Shapley value API

Computes exact Shapley values (fair marginal-contribution payouts) for a small cooperative game given the value of every coalition, and verifies efficiency. Answers 'How should a coalition's payoff be split fairly?', 'What is each player's Shapley value?'.

Price$0.1per request

MethodPOST

Route/v1/gametheory/shapley-value

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

game-theoryshapley-valuecooperativecoalitionfair-divisionmarginal-contributionpayoffdecision

API URLhttps://x402.hexl.dev/v1/gametheory/shapley-value

Integration docs

Example request

{
  "players": [
    "A",
    "B",
    "C"
  ],
  "coalitionValues": {
    "": 0,
    "A": 0,
    "B": 0,
    "C": 0,
    "A,B": 0,
    "A,C": 0,
    "B,C": 0,
    "A,B,C": 1
  }
}

Example response

{
  "players": [
    "A",
    "B",
    "C"
  ],
  "shapleyValues": {
    "A": 0.33333333,
    "B": 0.33333333,
    "C": 0.33333333
  },
  "grandCoalitionValue": 1,
  "sumOfShapley": 1,
  "efficient": true,
  "interpretation": "Shapley values (fair marginal-contribution shares) sum to the grand-coalition value 1: A=0.333, B=0.333, C=0.333."
}

Input schema

{
  "type": "object",
  "required": [
    "players",
    "coalitionValues"
  ],
  "properties": {
    "players": {
      "type": "array",
      "items": {
        "type": "string"
      },
      "examples": [
        [
          "A",
          "B",
          "C"
        ]
      ]
    },
    "coalitionValues": {
      "type": "object",
      "examples": [
        {
          "": 0,
          "A": 0,
          "B": 0,
          "C": 0,
          "A,B": 0,
          "A,C": 0,
          "B,C": 0,
          "A,B,C": 1
        }
      ]
    }
  }
}

Output schema

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