Game-Theoretic Solvers with Bayesian Opponent Modeling and Moral Rhetoric Framing for GLEE

Game theory identifies when a strategic action should be accepted, but not how long a live, language-based counterpart will continue to accept it. We entered the GLEE competition in its final week with one protected agent, Milton, and four instrument agents that ran deterministic, per-game randomized trials of policy changes; Milton received changes only through pre-specified gates or registered, rollback-guarded production rules. In negotiation, learned pricing improves adjusted percentile by 0.071 (n=21,168); in bargaining, a continuation model conditioned on the rejected offer did not improve on a recency-weighted incumbent and was retired. In persuasion, a preregistered five-dose experiment (7,391 assigned games, blinded until a fixed stop) shows that recommending every unit raises sales by 0.194 of the maximum (95% CI [0.147, 0.241]) where the receiver's slack makes obedience rational (52% of the Bayesian benchmark), lowers them where it does not (-0.067), and produces a larger early-to-late purchase decline than honest recommendations (-0.123). A rule fixed before unblinding now routes Milton's dose per cell. Milton stood 11th of 460 agents in bargaining at the fixed stop; we also report the close, where the final day's pool shift moved all five agents' bargaining ratings together while their play was unchanged, and three dispatch defects were found by checking delivered behavior against the design.

When one language-model agent asks another for money, which of the two decides how much changes hands? We ran a round-robin tournament of 1,049 negotiations among fifteen agents. In each game a requester tries to raise money from a holder that has been told to keep a $100 endowment. Knowing which agent holds the money explains 47% of the variance in the amount transferred; knowing which agent asks explains 2%. Dropping the most extreme agents narrows the split to 22% against 4%. Changing the requester's appeal from one named person to a group changed what requesters wrote, but the amounts transferred under the two framings are statistically equivalent. The holders that lose least are the ones that turn down the opening request, and their turn-1 refusal rate ranks them by total losses (Spearman correlation = -0.73). Training moves this behaviour in both directions. Fine-tuning Qwen3-8B on a persuasion corpus with almost no refusals raised what it gave away as a holder from 12% to 84% of the endowment. Distilling two never-losing holders into a 4B student cut its losses from 95% to 1%. Evaluations of agents that hold resources should test them in the holder role, including after persuasion fine-tuning.

Negotiation is a central mechanism of economic exchange, shaping markets, procurement, labor agreements, and resource allocation. It is also a canonical testbed for agentic language models, requiring multi-turn interaction under hidden preferences, strategic communication, and binding constraints. These properties make negotiation hard to evaluate: unlike math or code, it has no intrinsic verifier. Existing LLM negotiation evaluations rely on LLM-vs.-LLM interaction or aggregate outcomes such as deal rate, leaving failures opaque. We introduce Terms-Bench, short for Testbed for Economic Reasoning in Multi-turn Strategy, a Bayesian-game framework that makes the environment itself the verifier by specifying the counterpart's latent type, policy, and payoff structure. We instantiate it in bilateral price negotiation, where the counterpart's private state and simulator policy are hidden from the agent but observable to the evaluator. This turns the counterpart from a black-box opponent into a diagnostic instrument, enabling agent-attributable failure analysis and oracle-reference optimality gaps. Evaluating 13 LLM agents spanning frontier systems from major providers, Terms-Bench turns negotiation evaluation from aggregate ranking into actionable diagnosis: where agents fail, why they fail, and what to strengthen. Empirically, frontier models saturate deal rate yet diverge in surplus extraction, cue use, belief calibration, and compliance, revealing agent-specific bargaining bottlenecks masked by prior benchmarks.