BIRCPG Multi-Agent Task Allocation: Simulation Code, Synthetic Results, and Numerical Theory Checks

This research software package provides Python scripts, synthetic simulation outputs, and numerical checks supporting the R1 revision of manuscript games-4606179. It investigates decentralized task allocation in a congestion-game model in which agents share task rewards, incur congestion and private costs, and select actions subject to individual feasibility constraints, with an outside option of zero payoff.

The simulation compares seven methods: trace-biased logit (PL), uncertainty-gated asynchronous improvement (PR), independent greedy allocation (B1), uniform-reference logit (B2), a trace-guided heuristic without the congestion game (B3), exact-information asynchronous best response (B4), and an exact centralized welfare benchmark obtained by linear assignment (B5). The experimental design comprises 10, 30, and 50 agents; five conditions covering nominal operation, cost-estimation noise, occupancy-information losses, environmental changes, and combined disturbances; and 30 random seeds per configuration. The resulting 3,150 runs each span 100 epochs. Recorded indicators include welfare relative to the centralized optimum, unilateral-deviation gaps, the frequency of approximate equilibrium, payoff-evaluation counts, and short-window performance following changes. Summary estimates include bootstrap confidence intervals and selected paired method comparisons.

Additional scripts numerically examine stationary-distribution sensitivity to trace perturbations, private-cost estimation errors, trace tracking under drift and delay, and an illustrative conformal-calibration setting. The package includes the original machine-readable outputs, a plotting script and figure, a tabular summary, dependency specifications, execution instructions, provenance records, and a verification report.

All environments and observations are computationally generated; the package contains no field measurements. Numerical checks supplement, but do not replace, mathematical proofs. The centralized optimum is an evaluation benchmark, and equilibrium proximity does not imply welfare optimality. Conclusions are restricted to the implemented model, parameter settings, and tested system sizes.