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Delegate Pricing Decisions to an Algorithm? Experimental Evidence

Hans-Theo Normann, Nina Rulié, Olaf Stypa, Tobias Werner

TL;DR

This paper tackles whether firms should delegate pricing to a self-learning algorithm in a repeated Bertrand setting and how endogenous adoption and control affect outcomes. It uses three treatments—Baseline, Outsourcing, and Recommendation—with a fixed Q-learning pricing agent trained in self-play to implement a WSLS-like strategy, and where adoption decisions are made at the start of each supergame. The key finding is that adoption is substantial and higher when override is allowed, yet prices generally decline over time in the algorithmic treatments, and by the final supergame Baseline prices exceed those with algorithm use, indicating that human oversight can suppress algorithmic collusion. Overall, the results highlight the importance of endogenizing adoption and human factors, showing that algorithms do not automatically raise prices and can even enhance competition in mixed human–machine environments.

Abstract

We analyze the delegation of pricing by participants, representing firms, to a collusive, self-learning algorithm in a repeated Bertrand experiment. In the baseline treatment, participants set prices themselves. In the other treatments, participants can either delegate pricing to the algorithm at the beginning of each supergame or receive algorithmic recommendations that they can override. Participants delegate more when they can override the algorithm's decisions. In both algorithmic treatments, prices are lower than in the baseline. Our results indicate that while self-learning pricing algorithms can be collusive, they can foster competition rather than collusion with humans-in-the-loop.

Delegate Pricing Decisions to an Algorithm? Experimental Evidence

TL;DR

This paper tackles whether firms should delegate pricing to a self-learning algorithm in a repeated Bertrand setting and how endogenous adoption and control affect outcomes. It uses three treatments—Baseline, Outsourcing, and Recommendation—with a fixed Q-learning pricing agent trained in self-play to implement a WSLS-like strategy, and where adoption decisions are made at the start of each supergame. The key finding is that adoption is substantial and higher when override is allowed, yet prices generally decline over time in the algorithmic treatments, and by the final supergame Baseline prices exceed those with algorithm use, indicating that human oversight can suppress algorithmic collusion. Overall, the results highlight the importance of endogenizing adoption and human factors, showing that algorithms do not automatically raise prices and can even enhance competition in mixed human–machine environments.

Abstract

We analyze the delegation of pricing by participants, representing firms, to a collusive, self-learning algorithm in a repeated Bertrand experiment. In the baseline treatment, participants set prices themselves. In the other treatments, participants can either delegate pricing to the algorithm at the beginning of each supergame or receive algorithmic recommendations that they can override. Participants delegate more when they can override the algorithm's decisions. In both algorithmic treatments, prices are lower than in the baseline. Our results indicate that while self-learning pricing algorithms can be collusive, they can foster competition rather than collusion with humans-in-the-loop.

Paper Structure

This paper contains 27 sections, 19 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Experimental design
  3. Market game and equilibria
  4. Treatments
  5. Algorithm
  6. Procedures
  7. Hypotheses
  8. Results
  9. Algorithm adoption
  10. Prices
  11. Market prices across supergames and treatment comparison
  12. Market prices in the initial periods
  13. Discussion
  14. Coordination failure at the stage of algorithm choice
  15. Failure to collude in Outsourcing
  16. ...and 12 more sections

Figures (19)

  • Figure 1: Algorithm adoption rates across supergames.
  • Figure 2: Distribution of market types across treatments and supergames. AA refers to fully algorithmic, AH to mixed human-algorithm, and HH to fully human markets.
  • Figure 3: Average market price across supergames
  • Figure 4: Average first round market price $P_1$ and difference between second and first round $\Delta P_{2-1}$
  • Figure 5: Frequency of joint monopoly pricing outcomes ($p_1 = p_2 = 4$) in the first three rounds (I, II, III) of Supergames 1 (solid bars) and 5 (hatched bars), by treatment.
  • ...and 14 more figures