NegotiationArena Framework for Multi-Turn Negotiation

• NegotiationArena Framework is a formal simulation environment for multi-turn negotiation dialogues, defining agents, game protocols, state spaces, and utility functions.
• It enables benchmarking and evaluation of language models and reinforcement learning agents in diverse scenarios such as buyer–seller, ultimatum, and resource exchange games.
• The framework’s modular design supports extensible scenario definitions and detailed analysis of strategic biases, equilibrium behavior, and negotiation performance metrics.

NegotiationArena is a flexible, formalized environment for simulating, benchmarking, and analyzing multi-turn negotiation dialogues between autonomous agents, with applications spanning natural language dialogue, stochastic games, and algorithmic optimization. The framework provides precise abstractions for agents, game protocol, state and action spaces, utility functions, and evaluation metrics, making it central to the empirical study of LLM negotiation, reinforcement learning algorithms, transfer learning, and the computational modeling of multi-agent bargaining scenarios (Laroche, 2017, Ríos et al., 10 Dec 2025, Bianchi et al., 2024).

1. Formal Structure and Game-Theoretic Foundations

NegotiationArena models negotiation as an episodic, partially observable stochastic game between two agents. The general instance is defined by the tuple:

$$G = \langle \mathcal{P}, S, \{A^i\}_{i \in \mathcal{P}}, \{O^i\}_{i \in \mathcal{P}}, T, \{R^i\}_{i \in \mathcal{P}}, \gamma \rangle$$

where $\mathcal{P} = \{\mathcal{p}_s, \mathcal{p}_u\}$ are the system and user (or two agents), $S$ is the state space tracking grounded features, proposals, and the turn marker; $A^i$ is each agent's available action set (e.g., proposing features, repeating, accepting, terminating); $O^i$ is the agent’s observation space, including noisy views with feature error rate ($FER$); $T$ is the transition function, including deterministic state transition and stochastic observation; $R^i$ is the reward function with flexible definition (option-specific costs, feature costs, cooperation parameter $\alpha^i$); and $\gamma$ is a discount factor (Laroche, 2017).

The state space captures—in full generality—the negotiated features, last moves, and party turn. Actions can include partial or full proposals, acceptance, or negotiation withdrawal. Payoff functions account for private costs, intrinsic utilities, and inter-agent cooperation. The interaction ends upon mutual acceptance or explicit withdrawal, leading to terminal states.

Equilibrium behavior depends on game settings: For $\alpha^i = -1$ the game is zero-sum and admits minimax stationary policies (Shapley 1953); the general-sum case admits Nash or correlated equilibria under standard conditions, but exact policy computation is PSPACE-hard for growing feature count and episode horizon (Laroche, 2017).

2. Dialogue Protocols and Scenario Variants

NegotiationArena incorporates a precisely defined turn-taking mechanism (initial agent chosen by coin flip or by protocol, then strict alternation), support for multi-turn dialogue, and a compositional speech-act interface. All negotiation scenarios are instantiated by specifying: initial resource endowments, permissible action types, utility functions, and explicit termination predicates. Prominent implemented scenarios include:

Scenario	Resource Domain	Agent Roles	Utility Specification
Buyer–Seller	Scalar (currency)	Seller, Buyer	$u_{seller}(P) = P - v_s$; $u_{buyer}(P) = v_b - P$
Ultimatum	Scalar split	Proposer, Responder	$u_{proposer} = C - x$; $u_{responder} = x$
ResourceExchange	Vector-valued	Two traders	$u_i = \sum_k (q_{i,k}^{final} - q_{i,k}^{initial})$

Messages are serialized as structured turns (XML-tags or natural text), with public and private state components rigorously parsed and logged (Bianchi et al., 2024, Ríos et al., 10 Dec 2025). Acceptance can occur at any turn, otherwise T-step bounds enforce endpoints.

3. System Architecture, API, and Extensibility

NegotiationArena is modular—separating scenario management (rules, payoffs, transitions), agent interfaces (wrappers for LLMs, scripted heuristics, or RL policies), the dialogue engine (turn-taking and prompt orchestration), and persistent logging for evaluation. New scenarios are defined by subclassing BaseScenario (specifying initial_state, valid_actions, transition, and payoff methods). The agent interface requires a single respond(state, history) method, making the platform amenable to plug-and-play LLMs or other agentic systems (Bianchi et al., 2024).

Integration with major LLM APIs (OpenAI, Anthropic) and compatibility with reinforcement learning agents are realized in Python, with ecosystem support including structured serialization (Pydantic) and analysis modules (pandas). This design supports repeatable benchmarking and detailed post hoc behavioral analysis.

