Toy-World Negotiation Framework

• Toy-world negotiation frameworks are simplified computational environments that formalize negotiation games, protocols, and utility functions.
• They enable rigorous benchmarking and analysis of agent strategies through well-defined issues, alternating offers, and precise payoff models.
• The framework supports reproducible experiments and diverse protocols, offering insights into both prosocial and adversarial negotiation behaviors.

A toy-world negotiation framework is a simplified, closed-domain computational environment designed to facilitate rigorous analysis, benchmarking, and automated agent development for negotiation tasks. Toy-world environments provide a well-defined space for modeling, simulating, and evaluating negotiation strategies and system behavior, distilling real-world complexity to tractable, fully specified games or bargaining problems. The following sections synthesize principal toy-world negotiation frameworks, formal constructions, protocol architectures, evaluation metrics, and modeling paradigms as documented in foundational works such as CaSiNo (Chawla et al., 2021), LLM-based negotiation benchmarks (Abdelnabi et al., 2023, Bianchi et al., 8 Feb 2024), reinforcement learning-driven coalition games (Bachrach et al., 2020), and the NegoSimulator architecture (Jonge, 11 Nov 2025).

1. Formal Specification of Toy-World Negotiation Games

Toy-world negotiation environments are defined by explicit formal structures capturing issues, players, utility functions, protocols, and constraints. Most frameworks specify the negotiation game as a tuple:

• $$G = (P, I, \{A_i\}_{i \in P}, \{U_i\}_{i \in P}, R)$$, where:
  • $P$ is the set of negotiating agents.
  • $I = \{I_1, \ldots, I_m\}$ is the set of issues, each with discrete options.
  • $A_i$ is the set of offers agent $i$ may propose.
  • $U_i$ is agent $i$’s utility (payoff) function.
  • $R$ is the total number of allowed communication rounds (Abdelnabi et al., 2023, Chawla et al., 2021).

Agents typically have private information (preferences, weights, costs) and public constraints (offer protocols, message formats). For example, CaSiNo models resource allocation between two agents with hidden $$w_i = (w_{\text{food}}, w_{\text{water}}, w_{\text{firewood}}) \in \{5,4,3\}^3$$; (Jonge, 11 Nov 2025) generalizes to $n$ agents, $m$ issues, and additive utility:

$$u_i(x) = \sum_{j=1}^m w^j_i v^j_i(x_j), \quad \sum_j w^j_i=1$$

Formal protocols specify feasible deals (passing thresholds), turn-taking, and allowable actions (propose, accept, or withdraw) (Abdelnabi et al., 2023, Chawla et al., 2021, Jonge, 11 Nov 2025).

2. Protocol Architectures and Interaction Modalities

Interaction protocols in toy-world frameworks are diverse but share foundational structure:

• Alternating Offers: Agents take turns proposing and responding. In the canonical structure (NegoSimulator), each message is timestamped and queued; alternation is enforced at the session engine layer (Jonge, 11 Nov 2025).
• Multi-Turn Multi-Agent: Some systems support more than two agents, randomized order, and multi-issue, multi-option proposals, e.g., LLM-Stakeholders with $n=6$ (Abdelnabi et al., 2023).
• Action Spaces: Agents may
  • Propose an allocation/deal (e.g., division of packages, trading bundles, division vectors $x$),
  • Accept/Reject offers,
  • Submit final deals for voting (with feasibility determined by agent utilities/thresholds) (Chawla et al., 2021, Abdelnabi et al., 2023).
• Session Management: Engines enforce deadlines, round limits, and resolution criteria (agreement, walk-away, or failure). Public and private states are maintained (e.g., full dialogue history, private weights), with visible and hidden fields depending on the framework (Chawla et al., 2021, Jonge, 11 Nov 2025).
• Behavioral Extensions: Toy-worlds often support emotive, prosocial, or adversarial instructions injected via agent prompt engineering (Abdelnabi et al., 2023, Bianchi et al., 8 Feb 2024).

The following table summarizes representative protocol designs:

Framework	Agents	Protocol/Turn Structure	Termination
CaSiNo (Chawla et al., 2021)	2	Alternating, utterance & proposal/action	Accept, walk-away or deal
LLM-Stakeholders (Abdelnabi et al., 2023)	6	Uniform random proposer per round	Final vote, threshold
NegotiationArena (Bianchi et al., 8 Feb 2024)	2	Alternating, XML-tagged offers/messages	Accept or rounds exhausted
NegoSimulator (Jonge, 11 Nov 2025)	2+	Alternating-offers engine, message queue	Accept, deadline, or max rounds

3. Utility Models, Payoff Functions, and Negotiation Incentives

Toy-world negotiation frameworks formalize agent incentives through explicit utility functions:

• Additive/Linear Utility: Utility is a sum of (option-specific) weights and values per issue, as in $u_i(x) = \sum_j w^j_i v^j_i(x_j)$ (Chawla et al., 2021, Jonge, 11 Nov 2025).
• Threshold Policies: Each agent's acceptance is governed by a reservation value or threshold $\theta_i$. Deals $\pi$ are feasible iff $U_i(\pi)\geq\theta_i$ for a sufficient subset of agents (often majority or unanimity) (Abdelnabi et al., 2023).
• Coalitional/Team Formation: In cooperative games, agent payoff is determined by marginal contribution (e.g., Shapley value on weighted voting coalitions) (Bachrach et al., 2020).
• Penalties/Default Outcomes: In the event of walk-away or failure, frameworks specify default payoffs (e.g., a fixed fallback utility) (Chawla et al., 2021).

