In your custom app file _app.js:

import Cookies from "cookies";
import { v4 as uuidv4 } from "uuid";

function MyApp({ Component, pageProps }) {
  return (...)
}

MyApp.getInitialProps = async (appContext) => {
  const appProps = await App.getInitialProps(appContext);
  const { req, res } = appContext.ctx;
  const cookies = new Cookies(req, res);

  let playerId = cookies.get("playerId");
  if (!playerId) {
    playerId = uuidv4();
    cookies.set("playerId", playerId);
  }
  return { ...appProps, playerId };
};

export default MyApp;