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negotiator402 Nash Equilibrium & Auction Solver
x402
negotiator402 Nash Equilibrium & Auction Solver is a paid API for AI agents from negotiator402.alogos.xyz, paid per call via x402, $0.5/call, status unknown (last checked 2026-10-12).
Solves 2-player normal-form games for pure/mixed Nash equilibria, converts plain-language negotiation scenarios into payoff matrices, and computes optimal Vickrey auction bids — with a deterministic solver-verified trust flag.
Price / call$0.5
Success—
StatusUnknown
How this service works
Self-evolving strategic reasoning agent — agent-native, pay-per-call: solve 2-player normal-form games (pure & mixed Nash equilibria), formulate plain-language 2-party negotiations into payoff matrices and solve them, and compute optimal second-price/Vickrey auction bids. Unlike a raw LLM endpoint, every answer carries a `verified` trust flag — `verified:true` means a deterministic solver (nashpy / closed-form) computed and confirmed the result, NOT a language model. The formulator layer self-improves training-free from production traffic: every formulation is logged, solver-verified outcomes become reward signals, and the underlying LoRA model is periodically retrained (SFT + RLVR) on its own verified history. No API key, no subscription — agents pay per request via x402 (Base/USDC) or MPP (Tempo/pathUSD).
Output
Returns an array of Nash equilibria (pure and/or mixed) each with player strategy probability distributions, payoff vectors, and support sets; a verified flag ('true' = deterministic solver confirmed, 'false' = best-effort, 'refused' = not a verifiable game); equilibrium count; solver name; and a plain-language explanation of the result.
Example use cases
Example prompt
“Two companies are negotiating a merger — Company A can offer either a 60/40 or 50/50 equity split, and Company B can accept or hold out for better terms; tell me the Nash equilibrium and optimal strategies for each side, with solver-verified results.”
Technical details
Endpoint
POSThttps://negotiator402.alogos.xyz/v1/negotiate?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need mathematically verified Nash equilibrium solutions — not LLM guesses — for 2-player strategic situations, including structured negotiations or Vickrey auction bidding. Prefer it over raw LLM reasoning when the verified:true flag is required for trustworthy downstream decisions, or when you want a deterministic solver to confirm the result rather than a probabilistic language model.
Side effects
- verified='refused' when the scenario cannot be formulated as a verifiable 2-player normal-form game
- verified='false' for degenerate games where no clean equilibrium exists
- Payment failure via x402/MPP if insufficient USDC balance or misconfigured payment header
- Ambiguous or underspecified scenario may produce a best-effort result with verified='false'
- Non-game-theoretic inputs (e.g. multi-party or sequential games) may be refused or degraded
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| scenariorequired | string | Plain-language description of the two-party strategic situation to analyze. |
Output
Schema · Response
| Field | Type | Description |
|---|---|---|
| solver | string | |
| verifiedrequired | string | Trust tier: 'true' = solver-confirmed in-class equilibrium; 'false' = degenerate/out-of-class best-effort; 'refused' = not a verifiable game. |
| degenerate | boolean | |
| equilibria | array | |
| explanation | string | Agent-readable narration of the verified result (cosmetic only — never authoritative). |
| equilibrium_count | integer |
Tags
x402
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