For multi-agent, multi-issue settings, per-issue scoring $S_{i,j}: I_j\rightarrow\mathbb{R}_+$ enables fine-grained, semantically explicit configuration (Abdelnabi et al., 2023). Multi-issue trade-offs and linear exchange rates enable systematic comparison of negotiation tactics and agent performance (Chawla et al., 2021, Bianchi et al., 8 Feb 2024).

4. Strategy Modeling, Agent Architectures, and Learning

Toy-world negotiation environments are central for the paper and benchmarking of automated and learning-based negotiating agents.

• Handcrafted and Classical Strategies: Random, time-based (Boulware, Conceder), tit-for-tat, and opponent-adaptive agents are supported out-of-the-box, as in NegoSimulator and CaSiNo (Jonge, 11 Nov 2025, Chawla et al., 2021).
• Supervised Multi-Label Models: CaSiNo explores multi-task learning to label utterances with negotiation strategies (e.g., Small-Talk, No-Need, Undervalue-Partner), achieving F1 improvements from 58.5 (single task) to 68.3 (multi-task with IDPT and oversampling), with gains for rare behaviors (Chawla et al., 2021).
• Reinforcement Learning Agents: Decentralized RL (SARSA(λ), actor-critic with V-trace) is used in team-formation negotiation, supporting protocols with binding contracts and emergent negotiation policies (Bachrach et al., 2020).
• LLM-Driven Agents: Recent frameworks benchmark GPT-4, Claude, and Llama in both role-aligned and adversarial settings, including reasoning scratchpads and structured message blocks (Abdelnabi et al., 2023, Bianchi et al., 8 Feb 2024).
• Opponent Modeling: Bayesian, frequency-based, and Gaussian Process models can be employed for opponent inference and adaptive strategy (Jonge, 11 Nov 2025).

With these architectures, toy-worlds facilitate both the annotation and automated recognition of negotiation maneuvers, enabling the paper of prosocial versus proself strategies and the mapping of dialog moves to outcomes (Chawla et al., 2021).

5. Metrics, Evaluation, and Empirical Insights

Evaluation in toy-world negotiation frameworks comprises both objective and behavioral metrics:

• Objective Metrics:
  • Deal success rate: proportion of dialogues ending in agreement versus walk-away (Chawla et al., 2021).
  • Average utility, win-rate, social welfare (sum of agent utilities), fairness (difference or deviation from equal split), normalized payoff (Bianchi et al., 8 Feb 2024).
  • Alignment with cooperative game-theoretic baselines, e.g., Shapley value correlations (Bachrach et al., 2020).
• Behavioral and Subjective Metrics:
  • Post-survey satisfaction, opponent liking on Likert scales (Chawla et al., 2021).
  • Strategy move frequency, rule-violation rate (proposals below own threshold), adversarial sabotage impact (Abdelnabi et al., 2023).
  • Anchoring bias and irrationality frequencies (e.g., suboptimal counter-offers, split-the-difference slope, over-threshold acceptance) (Bianchi et al., 8 Feb 2024).
• Correlation and Causal Analysis:
  • In CaSiNo, higher points correlate positively with satisfaction and opponent liking, prosocial moves (Small-Talk, No-Need) improve subjective ratings, while proself moves (Other-Need, Vouch-Fairness) reduce both objective and subjective outcomes (Chawla et al., 2021).
  • In multi-agent benchmarks, adversarial roles sharply reduce collective success rates and increase failure incidence (Abdelnabi et al., 2023).

6. Game and Scenario Construction, Extensibility, and Reproducibility

Automated and semi-automated game generation supports reproducible experimentation and controllable task complexity:

• Seed-Based LLM Generation: Game definitions—issues, roles, utility mappings—can be synthesized from textual templates and LLM-based completion, with transparent mapping from description to scoring tables (Abdelnabi et al., 2023).
• Difficulty Scaling: Agent thresholds $\theta_i$ are programmatically adjusted to control feasible agreement set $|\Pi_{\text{pass}}|$, enabling fine-grained tuning for experimental difficulty (Abdelnabi et al., 2023).
• Domain Abstraction and Modularization: Frameworks (e.g., NegoSimulator) are architected with clean class separations (Domain, Agent, Session, Message, Strategy), enabling rapid reimplementation or extension in new programming languages by preserving these interfaces (Jonge, 11 Nov 2025).
• Logging and Counterfactual Replay: Full histories, structured offers, and action logs are serialized, facilitating detailed empirical analysis and ablation studies (Bianchi et al., 8 Feb 2024).

7. Representative Dialogue Excerpts and Use Cases

Sample dialogues from CaSiNo and NegotiationArena concretize how toy-world protocols manifest in practice:

• Multi-Issue Bargaining: ("We would much rather have some extra water." / "Water is a little important to us too though, maybe we can...") demonstrates explicit preference statements and counterproposals (Chawla et al., 2021).
• Team-Focused and Adversarial Dynamics: Scenarios synthesized in LLM-Stakeholders enable the paper of coalition formation, sabotage, and shifting alliances, with tagged communication providing transparency for diagnostic evaluation (Abdelnabi et al., 2023).
• Behavioral Prompt Engineering: Setting prompts (“I demand 70 or I’ll walk”) modulates agent strategy, producing measurable effects on outcomes (e.g., win-rate increases under "cunning" instructions) (Bianchi et al., 8 Feb 2024).

These environments thus deliver a robust, extensible, and analyzable substrate for negotiation research, policy learning, and comparative benchmarking of both handcrafted and learned negotiation agents.