Zero-sum minimax API

Computes maximin/minimax over a zero-sum payoff matrix, detects a pure saddle point and reports the game value or the bound interval requiring mixed play. Answers 'Does this zero-sum game have a saddle point?', 'What is the value of this matrix game?'.

Price$0.06per request

MethodPOST

Route/v1/gametheory/zero-sum-minimax

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

game-theoryminimaxmaximinzero-sumsaddle-pointmatrix-gamevaluedecision

API URLhttps://x402.hexl.dev/v1/gametheory/zero-sum-minimax

Integration docs

Example request

{
  "payoffs": [
    [
      4,
      5,
      6
    ],
    [
      3,
      2,
      7
    ],
    [
      8,
      1,
      0
    ]
  ]
}

Example response

{
  "rows": 3,
  "cols": 3,
  "rowMins": [
    4,
    2,
    0
  ],
  "colMaxs": [
    8,
    5,
    7
  ],
  "maximin": 4,
  "maximinRow": 0,
  "minimax": 5,
  "minimaxCol": 1,
  "hasSaddlePoint": false,
  "valueOfGame": null,
  "saddlePoint": null,
  "interpretation": "No pure saddle point (maximin 4 < minimax 5); the game requires mixed strategies and its value lies in [4, 5]."
}

Input schema

{
  "type": "object",
  "required": [
    "payoffs"
  ],
  "properties": {
    "payoffs": {
      "type": "array",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "examples": [
        [
          [
            4,
            5,
            6
          ],
          [
            3,
            2,
            7
          ],
          [
            8,
            1,
            0
          ]
        ]
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}