4. Benchmarking Methodology and Evaluation Metrics

The benchmarking workflow draws cost/utility distributions, initializes agent policies, and runs N-episode tournaments, each recording stepwise state, observed moves, and outcomes. Evaluation dimensions span:

• Algorithms: Standard and multi-agent RL, policy gradient, transfer and one-shot learning.
• Performance metrics: Average episode return, win rate, success rate (agreement frequency), dialogue length, convergence speed (episodes to policy stability), robustness to $FER$, $SER$.
• Behavioral metrics: Anchoring correlation (Spearman $\rho$ between initial and final proposals), split-the-difference heuristics, rate of irrational counteroffers, generalization gaps in variant scenarios.
• Experimental controls: Feature counts $\ell$, resource set sizes $|\mathcal{F}^k|$, cooperation parameters $\alpha^i$, and repeated random seeds for statistical rigor (Laroche, 2017, Bianchi et al., 2024).

Key agent evaluation involves systematic pairing of LLM variants (e.g., GPT-4, Claude-2.1, Gemini 2.5 Pro), cross-roles, and exhaustive round-robin tournaments (Ríos et al., 10 Dec 2025).

5. Empirical Findings and Behavioral Analysis

NegotiationArena reveals pronounced model-dependent strategic profiles and persistent behavioral biases:

• Strategic divergence: Rather than converging to focal Nash or equitable splits, frontier LLMs manifest distinct, model-specific equilibrium behaviors in both bilateral and multilateral settings (Ríos et al., 10 Dec 2025).
• Anchoring effects: Strong numeric anchoring persists across agent families (Spearman $\rho \approx 0.7$–$0.9$ between initial ask $p_1$ and final price $p_f$), robust to temperature variation. Semantic anchoring manifests as preference for discrete, rounded proposals (Ríos et al., 10 Dec 2025, Bianchi et al., 2024).
• Dominance patterns: Systematic win-rate and payoff asymmetry exist—some models (e.g., Gemini 2.5 Pro) attain persistent dominance in proposer roles, with weaker agents (e.g., GPT-4.1 mini) confined to lower payoffs (Ríos et al., 10 Dec 2025).
• Human-like irrationality: LLMs overvalue in buyer roles, fall into split-the-difference heuristics, and display theory-of-mind limitations (e.g., failing to exploit classical equilibrium in extended ultimatum settings) (Bianchi et al., 2024).

The core implication is that LLM scaling does not eliminate negotiation biases nor drive convergence to rational economic equilibria.

6. Limitations and Prospective Extensions

NegotiationArena, while highly general as a two-agent, discrete-feature testbed, faces clear limitations:

• Complexity: The state-action space scales exponentially in features ($|S| \approx 2^\ell |\mathcal{F}|^\ell$), rendering exact equilibrium computation intractable beyond moderate $\ell$ (Laroche, 2017).
• Scenario scope: The canonical implementation is two-party; multi-party ($m>2$) negotiation introduces substantial combinatorial and strategic challenges.
• Abstraction: The framework employs abstract speech acts; genuine open-vocabulary, end-to-end language negotiation remains to be robustly integrated.
• Static preferences: Current models assume fixed, known cost distributions and utility profiles.

Proposed extensions include dynamic preference modeling, hierarchical/bundled feature sets, support for coalition formation, and hybridization with end-to-end neural agents. The architecture explicitly anticipates integration with RL dialogue agents and natural language generation/understanding modules (Laroche, 2017, Bianchi et al., 2024).

7. Practical Implications and Research Outlook

Empirical deployments demonstrate that NegotiationArena exposes both strengths and endemic flaws in LLM-based negotiation. Model-specific bias, anchoring, and exploitable equilibria undermine the assumption that scaling or basic fine-tuning suffices for robust autonomous bargaining (Ríos et al., 10 Dec 2025). Recommended mitigation measures include adversarial de-biasing, reward shaping targeting anchor-correlation, integration with explicit payoff calculators, and calibrated fallback negotiation protocols.

This suggests that ongoing research should prioritize developing hybrid architectures—combining LLMs with strategic RL components—and extending the platform to n-agent settings and human–AI mixed negotiation. Auditability (e.g., of initial proposals), fairness constraints, and theory-of-mind diagnostics are critical as NegotiationArena informs both theoretical advances and real-world deployment safety in autonomous negotiation systems (Ríos et al., 10 Dec 2025, Bianchi et al., 2024, Laroche, 2017).