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Trusting AI in Competitive Markets

Jussi Keppo, Yuze Li, Gerry Tsoukalas, Nuo Yuan

arXiv:2608.26539v1cs.GT

TL;DR

The paper examines why AI pricing recommendations produce divergent outcomes across gender compositions and how sellers’ adherence changes with profits. It reports composition-specific associations between profit and subsequent AI adherence, while noting limitations in the recommendation’s presentation.

  • Problem

    What governs people’s choice to follow AI advice repeatedly is not fully understood.

  • Method

    An experiment tests predictions about AI pricing recommendations in strategic groups, linking sellers’ attribution of outcomes to subsequent adherence.

  • Results

    AI pricing recommendations significantly raise prices and profits in female-only clusters but have no significant effect in male-only or mixed-gender clusters, with opposite profit-adherence associations across compositions.

  • Takeaways & Limitations

    AI pricing recommendations can produce divergent market outcomes across gender compositions, with adherence patterns consistent with coordination-sustaining or coordination-breaking dynamics.

  • Takeaways & Limitations

    The treatment presents the AI recommendation as a bare number with no rationale.

Abstract

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Problem definition: People's trust in AI advice diverges as they use it, deepening for some and eroding for others. We study this divergence in oligopoly pricing, where advice cannot prove itself: rivals' responses decide whether it pays off. Methodology/results: In a laboratory experiment, 273 sellers compete across 91 three-seller markets over 30 rounds; we vary the presence of AI pricing recommendations and the gender composition of the market (female-only, male-only, or mixed). We find that the gender composition of the market shapes how sellers learn from the advice, and where prices settle as a result. In female-only markets, recommendations raise prices by 29% and profits by 39%; in male-only and mixed-gender markets, they have no significant effect. A Non-Homogeneous Hidden Markov Model reveals a composition-specific dynamic association: profitable rounds predict rising adherence to the AI in female-only markets and declining adherence otherwise, a pattern consistent with learned trust and self-serving attribution. The pattern reverses what recent evidence on gender and AI would predict. Managerial implications: We discuss implications for platform governance and regulatory oversight, which should focus not only on the algorithm but on the human side that shapes its effects.

1 Introduction

The paper studies how sellers’ reliance on AI pricing advice evolves in strategic markets, finding that gender composition shapes both adherence and market outcomes. In female-only markets, sellers coordinate on supra-competitive recommendations, whereas male-only and mixed-gender markets do not.

  • Research problem: Repeated pricing makes AI advice’s success depend on rivals’ strategic responses and creates feedback between sellers’ interpretations, adherence, and market outcomes.A profitable outcome can be attributed to the AI or to personal judgment, changing subsequent adherence and rivals’ earnings.
  • Approach: The experiment randomizes market gender composition and follows sellers’ reliance on AI recommendations round by round in repeated three-seller pricing markets.Markets use a repeated Bertrand game with differentiated products and vary AI presence and female-only, male-only, or mixed-gender composition.
  • Implications: The paper argues that supra-competitive coordination is a property of the coupled human–AI system, because market composition shapes the feedback paths and outcomes of the same algorithm.It therefore frames adherence elicited by the algorithm, alongside algorithm-side oversight, as a relevant governance concern.
  • AI recommendations: The AI recommends prices averaging 52% above static Nash equilibrium, providing similar supra-competitive price signals to sellers within each market.Recommendations are tightly clustered, with a within-round range of only $0.18.
  • Market outcomes: 29% higher average market prices and 39% higher aggregate cluster profits occur in female-only markets with AI recommendations, with effects sustained across rounds.The pooled price increase is driven entirely by female-only markets; male-only and mixed-gender markets show no significant price or profit effect.
  • Reliance dynamics: Profitable rounds predict stronger AI adherence in female-only markets but weaker adherence in male-only and mixed-gender markets.Female-only markets show convergence toward the AI’s supra-competitive recommendation, while other compositions show subsequent deviation and possible coordination unravelling.

2 Experimental Design

The experiment places three sellers in repeated differentiated-product Bertrand markets, varying AI pricing recommendations and gender composition while keeping participants unaware of their competitors’ identities and composition. Sellers receive market feedback each round and compete for cumulative profit under either control or AI-assisted pricing.

  • Market Environment: 273 participants compete in repeated three-seller differentiated-product Bertrand markets with simultaneous pricing and uncertain game length.Each seller has marginal cost c = 1.0 and earns profit from its price and market share.
  • Market Environment: Demand follows a multinomial logit model in which lower prices attract more demand without capturing the entire market.Market share depends on the price vector and differentiation parameters a = 2.0, a0 = 0.0, and µ = 0.25.
  • Market Environment: Prices are evaluated against a Bertrand-Nash benchmark of p∗ = 1.37 and a joint-monopoly benchmark of pm = 2.00.Prices above p∗ and approaching pm indicate supra-competitive pricing.
  • Experimental Design: The between-subjects design crosses AI recommendations with female-only, male-only, and mixed-gender market compositions.AI treatment is randomized across sessions and composition-specific effects are estimated separately before being contrasted.
  • Treatment Conditions: Control participants price independently, whereas treatment participants receive one AI-generated price each round and may follow, partially follow, or ignore it.The disclosed AI source is GPT-5 mini; recommendations are shown without rationale and cannot be queried or modified.
  • Treatment Conditions: The adaptive recommendation uses each market’s pricing history and the same information set available to human participants, without revealing individual competitor prices or profits.The prompt asks the LLM to maximize long-run profit and excludes benchmark information or coordination instructions.

3 Data and Empirical Strategy

The study uses 273 participants in 91 three-seller clusters over 30 rounds, with AI treatment and gender composition varying across the experimental design. It estimates effects on cluster prices and profits and models individual adherence dynamics.

  • Data: Participants were predominantly Asian, had a mean age of 21.5 years, and 67.8% majored in business administration or economics.
  • Data: 273 participants formed 91 three-seller clusters, each playing 30 rounds.
  • Data: 2,430 valid cluster-round observations came from 30 female-only, 30 male-only, and 31 mixed-gender clusters.
  • Empirical strategy: The analysis models cluster average price and aggregate profit using treatment, composition indicators, controls, and round fixed effects.
  • Empirical strategy: A Non-Homogeneous Hidden Markov Model characterizes individual adherence through latent high- and low-adherence states and outcome-driven transitions.

4 Results

AI recommendations consistently favor supra-competitive prices and become increasingly aligned across sellers, but their market effects diverge sharply by gender composition. Prices and profits rise significantly in female-only markets, while effects are absent or transient in male-only and mixed-gender markets.

  • AI recommendation characteristics: $2.08 mean recommendations were roughly 52% above the $1.37 Nash equilibrium.Every recommendation in the experiment-relevant window exceeded Nash.
  • AI recommendation characteristics: The AI’s recommendations were aligned across sellers, with a $0.18 mean within-round price range and temporal spread falling from $0.17 to $0.06.The decline compares rounds 1–10 with rounds 21–30.
  • AI recommendation characteristics: 84.7% of treatment seller-rounds received recommendations above Nash, while 73.2% of cluster-rounds gave all three sellers supra-Nash recommendations.Treatment recommendations averaged $1.84, a 34% premium over Nash.
  • Treatment effects by composition: 29% higher prices and 39% higher profits occurred in female-only clusters receiving AI recommendations.The corresponding estimated effects were $0.447 for price and $0.173 for aggregate profit.
  • Treatment effects by composition: Male-only clusters showed no significant price or profit effects, and mixed-gender clusters showed no significant effect on either outcome.Male-only estimates were -0.026 for price and 0.035 for profit; mixed-gender estimates were 0.020 and -0.020.
  • Treatment effects by composition: Female-only treatment effects persisted across all phases, whereas male-only effects remained negligible and mixed-gender effects vanished after the first phase.Female-only price effects were +$0.54, +$0.41, and +$0.37 across successive phases.

5 Discussion

AI recommendations produce divergent market outcomes across gender compositions: they raise prices and profits in female-only markets but not in male-only or mixed-gender markets. Opposite profit-adherence dynamics and source-specific rationales are consistent with learned trust in female-only markets and self-serving attribution in male-only markets, while the findings are bounded by the controlled setting and passive, explanation-free AI interface.

