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Causal Strategic Learning with Competitive Selection
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Studies causal strategic learning where decision makers both evaluate and select agents, deriving optimal selection rules, identifiability via mean-shift regression, and a cooperative protocol for multiple competing decision makers.
Problem
Causal strategic learning ignores that decision makers also select agents, which introduces selection bias, and with multiple competing decision makers interference between selection rules further biases estimation of causal parameters.
Approach
Derives the utility-maximising selection parameter as a trade-off between base performance and performance improvement, gives conditions to protect agent welfare, and estimates causal parameters via mean-shift linear regression using scaled selection parameters, with a cooperative protocol among decision makers to remove competitive interference.
Key results
- Estimated optimal selection parameter theta_AO achieves the highest DM utility (2.530 ± 0.006) versus OLS-based (2.511) and causal-parameter-based (2.511) selection rules.
- Mean-shift linear regression yields asymptotically unbiased estimates of the causal parameter, whereas 2SLS and OLS estimates are biased.
- With cooperative (synchronous) deployment, DMs obtain unbiased estimates of the high-school GPA causal effect; partial cooperation benefits all coalition members.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the estimated optimal parameter instead of the OLS parameter | Single DM selection · Single DM simulation | utility: 2.511 ±0.006 -> 2.530 ±0.006 | Helped |
| Use the estimated optimal parameter instead of the causal parameter | Single DM selection · Single DM simulation | utility: 2.511 ±0.006 -> 2.530 ±0.006 | Helped |
| Use AO θ1 instead of OLS θ1 | Competitive selection with AO θ2 · Competitive selection simulation | utility Q1: 2.507 ±0.029 -> 2.529 ±0.028 | Helped |
| Use AO θ1 instead of causal θ1 | Competitive selection with AO θ2 · Competitive selection simulation | utility Q1: 2.506 ±0.029 -> 2.529 ±0.028 | Helped |
| Use AO θ1 instead of OLS θ1 | Competitive selection with OLS θ2 · Competitive selection simulation | utility Q1: 2.546 ±0.029 -> 2.561 ±0.028 | Helped |
| Use AO θ1 instead of causal θ1 | Competitive selection with OLS θ2 · Competitive selection simulation | utility Q1: 2.545 ±0.029 -> 2.561 ±0.028 | Helped |
| Use AO θ1 instead of OLS θ1 | Competitive selection with causal θ2 · Competitive selection simulation | utility Q1: 2.546 ±0.029 -> 2.560 ±0.029 | Helped |
| Use AO θ1 instead of causal θ1 | Competitive selection with causal θ2 · Competitive selection simulation | utility Q1: 2.544 ±0.029 -> 2.560 ±0.029 | Helped |
Surprising findings
- The optimal selection rule relies on incorrect (non-causal) predictions, so it can unjustly reduce agents' admission chances even while maximising DM utility.
Limitations
- Relies on homogeneous effort conversion and homogeneous preference/compliance assumptions.
- Assumes linear outcome and agent models with bounded parameters.
- Analysis of multiple DMs uses partially additive interaction assumption (M1) and worst-case rival behaviour.
Experimental setup
Datasets: synthetic college admission data
Benchmarks: synthetic college admission simulation
Metrics: utility Q(theta) estimation error of causal parameters confidence intervals
Baselines: two-stage least squares OLS conditional OLS on selected agents
Builds on: causal strategic learning (Chen et al.) two-stage least squares instrumental variable regression
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