Pricing algorithms work best slow or fast depending on market rivalry
Delegate Pricing to Algorithms: When Slow and Steady Wins the Race
Computer Science and Game Theory
Summary
This paper looks at how companies choose the speed of their pricing algorithms when competing continuously over time. The researchers found two key cases: when companies’ prices push each other in opposite directions, it's best to use fast algorithms to quickly gain advantage. But when prices encourage companies to match each other, slower algorithms are better because rushing leads to quick competition and less profit. So companies can benefit by deliberately designing slower pricing strategies in certain competitive situations.
What this means in practice
- •For online retailers: Design pricing algorithms that intentionally slow down updates to maintain profit margins in competitive markets with matching price incentives.
- •For energy market operators: Set algorithm speeds for price bidding that account for whether competitors’ reactions slow or accelerate market price changes.
Authors
Galit Ashkenazi-Golan, Edward Plumb, Clemens Possnig, Yufei Zhang
Abstract
We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, firms unambiguously prefer the fastest possible algorithms to rapidly exploit a gradually adjusting opponent. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a strictly dominant action in the underlying stage game, we prove that firms optimally design sluggish algorithms, extracting surplus during a prolonged convergence to the competitive equilibrium.