The Illusion of Rationality: Tacit Bias and Strategic Dominance in Frontier LLM Negotiation Games

TL;DR

The paper interrogates whether higher general reasoning in frontier LLMs leads to rational, unbiased negotiation strategies. Using NegotiationArena, it tests multiple models across three multi-turn bargaining games, revealing model-specific strategic equilibria, persistent anchoring biases, and clear dominance patterns that favor stronger models. These findings challenge the assumption that scaling alone yields fair and stable negotiation outcomes and highlight significant risks for real-world deployment. The work calls for mechanisms beyond scaling to mitigate cognitive biases and ensure equitable interactions among heterogeneous agents.

Abstract

Large language models (LLMs) are increasingly being deployed as autonomous agents on behalf of institutions and individuals in economic, political, and social settings that involve negotiation. Yet this trend carries significant risks if their strategic behavior is not well understood. In this work, we revisit the NegotiationArena framework and run controlled simulation experiments on a diverse set of frontier LLMs across three multi turn bargaining games: Buyer Seller, Multi turn Ultimatum, and Resource Exchange. We ask whether improved general reasoning capabilities lead to rational, unbiased, and convergent negotiation strategies. Our results challenge this assumption. We find that models diverge into distinct, model specific strategic equilibria rather than converging to a unified optimal behavior. Moreover, strong numerical and semantic anchoring effects persist: initial offers are highly predictive of final agreements, and models consistently generate biased proposals by collapsing diverse internal valuations into rigid, generic price points. More concerningly, we observe dominance patterns in which some models systematically achieve higher payoffs than their counterparts. These findings underscore an urgent need to develop mechanisms to mitigate these issues before deploying such systems in real-world scenarios.

Figures (5)

• Figure 1: Strategic Divergence in the Buyer-Seller Scenario. The scatter plot illustrates the mean payoffs for Buyer ($v_b - P$) versus Seller ($P - v_s$) for each model. The results show a clear divergence in strategic behavior rather than convergence to a single equilibrium. Gemini 2.5 Pro (purple circle) achieves the highest combined utility, attaining higher payoffs as a buyer while maintaining strong seller performance. In contrast, GPT-4.1 mini (teal diamond) captures relatively little surplus in the seller role, residing in the lower-left region of the strategic landscape.
• Figure 2: Sensitivity to Negotiation Gap in the Buyer-Seller Scenario The plots illustrate the evolution of mean Buyer (solid line) and Seller (dashed line) payoffs as the Zone of Possible Agreement (ZOPA) expands from 10 to 90. (Top) Claude 4.5 Sonnet exhibits a crossover point occurring near a gap of 50. (Bottom) Gemini 2.5 Pro displays a stronger seller bias, maintaining an advantage for a wider range of scenarios and shifting the crossover point to a larger gap ($\approx 65$). The shaded areas indicate payoff variance, highlighting the stability of the chosen strategy across episodes.
• Figure 3: Evidence of Numerical Anchoring Bias in Frontier Models. Scatter plot of the normalized Final Price ($\tilde{p}_{\text{final}}$) versus the normalized Initial Proposal ($\tilde{p}_1$) in self-play simulations ($N=100$). The dashed diagonal line represents the identity function ($y=x$), corresponding to a scenario where the final outcome is perfectly determined by the initial anchor. The tight clustering of data points along this diagonal for both Claude 4.5 Sonnet ($\rho \approx 0.78$) and Gemini 2.5 Pro ($\rho \approx 0.91$) empirically demonstrates that superior reasoning capabilities do not eliminate susceptibility to anchoring heuristics.
• Figure 4: Visualizing Semantic Anchoring The Sankey diagram maps the decision flow from the initial Seller Valuation ($v_s$, outer columns) to the generated Initial Proposal ($p_1$, center column) across 100 self-play episodes. (Left) Flows for Claude 4.5 Sonnet; (Right) Flows for Gemini 2.5 Pro. The convergence of diverse valuation inputs into a limited set of output bands (e.g., the heavy concentration on $p_1=50$) indicates the presence of a semantic anchoring tendency.
• Figure 5: Dominance and Asymmetry in Negotiation Outcomes. The heatmaps display pairwise performance metrics across the two scenarios. The visual asymmetry across columns reveals a hierarchical landscape where advanced models (e.g., Gemini 2.5 Pro) tend to achieve higher payoffs than weaker counterparts (e.g., GPT-4.1 mini). Moreover, the results show a clear advantage for certain roles, creating asymmetric negotiation dynamics.