Mapping over array using Async/Await with Puppeteer to return result

I'm new to working with async programming, so there may be something simple I'm missing out on here.

I have an express project, I'm passing an array in the body of my request.

Inside my function, I validate the body then parse the array and use a promise as I map over the array.

const games = JSON.parse(JSON.stringify(req.body.games));

const gamesMap = games.map((game) => gameSearch(game));

return Promise.all(gamesMap)
    .then(function(g) {
        // async is still running here, I want to wait until it returns 
        console.log(g); // returns [ undefined, undefined, ... ]
    });

The game search function uses puppeteer to use a headless browser to return prices of the game passed in array. However, it doesn't wait until the array is returned before Promise.all is called, so the console.log(g); above returns an undefined array. I assume it is something to do with using async await inside the gameSearch function, although I'm not sure what I am supposed to do here? Any help would be greatly appreciated.

function gameSearch(game) {
  (async () => {
    const url = '.....' + game;
    try {
      const browser = await puppeteer.launch();
      const page = await browser.newPage();
      await page.setUserAgent('Mozilla/5.0 (Macintosh; Intel Mac OS X 10_11_6) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/69.0.3497.100 Safari/537.36');
      await page.goto(url);
      const selector = '.searchRcrd';
      await page.waitForSelector(selector);

      const searchRcrds = await page.$$(selector);

      const records = [];

      for (let i = 0; i < searchRcrds.length; i++) {
        const searchRcrd = searchRcrds[i];
        const title = await searchRcrd.$eval('h1', (h1) => h1.innerText.trim());
        const buyFor = await searchRcrd.$eval('.desc .prodPrice div:nth-child(2) .priceTxt:nth-child(1)', (buy) => buy.innerText.trim());
        const inStoreFor = await searchRcrd.$eval('.desc .priceTxt:nth-child(2)', (inStore) => inStore.innerText.trim());
        const imgSrc = await searchRcrd.$eval('div.thumb > a > img', (img) => img.src.trim());

        records.push({
          'title': title,
          'buyFor': buyFor,
          'inStoreFor': inStoreFor,
          'imgSrc': imgSrc
        });
      }

      await browser.close();

      return records;
    } catch (err) {
      next(err);
    }
  })();
}