue that dynamic pricing squeezes consumers, and that it leads to reduced customer loyalty (Dublino, 2023). On the other hand, according to one study from the National Bureau of Economic Research, “when aggregated over markets, welfare is higher under dynamic pricing than under uniform pricing” (Williams, 2021). We can get insights into dynamic pricing from taking a high level view of the math and algorithms behind it.

Dynamic pricing algorithms are typically functions of several variables: production costs, market trends, customer behavior, and even substitute or competitor prices (Dilmegani, 2021). In today’s market, machine learning and artificial intelligence are heavily utilized in dynamic pricing algorithms (Dilmegani, 2021). The simple, yet fundamental idea behind determining at which price companies should sell a good is as follows:

This equation describes how companies try to set their price in such a way that it maximizes profit. 

In a Bayesian model, for example, density models are used to calculate the probability of different demand scenarios at various prices based on the available data. The model then uses these different demand values to determine the profit-maximizing price. Such an algorithm would use historical pricing and demand information, all critical data in training a dynamic pricing model (Azaria, 2023). 

Another algorithm is called the decision tree model, where the possible consequences of pricing decisions are displayed in a tree-like manner. In this model, different parameters are altered and these alterations’ effects are displayed to help predict a price range most suitable for the company’s goals (Dilmegani, 2021).

Dynamic pricing is applied all around us, from Uber rides to the airport to the shifting prices of products on Amazon. With the prevalence of these algorithms and pricing strategies, it is important for us as consumers to understand how machine learning and math is applied to these algorithms. Those Fred Again tickets I tried to buy could have drastically increased for a multitude of reasons such as demand rising due to other stragglers like me or Seatgeek’s models predicting that demand would become less elastic over time.

Edited by Sherry Cai

References

Azaria, N. (2023). Dynamic Pricing models: Types, algorithms, and best practices. Aporia. https://www.aporia.com/learn/machine-learning-for-business/dynamic-pricing-models-types-algorithms-and-best-practices/

Dilmegani, C. (2021). Dynamic Pricing Algorithms: In-Depth Guide With 3 Models. Research.aimultiple.com. https://research.aimultiple.com/dynamic-pricing-algorithm/

Dublino, J. (2023). What Is Dynamic Pricing & How Does It Affect Ecommerce? Business.com; business.com. https://www.business.com/articles/what-is-dynamic-pricing-and-how-does-it-affect-ecommerce/

Flipkart Commerce. (2023). Dynamic Pricing Algorithm: How it works? Flipkart Commerce Cloud. https://www.flipkartcommercecloud.com/dynamic-pricing-algorithm/

Williams, K. (2021). The Welfare Effects of Dynamic Pricing: Evidence from Airline Markets. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3880222

Pines, T. (n.d). The Figures : Budgeting [Pigment, vintage paper, and cotton thread on rice paper]. Flickr. https://www.flickr.com/photos/tsillipines/3998940133/