{"uid":"cap_-6VstqSjADKb104JQMVra","slug":"negotiator402-nash-equilibrium-auction-solver-283258be","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/negotiate?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","required":["scenario"],"properties":{"scenario":{"type":"string","description":"Plain-language description of the two-party strategic situation to analyze."}}},"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":"0.5","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":"$0.5/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.5","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.5","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_fOE1eWGASZUCnReBdnhgx","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.5","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/mixed Nash equilibria, converts plain-language negotiation scenarios into payoff matrices, and computes optimal Vickrey auction bids — with a deterministic solver-verified trust flag.","exampleAgentPrompt":"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.","exampleUseCases":null,"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-12T06:36:43.583Z","isFirstParty":false,"canonicalSlug":"negotiator402-nash-equilibrium-auction-solver-283258be"}