# negotiator402 Nash Equilibrium & Negotiation Solver

> negotiator402 Nash Equilibrium & Negotiation Solver is a paid API for AI agents from negotiator402.alogos.xyz, paid per call via x402, $3/call, status unknown (last checked 2026-09-15).

Solves 2-player normal-form games (pure & mixed Nash equilibria), translates plain-language negotiations into payoff matrices, and computes optimal Vickrey auction bids — with deterministic solver-verified results.

## Facts

- Endpoint: POST https://negotiator402.alogos.xyz/v1/negotiate-strategy
- Price: $3/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/negotiator402-nash-equilibrium-negotiation-solver-fe882cb4
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_vBnvkqOEIP36Z3nGw2shz

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability negotiator402-nash-equilibrium-negotiation-solver-fe882cb4 -d '<json body>'
```

Example prompt: Two companies are negotiating a licensing deal — Company A can either demand high royalties or offer a discount, and Company B can either accept or walk away and build in-house. Use solver-verified game theory to find the Nash equilibrium and tell me what each side's optimal strategy is.

## When to prefer this

Choose this endpoint when you need game-theoretic rigor with a verifiability guarantee — specifically when the answer must come from a deterministic solver (nashpy), not just an LLM's reasoning. Ideal for 2-player strategic scenarios, negotiations, or Vickrey auctions where you want to know whether the result is mathematically confirmed (verified:true) vs. model-inferred. Prefer over raw LLM reasoning when trust and auditability of the equilibrium calculation matters.

## Known failure modes

- Scenario too vague or underspecified to formulate a payoff matrix — returns verified:'refused'
- More than 2 players described — out of scope, likely refused or degraded
- Degenerate game (e.g. all payoffs equal) — solved but flagged with degenerate:true
- Payment failure via x402/MPP — request blocked before processing
- LLM formulation succeeds but solver cannot confirm — returns verified:'false' with caveat

## 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 a structured object containing: verified flag ('true' only when deterministic solver confirms the result), list of equilibria with player strategies and payoffs (pure or mixed), the formulated payoff matrices for both players, action labels, scenario analysis with incentive counterfactuals, equilibrium count, and a narrative explanation. Also includes which solver was used and whether the game is degenerate.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "scenario"
 ],
 "properties": {
  "scenario": {
   "type": "string",
   "description": "Plain-language description of the two-party strategic situation."
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "verified"
 ],
 "properties": {
  "solver": {
   "type": "string"
  },
  "verified": {
   "enum": [
    "true",
    "false",
    "refused"
   ],
   "type": "string",
   "description": "Overall trust tier. 'true' only when the base model is solver-confirmed in-class."
  },
  "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": "Narrative explanation (inferred; omitted when it contradicts the base solver)."
  },
  "payoff_model": {
   "type": "object",
   "properties": {
    "notes": {
     "type": "string"
    },
    "players": {
     "type": "integer"
    },
    "matrix_p1": {
     "type": "array",
     "items": {
      "type": "array",
      "items": {
       "type": "number"
      }
     },
     "description": "Row-major 2D payoff matrix (one row per player-1 strategy, one column per player-2 strategy)."
    },
    "matrix_p2": {
     "type": "array",
     "items": {
      "type": "array",
      "items": {
       "type": "number"
      }
     },
     "description": "Row-major 2D payoff matrix (one row per player-1 strategy, one column per player-2 strategy)."
    },
    "p1_actions": {
     "type": "array",
     "items": {
      "type": "string"
     }
    },
    "p2_actions": {
     "type": "array",
     "items": {
      "type": "string"
     }
    }
   },
   "additionalProperties": true
  },
  "explanation_note": {
   "type": "string"
  },
  "equilibrium_count": {
   "type": "integer"
  },
  "scenario_analysis": {
   "type": "array",
   "items": {
    "type": "object",
    "properties": {
     "cell": {
      "type": "array",
      "items": {
       "type": "integer"
      },
      "maxItems": 2,
      "minItems": 2
     }
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/negotiator402-nash-equilibrium-negotiation-solver-fe882cb4/health.json
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