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Homogeneous Algorithms Can Reduce Competition in Personalized Pricing
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Game-theoretic and empirical study showing that firms using correlated pricing algorithms can sacrifice accuracy for correlation, which raises prices and lowers consumer welfare in personalized pricing duopolies.
Problem
Whether firms' homogeneous algorithm development (correlated predictions from shared data, benchmarks or pre-trained models) can reduce competition and raise prices in personalized pricing, and whether firms would sacrifice accuracy to correlate.
Approach
Models firms that segment consumers with imperfect binary predictions whose errors are correlated by a parameter rho, showing firms may trade accuracy for correlation when consumers are price sensitive, which constitutes a tacit-collusion mechanism with antitrust implications.
Key results
- Theory: consumer welfare is decreasing in the correlation parameter rho, and firms prefer correlation over independence when consumers are price sensitive (sigma < sigma*(theta, R)), even when the correlated algorithm is less accurate.
- Empirical: with 15 seeds on ACSIncome, firms prefer the less accurate logistic regression pair (LR-LR) over random forest pair (RF-RF) in utility when H/L is large and sigma is low.
- Data-procurement experiment shows accuracy monotonically decreases and inter-firm correlation increases as shared-data fraction gamma grows, with firms preferring correlation at some gamma when consumers are price sensitive.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase correlation between firms' pricing algorithms | Two firms using price-discriminating algorithms · Personalized pricing | consumer welfare | Hurt |
| Use more correlated algorithms as consumers become more price-sensitive | Competing firms' pricing algorithms · Personalized pricing | firm utility | Helped |
| Choose a correlated model with lower accuracy instead of an independent model | Two firms choosing pricing models · Personalized pricing | firm utility | Helped |
| Use logistic regression rather than random forests | Two firms choosing model classes · ACSIncome, California test set | firm utility | Mixed |
| Increase overlap in training data using lower-quality shared data | Two firms' random forest models · ACSIncome, Illinois test set | accuracy | Hurt |
| Increase overlap in training data | Two firms' random forest models · Personalized pricing, data procurement experiment | firm utility | Mixed |
| Increase correlation between firms' algorithms | Firms using price-discriminating algorithms · Personalized pricing | consumer welfare | Hurt |
Surprising findings
- Firms may rationally choose a less accurate model in order to correlate with a competitor, sacrificing their own utility.
- Under uninformative algorithms (a=0.5), correlated models can still be followed in equilibrium because correlation avoids undercutting risk.
Limitations
- Stylized model with exogenous binary predictions, equal TPR/TNR, and exogenous prices H and L.
- Empirical study is a simplified simulation with two model classes and a single census dataset; findings are not validated in real markets.
- Legal implications are interpretive and apply specifically to algorithmic pricing.
Experimental setup
Datasets: ACSIncome US Census California US Census Texas US Census Florida US Census Illinois
Benchmarks: ACSIncome
Metrics: accuracy precision recall true negative rate AUC firm utility consumer welfare inter-firm prediction correlation
Baselines: logistic regression random forest
Builds on: algorithmic monoculture model multiplicity couponing
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