# Microgram: game-theory-nash-2x2

`station__algovigilance__microgram-game-theory-nash-2x2` · native (always callable) · domain `algovigilance` · pv-relevance `pv-core`

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

## Agent metadata

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

## Input schema

- `row_payoffs` *object* (required) — 2x2 row player payoffs [[a,b],[c,d]]
- `col_payoffs` *object* (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__algovigilance__microgram-game-theory-nash-2x2",
    "arguments": {
      "row_payoffs": {},
      "col_payoffs": {}
    }
  }
}
```

## Related

- [/tools](/tools) — all 7718 tools
- [/tools/algovigilance__microgram-game-theory-nash-2x2](/tools/algovigilance__microgram-game-theory-nash-2x2) — HTML page
- [/tools/algovigilance__microgram-game-theory-nash-2x2/json](/tools/algovigilance__microgram-game-theory-nash-2x2/json) — JSON form (agent-friendly)
- [/api/mcp](/api/mcp) — endpoint
- [/AGENTS.md](/AGENTS.md) — agent guide