Scaffolding the Strategist: Architecture-Dependent Reasoning Interventions in Hotelling Spatial Markets
Authors: Pratyush Singh
Organizations: Computing + Mathematical Sciences California Institute of Technology Pasadena, CA 91125, USA
Abstract
We investigate whether structured reasoning interventions improve the strategic economic reasoning of large language models, and whether their effects depend on model architecture. Using Hotelling's linear city model as a diagnostic vehicle, we evaluate GPT-4.1-mini (a standard instruction-following model) and GPT-5-mini (a reasoning-optimized model) under five conditions - an unscaffolded baseline and four reasoning interventions - across eight questions spanning deductive and abductive reasoning, three prompt framings, and three repetitions per condition, yielding 720 individually judged responses. We find a statistically significant crossover interaction between scaffolding type and model architecture (t(7)=4.79, p=0.002, d=1.69): commitment scaffolding improves the standard model (+0.21) while degrading the reasoning model (−0.63), and principled separation shows the opposite pattern (−0.40 vs. +0.31). Both crossovers are individually significant (commitment: p=0.040; separation: p=0.002) and hold across all eight questions with 7/8 directional consistency. Adversarial stress-testing harms both models, with 2.6× greater degradation for the reasoning model (−1.47 vs. −0.57; p=0.038), and the damage correlates negatively with baseline difficulty (R2=0.36, p=0.014). We further document a persistent declarative-procedural gap in which both models identify correct strategies at rates far exceeding their ability to execute them; separation fully closes this gap for the reasoning model while no intervention helps the standard model.
Large reasoning models (LRMs) substantially outperform their base LLM counterparts on challenging reasoning benchmarks, yet it remains poorly understood where base models go wrong during token-by-token generation and how to narrow this gap efficiently. We study the base-reasoning gap through quantifying token-level distributional disagreement between a base model and a stronger reasoning model using likelihood-based divergences. Across benchmarks, we find that the reasoning advantage is highly sparse and concentrates on a small set of early, planning-related decision tokens. For instance, on Qwen3-0.6B, only ~8% of generated tokens account for the salient disagreement, and these tokens concentrate early in the response, are strongly enriched in planning-related decisions (17x), and coincide with high base-model uncertainty -- suggesting that base models fail mainly at early planning points that steer the subsequent reasoning trajectory. Building on these findings, we propose disagreement-guided token intervention, a simple inference-time delegation scheme that performs a one-token takeover by the reasoning model only at high-disagreement positions and immediately switches back to the base model. With a small intervention budget, this sparse delegation substantially recovers and can even surpass the performance of a same-size reasoning model on challenging reasoning tasks. Code is available at https://github.com/AlphaLab-USTC/RRTokenIntervention.
Reasoning modes of language models outperform their non-reasoning counterparts on multi-step agentic tasks, but pay a 3-6x premium in output tokens on every episode -- much of it spent re-deriving procedures that are shared across episodes of the same domain. We show this recurring cost can be amortized: a coding agent analyses a small corpus of existing trajectories from a training split and compiles a compact natural-language skill that is injected into the non-reasoning model's system prompt. Across four agentic benchmarks (ALFWorld, tau2-bench telecom and retail, and SpreadsheetBench-Verified), skills recover 55%-100%+ of the reasoning gap for GPT-5.4-mini on held-out tasks -- exceeding the reasoning mode outright on two of four -- while emitting 2.7-6x fewer output tokens and zero reasoning tokens. Notably, reasoning traces are not a prerequisite: skills distilled from non-reasoning trajectories alone remain competitive with skills distilled from paired reasoning/non-reasoning corpora, with domain-dependent differences between the two sources. We interpret these results through a search lens: test-time reasoning is deep search inside a single episode, re-paid at every deployment, while corpus distillation is wide search across episodes, paid once. The two recover overlapping procedural knowledge, and width over cheap trajectories is often the better buy -- with the residual gap on some domains (telecom, SpreadsheetBench) delineating where genuinely per-instance deep search remains necessary.
Large language models (LLMs) are increasingly deployed as economic agents in marketplaces, auctions, and bidding settings. Anticipating their behavior in any specific deployment is hard. Existing strategic-reasoning benchmarks evaluate models on fixed canonical games. These benchmarks may saturate as the frontier improves, and they do not allow evaluators to generalize with confidence from benchmark performance to the varied and messy strategic environments that actual deployments involve. We introduce GENSTRAT, which uses procedurally generated strategic environments to address these challenges. Concretely, we generate a distribution of two-player zero-sum imperfect-information card games. The generator can draw fresh games on demand, allowing for evergreen evaluation and resistance to contamination. We pair the game distribution with a capability-profile methodology that decomposes model competence across six axes (state space, temporal depth, information sensitivity, opponent modeling, risk, and brittleness). We also introduce a jaggedness measure of within-distribution smoothness that detects when a model's advantage jumps unpredictably between strategically similar games. We sample 50 benchmark games from a 2,000-game generated pool and evaluate nine frontier and open-weight LLMs in a head-to-head tournament with over 36,000 matches. Newer frontier-tier models score higher on average. Beyond that average, models with near-identical overall strength show qualitatively different capability profiles, and two of the top three leaderboard models (gpt-5 and claude) are noticeably more locally volatile than the third (gemini-3.1-pro), despite being close in overall strength. Together, the capability profile and the jaggedness measure give a deployment-relevant diagnostic that the overall ranking alone cannot provide.