  • Divergent market outcomes: AI recommendations significantly raise prices and profits in female-only clusters but have no significant effect in male-only or mixed-gender clusters.The paper describes the pooled price effect as driven entirely by female-only markets.
  • Divergent market outcomes: Higher profit predicts stronger subsequent AI adherence in female-only markets but weaker adherence in male-only markets.These opposite associations are consistent with coordination-sustaining and coordination-breaking dynamics, respectively.
  • Behavioral mechanisms: In female-only markets, profitable adherence is associated with rising reliance on the AI and convergence toward its supra-competitive price anchor.Higher profits feed back into the cycle, consistent with sustained coordination.
  • Behavioral mechanisms: In female-only markets, profit earned while following the AI increases the probability that the next rationale cites the AI as the pricing basis (γ̂3 = 1.56, p = 0.040).The same interaction is not significant in male-only markets (γ̂3 = −0.08, p = 0.708) or mixed-gender markets (γ̂3 = −0.08, p = 0.772).
  • Behavioral mechanisms: In male-only markets, profitable outcomes are associated with declining reliance and rationales that shift toward personal skill and strategy.Adherence oscillates rather than collapsing monotonically, but the net association prevents sustained coordination.
  • Implications and boundaries: The same adaptive AI system produces different recommendation sequences and market outcomes depending on who sets prices, making adherence a governance-relevant signal.The paper argues that oversight should attend to the adherence the algorithm elicits, not only the algorithm itself.
  • Implications and boundaries: Adherence patterns can serve as a practical risk-screening signal: submarkets with consistently high adherence warrant closer review for coordination.The finding concerns supra-competitive focal-point coordination in a controlled game, not coordination at scale across real-world submarkets.
  • Implications and boundaries: The composition-specific trust and attribution dynamics remain constrained by the passive, explanation-free AI treatment studied here.Participants saw a bare recommendation number and could not query or converse with the AI; whether richer interaction changes the dynamics remains open.

B Covariate Balance

Most covariates are well balanced across treatment and control within each gender composition, although several within-composition differences and higher prior GPT trust occur in specified cells. The analyses include covariates as controls to absorb these imbalances.

  • Balance assessment: Most covariates are well balanced across treatment and control within each gender composition.Balance is assessed using Welch’s t-test on cluster-level covariate means.
  • Measurement: The rationale-input interface prompted participants to submit a free-text pricing explanation after each round.The interface displayed a “Your Rationale” field and a “Save Rationale” button.
  • Within-composition differences: Age, ethnicity/race, and major diversity are higher in female-only control clusters, while e-commerce prevalence is higher in mixed-gender treatment clusters.The reported differences are significant at the 5% level.
  • Within-composition differences: Prior GPT trust is significantly higher in treatment clusters in the pooled sample and in female-only clusters.The reported p-values are 0.005 for the pooled sample and 0.045 for female-only clusters.
  • Adjustment: All covariates are included as controls in the regression specifications, so the observed imbalances are absorbed.This adjustment is part of the estimation strategy.

C Robustness to Session-Level Clustering

Session-level clustering and small-cluster inference preserve the central female-only AI effects, while male-only and mixed-gender estimates remain null.

  • Session-robust standard errors address possible understatement from shocks shared within sessions, where treatment is randomized.The analysis uses session-level clustering because cluster-level standard errors may be anti-conservative under session-level shocks.
  • 0.1%: the female-only price effect remains significant under session-robust errors with t6 critical values (p = 0.0009).
  • 0.1%: the female-only profit effect remains significant under session-robust errors with t6 critical values (p = 0.0006).
  • p > 0.47: male-only and mixed-gender treatment effects remain statistically insignificant under session-level clustering.
  • Small-cluster procedures supplement t(G − 1) inference with wild cluster bootstrap and Fisher randomization inference.The bootstrap imposes the null and enumerates session-level Rademacher weights; randomization inference permutes session-level assignments.
  • 0.047 and 0.114: female-only price-effect p-values from WCB and RI are near conventional thresholds because few sessions limit resolution.The corresponding profit-effect p-values are 0.039 and 0.114, with lower bounds mechanically limited by 1/128 and 1/35.

C.1 Minimum Detectable Effect at the Session Level

Session-level power and pooled interaction analyses reinforce the female-only price result, while profit heterogeneity and null cells are less precisely estimated.

  • 1.83: the female-only price effect exceeds the session-level minimum detectable effect by this factor.
  • 1.97: the female-only profit effect exceeds the session-level minimum detectable effect by this factor.
  • Every leave-one-session-out estimate keeps the female-only price effect positive, ranging from 0.324 to 0.530, and significant at the 10% level or better.The profit effect also remains positive under every omission, though finite-session limitations remain.
  • 0.412, p < 0.001: the Treatment × FemaleOnly interaction confirms a larger price effect in female-only than male-only clusters.
  • −0.007, p = 0.885: the baseline AI treatment effect on prices in male-only clusters is essentially zero.
  • 0.091, p = 0.262: the Treatment × FemaleOnly profit interaction is positive but not statistically significant.The text attributes this to the noisier profit outcome.

E Direct Dynamic Adherence Model

A direct dynamic adherence model tests whether prior profit changes subsequent AI adherence across market compositions without relying on latent-state machinery.

