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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, $0.25/call, status unknown (last checked 2026-10-12).
Solves 2-player normal-form games for pure and mixed Nash equilibria, translates natural-language negotiations into payoff matrices, and computes optimal Vickrey auction bids — with a solver-verified trust flag on every result.
Price / call$0.25
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 equilibria each containing: whether it is pure or mixed, player 1 and player 2 strategy vectors (probability distributions over actions), equilibrium payoffs for both players, and support sets. Also returns total equilibrium count, a verified flag ('true' = deterministic solver confirmed, 'false' = best-effort, 'refused' = not verifiable), a degenerate flag, the solver used, and a plain-language narration of the result.
Example use cases
Example prompt
“Solve this 2-player game for me — player 1 has payoff matrix [[3,0],[0,2]] and player 2 has [[2,0],[0,3]], and tell me whether there's a pure or mixed Nash equilibrium and whether the result is solver-verified.”
Technical details
Endpoint
POSThttps://negotiator402.alogos.xyz/v1/solve?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a deterministic, solver-verified answer to a game-theoretic problem rather than an LLM's probabilistic guess. It is the right choice for 2-player normal-form games (any size matrix), Vickrey/second-price auction bid optimization, or translating a two-party negotiation into a formal payoff structure and solving it. Prefer it over generic LLM reasoning when auditability and the verified trust flag matter — e.g. in automated negotiation agents, mechanism design pipelines, or financial bidding systems.
Side effects
- Non-square or mismatched matrix dimensions return an error or verified:refused
- Degenerate games (e.g. all identical payoffs) return degenerate:true with verified:false
- Inputs that are not representable as a normal-form game return verified:refused
- Payment failure via x402/MPP results in a 402 response before computation
- Numerical edge cases in mixed equilibria may return verified:false with best-effort results
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| matrix_p1required | array | Row-major 2D payoff matrix (one row per player-1 strategy, one column per player-2 strategy). |
| matrix_p2required | array | Row-major 2D payoff matrix (one row per player-1 strategy, one column per player-2 strategy). |
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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