Show HN: Mediator.ai – Using Nash bargaining and LLMs to systematize fairness | AI Paper Digest

TL;DR Highlight

Combining Nash equilibrium theory with LLMs, Mediator.ai automatically generates mutually acceptable settlement proposals for disputes, applicable to real-world scenarios like founder equity splits and contract disagreements.

Who Should Read

Developers and startup founders navigating negotiations—such as co-founder equity disputes, contract disagreements, or shared living expense allocation—as well as AI engineers interested in game theory-based decision-making systems powered by LLMs.

Core Mechanics

Mediator.ai operates based on the cooperative bargaining theory (Nash Bargaining Solution) proposed by economist John Nash in 1950. While this mathematical framework isn't new, the key is LLMs converting party statements written in natural language into a format processable by mathematics.
Each party independently inputs their position without knowing what the other has written. Mediator analyzes both statements, extracting key figures (monthly rent, actual working hours, amounts waived, revenue growth, etc.).
The system generates multiple candidate settlements, then iteratively evaluates and improves them using a Genetic Algorithm. Each candidate is scored against both parties’ requirements, and the process repeats 'until no further improvement is possible'.
In a bakery example, when Maya (60 hours/week operator) and Daniel (25 hours/week production) were at odds over 70/30 vs. 50/50 equity, the system proposed 62/38 initial equity + Daniel’s earn-back path (1% for every 200 hours, up to +5%). This structure itemizes contributions instead of a simple compromise.
The settlement details all contributions as individual items, such as Maya owing Daniel $4,800 in rent (with an additional 2% equity for repayment within 24 months), Daniel waiving $12,000 in distributions ($6,000 from investment, quarterly payments from profits), and Maya receiving a $1,800/month operating management fee (paid before profit distribution).
The intended use case is described as 'situations where both parties want an agreement but negotiations are stalled'—such as founder equity disputes, shared housing cost allocation, or contractor disputes. It assumes collaborative negotiation, unlike arbitration or litigation, which are binding.
Technically, the LLM converts natural language input into structured preferences (Utility Function), while Nash Bargaining Solution mathematics calculates the optimal settlement point.

Evidence

"A commenter with a background as a professional mediator pointed out that the tool is closer to arbitration than mediation. True mediation helps parties reach their own conclusions, rather than a mediator presenting a fair outcome, and emotional/human factors (a $50,000 dispute ending with an apology) are key—aspects this tool doesn’t address."

How to Apply

When co-founders have an equity dispute, separately inputting each person’s contributions (time, funds, opportunity cost) into Mediator.ai can explore third-party settlement structures (earn-back clauses, installment payments) that neither side considered.
In disputes with contractors over unpaid/overcharged amounts, inputting both sides’ positions into a Nash-based draft agreement before resorting to legal action can serve as a negotiation starting point. However, the results should be used as an exploratory framework, not a binding decision.
If you want to implement an LLM + game theory architecture yourself, this case—LLM converting natural language input into preference numbers → Nash Bargaining equations calculating the optimal point → Genetic Algorithm iteratively improving—can serve as a reference pipeline. Shapley Value is also a viable alternative framework.
Applying it first to emotionally sensitive but quantifiable situations (household chores, expense allocation) can help you understand the tool’s limitations and strengths. Expecting a complete agreement is unrealistic; using it to discover structures you hadn’t thought of is more practical.

Terminology

Nash Bargaining SolutionA theory proposed by economist John Nash in 1950 that mathematically finds the agreement point that maximizes the gains for both parties when cooperating.

Genetic AlgorithmAn optimization algorithm that mimics the evolutionary process of living organisms, creating multiple candidate solutions and iteratively finding better solutions by combining or modifying good ones.

Shapley ValueA methodology in game theory for fairly distributing the outcome created by the cooperation of multiple participants, also frequently used in the field of Explainable AI (XAI).

Utility FunctionA function in economics that numerically represents how valuable a choice or outcome is to a party. In Mediator.ai, the LLM converts natural language statements into this form.

Mediation vs ArbitrationMediation involves a neutral third party helping parties reach their own agreement, while arbitration involves a third party making a binding decision. Mediator.ai is criticized for functioning more like arbitration despite its name.

Show HN: Mediator.ai – Using Nash bargaining and LLMs to systematize fairness