R^3-Bench: LLMs Struggle with Resource-Rational Reasoning under Shared Budgets

Summary

Resource rationality in cognitive science asks how agents should allocate limited computation to maximize expected value. Most reasoning benchmarks use independent per-task budgets, and existing shared-budget studies do not calibrate against single-problem competence. We introduce R^3-Bench, evaluating six-problem suites under shared budgets across mathematics, competitive programming, and abstract reasoning, in both tool-free and agentic settings. Matched single-problem response curves define an offline empirical oracle. Across 72 main-table cells for six models, the oracle mean meets or exceeds the contest mean in all cells, strictly higher in 71. Under moderate tool-free pressure, equal-allocation replay also outperforms contest for four of six models. Trajectory diagnostics reveal limited strategy updating and pressure-dependent failures. In a three-model diagnostic under strong agentic pressure, at least one fixed scheduler exceeds contest mean in six of nine cells, but no policy dominates across domains. The results expose a persistent gap between demonstrated competence and shared-budget realization.