ForHosting KIT · Developer Utilities

Mixed strategy Nash equilibrium 2×2 calculator

A mixed-strategy Nash equilibrium is a profile of probability distributions over pure strategies such that no player can raise expected payoff by unilaterally changing their mix.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

In a two-by-two normal-form game each player has two actions, so a mix is a single probability on the first action and its complement on the second. The classic way to find an interior mixed equilibrium is indifference: the row player chooses the mix that equalizes the column player's expected payoffs from the two columns, and the column player chooses the mix that equalizes the row player's expected payoffs from the two rows. Students, tutors, and exam generators need those closed-form probabilities from eight payoff numbers without algebra slips. This mixed strategy Nash equilibrium 2×2 calculator takes the row and column payoff matrices, returns both mix probabilities and the expected payoffs under the equilibrium profile, and rejects games with no interior mixed equilibrium (for example pure-strategy dominant games). The same pure analytic path powers the free browser widget and the API, so homework keys and notebooks never disagree on matching-pennies or chicken-style indifference ratios.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/econ/mixed-strategy-2x2

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/econ/mixed-strategy-2x2 \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"a11":1,"a12":-1,"a21":-1,"a22":1,"b11":-1,"b12":1,"b21":1,"b22":-1}'

const res = await fetch("https://api.kit.forhosting.com/econ/mixed-strategy-2x2", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "a11": 1,
    "a12": -1,
    "a21": -1,
    "a22": 1,
    "b11": -1,
    "b12": 1,
    "b21": 1,
    "b22": -1
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/econ/mixed-strategy-2x2",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "a11": 1,
    "a12": -1,
    "a21": -1,
    "a22": 1,
    "b11": -1,
    "b12": 1,
    "b21": 1,
    "b22": -1
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/mixed-strategy-2x2", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"a11":1,"a12":-1,"a21":-1,"a22":1,"b11":-1,"b12":1,"b21":1,"b22":-1}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"a11":1,"a12":-1,"a21":-1,"a22":1,"b11":-1,"b12":1,"b21":1,"b22":-1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/mixed-strategy-2x2", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "a11": 1,
  "a12": -1,
  "a21": -1,
  "a22": 1,
  "b11": -1,
  "b12": 1,
  "b21": 1,
  "b22": -1
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "econ.mixed_strategy_2x2",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →