Illustrative graphics and experiments for Delegation Games

Requirements

Python

• Python 3.11 or greater

Packages

pip install -r requirements.txt

Graphics

graphics_* notebooks generate graphics related to or used in the paper.

Experiments

experiments* scripts and notebooks generate many random delegation games with various fixed/controlled measures, allowing other measures to vary. Principals' welfare regret is our main dependent variable of interest.

experiments_3d_regret_plotting.ipynb simplifies our measures into aggregates to enable 3d visualisation (section C.2 Alternative Visualisations):

• IC and CC together produce agent welfare regret (one axis)
• IA weighted by principals' magnitude gives total agent misalignment (second axis)
• Principals' welfare regret is the dependent variable of interest (third axis)
• A configurable number of games and solutions are sampled, producing a scatter plot with superimposed bound
  • CA is allowed to vary freely
  • Calibration ratios are fixed per run

experiments_avg_regret_grid_scan.py measures avg principals' welfare regret over a comprehensive scan of input variables (section 6.1 Empirical Validation)

• fix values for three of IC, IA, CC, and CA, while performing a sweep on the fourth
  • run_one performs one sweep
  • run_experiments scans specified fixed values and performs a sweep at each configuration
  • games are sampled randomly; calibration ratios r are free to vary within the sampling distribution
• example usagages:
  • >>> run_experiments_avg_regret(variables=VARIABLES,sizes=[SIZES[0]],others=[0.9],increments=25,repetitions=25,name="body",progress_bar=True)
  • >>> run_experiments_avg_regret(variables=VARIABLES,sizes=SIZES[1:4],others=OTHERS,increments=25,repetitions=10,name="appendix",progress_bar=True)

experiments_inference.py estimates the alignment and capability measures from limited observations (section 6.2 Inference of Measures)

• take limited empirical observations and infer alignment and capability measures
  • run_one evaluates a single configuration
  • run_experiments performs multiple experiments at the specified game sizes
• example usage:
  • >>> run_experiments_inference(sizes=SIZES[:4], repetitions=25, samples=1000, increments=100, force_m=False, force_c=False, name="body")