Verify Nash Equilibrium
curl --request POST \
--url https://api.fincept.in/quantlib/economics/games/nash-check \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"payoff_matrix_1": [
[
3,
0
],
[
5,
1
]
],
"payoff_matrix_2": [
[
3,
5
],
[
0,
1
]
],
"strategy_1": [
0,
1
],
"strategy_2": [
0,
1
]
}
'import requests
url = "https://api.fincept.in/quantlib/economics/games/nash-check"
payload = {
"payoff_matrix_1": [[3, 0], [5, 1]],
"payoff_matrix_2": [[3, 5], [0, 1]],
"strategy_1": [0, 1],
"strategy_2": [0, 1]
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({
payoff_matrix_1: [[3, 0], [5, 1]],
payoff_matrix_2: [[3, 5], [0, 1]],
strategy_1: [0, 1],
strategy_2: [0, 1]
})
};
fetch('https://api.fincept.in/quantlib/economics/games/nash-check', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/economics/games/nash-check",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'payoff_matrix_1' => [
[
3,
0
],
[
5,
1
]
],
'payoff_matrix_2' => [
[
3,
5
],
[
0,
1
]
],
'strategy_1' => [
0,
1
],
'strategy_2' => [
0,
1
]
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/economics/games/nash-check"
payload := strings.NewReader("{\n \"payoff_matrix_1\": [\n [\n 3,\n 0\n ],\n [\n 5,\n 1\n ]\n ],\n \"payoff_matrix_2\": [\n [\n 3,\n 5\n ],\n [\n 0,\n 1\n ]\n ],\n \"strategy_1\": [\n 0,\n 1\n ],\n \"strategy_2\": [\n 0,\n 1\n ]\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/economics/games/nash-check")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"payoff_matrix_1\": [\n [\n 3,\n 0\n ],\n [\n 5,\n 1\n ]\n ],\n \"payoff_matrix_2\": [\n [\n 3,\n 5\n ],\n [\n 0,\n 1\n ]\n ],\n \"strategy_1\": [\n 0,\n 1\n ],\n \"strategy_2\": [\n 0,\n 1\n ]\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/economics/games/nash-check")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"payoff_matrix_1\": [\n [\n 3,\n 0\n ],\n [\n 5,\n 1\n ]\n ],\n \"payoff_matrix_2\": [\n [\n 3,\n 5\n ],\n [\n 0,\n 1\n ]\n ],\n \"strategy_1\": [\n 0,\n 1\n ],\n \"strategy_2\": [\n 0,\n 1\n ]\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"is_nash_equilibrium": true,
"payoff": [
1,
1
]
}
}{
"detail": "Invalid API key"
}{
"detail": "Endpoint requires Basic tier or higher"
}{
"detail": [
{
"loc": [
"body",
"strategy_1"
],
"msg": "field required",
"type": "value_error.missing"
}
]
}quantlib-economics
Verify Nash Equilibrium
Check whether a given strategy profile (possibly mixed) is a Nash equilibrium. A strategy profile is a Nash equilibrium if no player can improve their expected payoff by unilaterally deviating. Also returns the expected payoffs for both players. Use to verify candidate equilibria or validate algorithmic solutions. [Tier: STANDARD, Credits: 2]
POST
/
quantlib
/
economics
/
games
/
nash-check
Verify Nash Equilibrium
curl --request POST \
--url https://api.fincept.in/quantlib/economics/games/nash-check \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"payoff_matrix_1": [
[
3,
0
],
[
5,
1
]
],
"payoff_matrix_2": [
[
3,
5
],
[
0,
1
]
],
"strategy_1": [
0,
1
],
"strategy_2": [
0,
1
]
}
'import requests
url = "https://api.fincept.in/quantlib/economics/games/nash-check"
payload = {
"payoff_matrix_1": [[3, 0], [5, 1]],
"payoff_matrix_2": [[3, 5], [0, 1]],
"strategy_1": [0, 1],
"strategy_2": [0, 1]
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({
payoff_matrix_1: [[3, 0], [5, 1]],
payoff_matrix_2: [[3, 5], [0, 1]],
strategy_1: [0, 1],
strategy_2: [0, 1]
})
};
fetch('https://api.fincept.in/quantlib/economics/games/nash-check', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/economics/games/nash-check",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'payoff_matrix_1' => [
[
3,
0
],
[
5,
1
]
],
'payoff_matrix_2' => [
[
3,
5
],
[
0,
1
]
],
'strategy_1' => [
0,
1
],
'strategy_2' => [
0,
1
]
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/economics/games/nash-check"
payload := strings.NewReader("{\n \"payoff_matrix_1\": [\n [\n 3,\n 0\n ],\n [\n 5,\n 1\n ]\n ],\n \"payoff_matrix_2\": [\n [\n 3,\n 5\n ],\n [\n 0,\n 1\n ]\n ],\n \"strategy_1\": [\n 0,\n 1\n ],\n \"strategy_2\": [\n 0,\n 1\n ]\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/economics/games/nash-check")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"payoff_matrix_1\": [\n [\n 3,\n 0\n ],\n [\n 5,\n 1\n ]\n ],\n \"payoff_matrix_2\": [\n [\n 3,\n 5\n ],\n [\n 0,\n 1\n ]\n ],\n \"strategy_1\": [\n 0,\n 1\n ],\n \"strategy_2\": [\n 0,\n 1\n ]\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/economics/games/nash-check")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"payoff_matrix_1\": [\n [\n 3,\n 0\n ],\n [\n 5,\n 1\n ]\n ],\n \"payoff_matrix_2\": [\n [\n 3,\n 5\n ],\n [\n 0,\n 1\n ]\n ],\n \"strategy_1\": [\n 0,\n 1\n ],\n \"strategy_2\": [\n 0,\n 1\n ]\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"is_nash_equilibrium": true,
"payoff": [
1,
1
]
}
}{
"detail": "Invalid API key"
}{
"detail": "Endpoint requires Basic tier or higher"
}{
"detail": [
{
"loc": [
"body",
"strategy_1"
],
"msg": "field required",
"type": "value_error.missing"
}
]
}Authorizations
API key for authentication. Get your key at https://api.fincept.in/auth/register
Body
application/json
Payoff matrix for Player 1
Example:
[[3, 0], [5, 1]]
Payoff matrix for Player 2
Example:
[[3, 5], [0, 1]]
Mixed strategy for Player 1 (probability distribution over strategies, must sum to 1)
Required range:
0 <= x <= 1Example:
[0, 1]
Mixed strategy for Player 2 (probability distribution over strategies, must sum to 1)
Required range:
0 <= x <= 1Example:
[0, 1]
⌘I
