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A Market for Accuracy: Classification Under Competition
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Studies learning classifiers for firms competing for users in an accuracy market, showing that market-share best responses reduce to weighted accuracy and that best-response dynamics converge quickly with welfare gains.
Problem
Classification when multiple service providers compete for consumers, where each provider's market share depends on which users it classifies correctly relative to competitors; standard accuracy maximization becomes suboptimal under competition.
Approach
Rewrites a provider's market share as a weighted expected accuracy with per-example weights 1/(1+number of other correct providers), so best responses can be learned with standard weighted empirical risk minimization; analyzes 2-player equilibria theoretically and runs best-response dynamics on real and synthetic data.
Key results
- Best-response dynamics converge after at most two rounds across settings; market share increases for all providers, up to +83.2% max share for COMPAS-arrest with 5 providers.
- Welfare gains reach up to +65% in the real-data experiments, and welfare reaches 1 with five providers on COMPAS-arrest before all providers have moved.
- For two threshold providers, the game reduces to a chicken-like anti-coordination structure where the second mover obtains the larger exclusive segment.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use competition-aware weighted accuracy best responses instead of optimizing accuracy naively | Providers in an accuracy market · COMPAS-Arrest; COMPAS-Violence; Adult | market share and welfare: +25.4% to +94.6% market share increase; +17.3% to +64.2% welfare increase | Helped |
| Increase the number of providers from 2 to 5 or more | Best-response dynamics · COMPAS-Arrest, COMPAS-Violence, and Adult | welfare | Helped |
| Restrict learning to use only two features rather than all features (ablation) | Competing predictors · COMPAS-Arrest, 2 providers | welfare: 1; 0.84 | Helped |
| Optimize accuracy naively rather than accounting for competition | Providers in an accuracy market · Accuracy markets | market outcomes | Hurt |
| Use proxy objectives to implement approximate best responses | Best-response dynamics · Real-data experiments | welfare | Helped |
| Move second rather than first | Provider in a two-provider market · Real-data experiments, 2 providers | market share: 3.6% mean; 4.8% median | Helped |
| Move first rather than second | Provider in a market with 3 or more providers · Real-data experiments, 3–6 providers | market share | Helped |
| Increase representation quality by using more features (ablation) | Competing predictors · COMPAS-Arrest, 2 providers | welfare: 1; 0.84 | Hurt |
Surprising findings
- Providers sacrifice accuracy to secure exclusive user segments; the top-share provider in a 3-provider COMPAS-arrest example had accuracy below 50%.
- With three or more providers, moving first is advantageous rather than moving last, reversing the two-player order-of-play result.
Limitations
- Assumes a single fixed data distribution accessible to all providers and full information sharing.
- Assumes users rationally choose an accurate provider independently at each step.
Experimental setup
Datasets: COMPAS-arrest COMPAS-violent Adult synthetic Gaussian data
Benchmarks: COMPAS-arrest COMPAS-violent Adult
Metrics: market share HHI welfare
Baselines: naive accuracy maximization
Builds on: accuracy markets model (prior work) performative prediction potential games
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