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

Peisong Wang; Zhiwei Ma; Bowen Liu; Feixue Liu; Aochuan Chen; Chenyi Zi; Hongchuan Zeng; Yuhan Li; Jia Li

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arXiv · 2608.16033

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

Peisong Wang·Zhiwei Ma·Bowen Liu·Feixue Liu·Aochuan Chen·Chenyi Zi·Hongchuan Zeng·Yuhan Li·Jia Li

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Abstract

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

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Peisong Wang, Zhiwei Ma, Bowen Liu, Feixue Liu, Aochuan Chen, Chenyi Zi, Hongchuan Zeng, Yuhan Li, Jia Li. 2026-08-17. $R^3$-Bench: LLMs Struggle with Resource-Rational Reasoning under Shared Budgets. https://arxiv.org/abs/2608.16033

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