# nash-2x2

`station__game-theory__nash-2x2` · external (needs EXECUTION_BACKEND_URL configured) · domain `game-theory` · pv-relevance `non-pv`

Find pure and mixed Nash equilibria for a 2x2 game. Provide row and column payoff matrices.

> **Note:** This tool routes through an external execution backend. If `EXECUTION_BACKEND_URL` is unset on the server, calls return JSON-RPC error `-32603 "Tool execution backend not configured"`. Tools with `backend: native` execute in-process and are always callable.

## Agent metadata

- `idempotent`: unknown
- `read_only`: unknown
- `expected_latency_ms`: unknown (not yet contract-tested)
- `cost_tokens_estimate`: unknown

## Input schema

- `row_payoffs` *array* (required) — 2x2 row player payoffs [[a,b],[c,d]]
- `col_payoffs` *array* (required) — 2x2 column player payoffs [[e,f],[g,h]]

## Example call

```json
POST /api/mcp
Content-Type: application/json

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/call",
  "params": {
    "name": "station__game-theory__nash-2x2",
    "arguments": {
      "row_payoffs": [],
      "col_payoffs": []
    }
  }
}
```

## Related

- [/tools](/tools) — all 3062 tools
- [/tools/game-theory__nash-2x2](/tools/game-theory__nash-2x2) — HTML page
- [/tools/game-theory__nash-2x2/json](/tools/game-theory__nash-2x2/json) — JSON form (agent-friendly)
- [/api/mcp](/api/mcp) — endpoint
- [/AGENTS.md](/AGENTS.md) — agent guide