Delegate Pricing Decisions to an Algorithm? Experimental Evidence

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.

• The paper demonstrates that algorithmic pricing, when adopted endogenously, disrupts sustained collusion in repeated duopoly experiments.
• It employs a Q-learning algorithm with override features to show that while override capability increases adoption, it simultaneously undermines long-term collusive behavior.
• The findings highlight coordination failures and strategic deviations that lead to declining prices and more competitive market outcomes over time.

Experimental Evidence on Delegating Pricing Decisions to Algorithms

Introduction

This paper investigates the strategic and behavioral dimensions of delegating pricing decisions to self-learning algorithms in repeated Bertrand duopoly experiments. Unlike prior work that treats algorithm adoption as exogenous, the study endogenizes adoption, allowing participants to choose whether to delegate pricing to a collusive Q-learning algorithm or retain manual control. The experiment contrasts three treatments: Baseline (manual pricing), Outsourcing (full delegation to the algorithm), and Recommendation (algorithmic suggestions with override capability). The central research questions concern the determinants of algorithm adoption, the impact of override capability on adoption rates, and the effect of algorithmic pricing on market outcomes when adoption is endogenous.

Experimental Design

The market environment consists of two firms producing a homogeneous good with perfectly inelastic demand from 60 consumers, each willing to pay up to 4 units per round. Firms select integer prices from 0 to 5, with the lowest price capturing the market. The repeated game structure employs a 95% continuation probability, ensuring a high likelihood of indefinite interaction and supporting the possibility of tacit collusion.

Treatments are defined as follows:

• Baseline: No algorithmic support; participants set prices manually.
• Outsourcing: Participants may delegate all pricing decisions to the algorithm for the duration of a supergame.
• Recommendation: Participants may receive algorithmic price recommendations but can override them in each round.

The Q-learning algorithm is pre-trained via self-play to implement a win-stay lose-shift (WSLS) strategy, colluding at the monopoly price (4) and punishing deviations with a one-period Nash equilibrium price (1). The algorithm does not learn during the experiment, reflecting practical deployment scenarios.

Algorithm Adoption Dynamics

Participants exhibit substantial algorithm adoption, with rates ranging from 45% to 86% across treatments and supergames. Adoption is consistently higher in Recommendation than Outsourcing, confirming that override capability increases willingness to delegate. However, adoption rates decline over time in both treatments, indicating dynamic reassessment of algorithmic value as participants gain experience.

Figure 1: Algorithm adoption rates across supergames, showing higher adoption in Recommendation and a declining trend over time.

Market composition analysis reveals that fully algorithmic markets (AA) are more prevalent in Recommendation, while mixed human-algorithmic markets (AH) dominate in Outsourcing. Belief elicitation demonstrates that participants can accurately infer their opponent's adoption decision, with higher accuracy in Outsourcing.

Figure 2: Distribution of market types (AA, AH, HH) across treatments and supergames, highlighting the prevalence of mixed markets in Outsourcing and fully algorithmic markets in Recommendation.

Market Price Outcomes

Contrary to the hypothesis that algorithmic pricing would raise market prices, the results show that prices in both algorithmic treatments decline over time and are ultimately lower than in Baseline. In the initial supergame, Outsourcing yields higher prices than Baseline, but this effect reverses in later supergames. Recommendation consistently produces lower prices than Baseline.

Figure 3: Average market price across supergames, illustrating the decline in algorithmic treatments and the upward trend in Baseline.

First-round prices are higher in algorithmic treatments due to the algorithm's collusive recommendations, but these prices rapidly decline in subsequent rounds, especially in Recommendation. The difference between first and second round prices is negligible in Baseline but substantial in algorithmic treatments.

Figure 4: Average first round market price $P_1$ and difference between second and first round $\Delta P_{2-1}$, showing rapid price declines in algorithmic treatments.

Analysis of joint monopoly pricing outcomes reveals that Baseline participants learn to coordinate on collusive prices over time, while algorithmic treatments fail to sustain such coordination, with Recommendation exhibiting a decline in collusive outcomes.

Figure 5: Frequency of joint monopoly pricing outcomes ($p_1 = p_2 = 4$) in the first three rounds of Supergames 1 and 5, by treatment.

Mechanisms Driving Market Outcomes

Coordination Failure in Algorithm Adoption

Coordination failure at the adoption stage leads to heterogeneous market compositions and distinct pricing outcomes. In Outsourcing, AA markets achieve monopoly pricing, but mixed markets experience cyclic deviation strategies, where non-adopters undercut the algorithm, triggering punishment and reducing profits for adopters. This dynamic discourages further adoption and drives prices downward.

Failure to Follow Algorithmic Recommendations

In Recommendation, participants frequently override algorithmic suggestions, especially during punishment phases, resulting in prolonged punishment and sustained downward price pressure. Deviations from recommendations are asymmetric, with downward deviations from collusive prices ($p=4$) and upward deviations from punishment prices ($p=1$) being common.

Figure 6: Adherence and deviations by type of algorithmic recommendations, showing frequent overrides and asymmetric deviation patterns.

Implications and Theoretical Considerations

The findings challenge the assumption that algorithmic pricing necessarily facilitates collusion. When adoption is endogenous and humans retain control, even highly collusive algorithms can foster competition rather than collusion. Behavioral factors such as algorithm aversion, strategic undercutting, and spite play a critical role in shaping market outcomes. The results underscore the importance of modeling human-algorithm interaction and endogenous adoption in theoretical and empirical analyses of algorithmic pricing.

Conclusion

The study demonstrates that the availability of a collusive pricing algorithm does not guarantee higher market prices when adoption is a strategic choice. Override capability increases adoption but also enables frequent deviations that undermine collusion. In both full delegation and recommendation settings, prices decline over time, and by the final supergame, algorithmic treatments yield more competitive outcomes than human-only markets. These results highlight the necessity of incorporating human behavioral dynamics into models of algorithmic pricing and caution against overestimating the anti-competitive risks of algorithmic collusion in real-world markets. Future research should further explore the interplay between human oversight, algorithm aversion, and strategic interaction in hybrid human-algorithm environments.