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

Eight years ago, my then-fiancée and I decided to get a prenup, so we hired a local mediator. The meetings were useful, but I felt there was no systematic process to produce a final agreement. So I started to think about this problem, and after a bit of research, I discovered the Nash bargaining solution.Yet if John Nash had solved negotiation in the 1950s, why did it seem like nobody was using it today? The issue was that Nash's solution required that each party to the negotiation provide a "utility function", which could take a set of deal terms and produce a utility number. But even experts have trouble producing such functions for non-trivial negotiations.A few years passed and LLMs appeared, and about a year ago I realized that while LLMs aren’t good at directly producing utility estimates, they are good at doing comparisons, and this can be used to estimate utilities of draft agreements.This is the basis for Mediator.ai, which I soft-launched over the weekend. Be interviewed by an LLM to capture your preferences and then invite the other party or parties to do the same. These preferences are then used as the fitness function for a genetic algorithm to find an agreement all parties are likely to agree to.An article with more technical detail: https://mediator.ai/blog/ai-negotiation-nash-bargaining/

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62

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VALIDATE

medium confidence

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Use LLM preference elicitation plus Nash bargaining to generate fair negotiation agreements, starting with prenups and divorces.

The pain

Mediation is expensive ($200-400/hour), slow (multiple sessions), and produces agreements that feel arbitrary rather than systematically fair. Parties often distrust the outcome because there's no transparent methodology, just a mediator's judgment. For high-stakes negotiations (prenups, divorce settlements, business splits), people want confidence they got a fair deal.

The gap

Nash bargaining solution exists mathematically but requires utility functions that are hard to construct manually. LLMs can't estimate utilities directly but excel at pairwise comparisons. No existing tool bridges this gap, mediators use intuition, not algorithms.

Build angle

Start narrow: prenups and uncontested divorces where both parties are motivated to reach agreement quickly and fairly. Build trust by showing the math (Nash solution is provably fair under specific axioms). Charge per agreement or subscription. Expand to business partnerships, co-founder splits, and commercial disputes once the core product works.

Strengths

  • Novel technical insight: using LLM comparisons to estimate utilities is clever and plausible
  • Real problem: mediation is expensive and feels subjective; systematic fairness is genuinely valuable
  • Founder has domain experience (went through prenup process, understands the friction)
  • Mathematical foundation (Nash bargaining) provides credibility and defensibility
  • Low marginal cost once built; software scales without adding mediators

Risks

  • Adoption risk: people may not trust an algorithm over a human mediator, especially in emotional/high-stakes situations like divorce
  • Legal risk: agreements generated by AI may face enforceability challenges; mediators have legal standing, software doesn't
  • Market size risk: prenups are niche (maybe 5-10% of marriages); divorce mediation is competitive with established players (lawyers, mediators)
  • Utility estimation risk: LLM comparisons may not actually produce stable or fair utility functions; no validation that genetic algorithm output matches Nash solution
  • Chicken-egg problem: both parties must participate; one party refusing kills the deal
  • Soft launch with no traction signals: no data on whether users actually complete the process or accept the output

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