  • The linear probability model predicts current adherence from lagged adherence, lagged profit, their interaction, and round fixed effects.The key coefficient is γ3, the interaction between lagged adherence and lagged profit.
  • Female-only markets show a significantly positive adherence-profit interaction (p < 0.001), so profitable AI-following predicts continued adherence.
  • Male-only markets show a significantly negative adherence-profit interaction (p = 0.009), so profitable AI-following predicts weaker subsequent adherence.
  • Mixed-gender markets show no significant interaction between lagged adherence and lagged profit.
  • The direct-model sign pattern aligns with the NHMM transition coefficients: positive for female-only markets and negative for male-only markets.The analysis is presented as a robustness check without imposing latent states, emission distributions, or parametric assumptions.

F Systematic Rationale Coding and Rationale-Based LPMs

Systematic coding of sellers’ rationales provides textual evidence consistent with composition-specific learned trust and self-serving attribution.

  • The analysis uses fixed-codebook LLM-assisted coding of treatment-group seller-round rationales into mutually exclusive categories.The model observes rationale text and category definitions, but not gender, composition, prices, profits, or subsequent behavior.
  • Trust-AI rationales explicitly reference following, trusting, relying on, or agreeing with the AI recommendation.
  • Own-strategy rationales reference sellers’ judgment, skill, analysis, personal strategy, or independent decision-making.
  • 1.557, p = 0.040: in female-only markets, profitable AI adherence significantly predicts subsequent trust-AI rationales, not own-strategy rationales.
  • 3.342, p < 0.001: in male-only markets, profitable AI adherence significantly predicts own-strategy rationales, not trust-AI rationales.
  • Mixed-gender markets show neither rationale pattern, while the overall results corroborate learned trust in female-only and self-serving attribution in male-only markets.

G.1 Overview

The model represents each seller’s adherence as an unobserved behavioral state and separates observed deviations, state transitions, and persistent individual differences.

  • Each round, sellers set a price after observing an AI-recommended price, and adherence is measured by absolute deviation from that recommendation.Smaller deviations indicate closer adherence; larger deviations indicate greater departure.
  • Sellers occupy hidden behavioral states representing distinct regimes, such as closely following or largely ignoring the AI.
  • The model combines emission distributions, transition probabilities, and participant-level random effects.These components capture observed behavior, switching across rounds, and persistent baseline adherence heterogeneity.

G.2 Emission Distributions

The model assigns deviations to ordered adherence states and estimates covariate-dependent transitions while integrating over participant-specific random effects.

  • Within each state, deviations follow a Gaussian distribution with state-specific mean and standard deviation.
  • States are ordered by adherence: State 0 has the smallest mean deviation, while higher-numbered states indicate larger deviations.
  • Transition probabilities depend on time-varying covariates, origin-state-specific coefficients, and participant-level random effects.Covariates include lagged prices, market outcomes, profits, cumulative profit, aggregate prices, and the AI recommendation.
  • Ordered cutpoints and the logistic cumulative-transition formulation ensure valid probabilities, with higher predictors shifting mass toward more adherent states.Individual transition probabilities are obtained by differencing cumulative probabilities.
  • For the paper’s N = 2 specification, the states are high adherence and low adherence, and positive covariate coefficients favor the adherent state.
  • The forward algorithm computes sequence likelihoods in O(N^2T) rather than enumerating NT hidden-state paths.
  • The unobserved participant effect is integrated out numerically using Q = 15 Gauss–Hermite quadrature nodes.
  • Parameters are estimated by maximizing the sample log-likelihood with BFGS, while reparameterizations enforce positivity, ordered cutpoints, and valid initial-state probabilities.

H Decomposition of AI-Signal and Human-Response Heterogene-

The decomposition test examines whether adherence differences reflect sellers’ responses to similar recommendations rather than differences in the AI’s signals. Controlling recommendation magnitude, female-only clusters show greater adherence, while mixed-gender clusters do not differ significantly from male-only clusters.

  • The analysis separates human-response heterogeneity from AI-signal heterogeneity by controlling nonparametrically for recommendation deciles.The model also includes recommendation gaps and lagged seller, market, and round covariates.
  • The test uses 3,687 seller-round observations from 147 treated sellers in 49 clusters after dropping the first round.
  • Female-only clusters deviate 0.140 less from the AI recommendation than male-only clusters within the same recommendation decile (p < 0.001).
  • This adherence difference survives recommendation-decile fixed effects, which absorb composition-specific patterns in AI recommendations.
  • Mixed-gender clusters do not differ significantly from male-only clusters (p = 0.185).
  • The evidence attributes the adherence divergence to heterogeneous human responses to similar AI signals, not merely heterogeneous AI signals across compositions.
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