{"uid":"cap_ykmSR0TaZwRzNH9SRXnfV","slug":"negotiator402-nash-equilibrium-auction-solver-bd3f6460","name":"negotiator402 Nash Equilibrium & Auction Solver","description":"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).","url":"https://negotiator402.alogos.xyz/v1/solve?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","required":["matrix_p1","matrix_p2"],"properties":{"matrix_p1":{"type":"array","description":"Row-major 2D payoff matrix (one row per player-1 strategy, one column per player-2 strategy)."},"matrix_p2":{"type":"array","description":"Row-major 2D payoff matrix (one row per player-1 strategy, one column per player-2 strategy)."}}},"responseSchema":{"type":"object","required":["verified"],"properties":{"solver":{"type":"string"},"verified":{"enum":["true","false","refused"],"type":"string","description":"Trust tier: 'true' = solver-confirmed in-class equilibrium; 'false' = degenerate/out-of-class best-effort; 'refused' = not a verifiable game."},"degenerate":{"type":"boolean"},"equilibria":{"type":"array","items":{"type":"object","properties":{"is_pure":{"type":"boolean"},"payoffs":{"type":"array","items":{"type":"number"},"maxItems":2,"minItems":2},"player1_support":{"type":"array","items":{"type":"integer"}},"player2_support":{"type":"array","items":{"type":"integer"}},"player1_strategy":{"type":"array","items":{"type":"number"}},"player2_strategy":{"type":"array","items":{"type":"number"}}},"additionalProperties":true}},"explanation":{"type":"string","description":"Agent-readable narration of the verified result (cosmetic only — never authoritative)."},"equilibrium_count":{"type":"integer"}},"additionalProperties":true},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.25","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.25/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.25","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.25","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_4txSuXTLTYjqqtvpGQw0O","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.25","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"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.","exampleUseCases":null,"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-12T18:33:43.770Z","isFirstParty":false,"canonicalSlug":"negotiator402-nash-equilibrium-auction-solver-283258be"}