updating Google play services in Emulator

Update On 18-Dec-2017

You can update Google Play Services via the Play Store app in your emulator just as you would on a physical Android device from API 24.

check Emulator new features added with stable update from Android Studio v 3.0

Google Play Support - From Google : We know that many app developers use Google Play Services, and it can be difficult to keep the service up to date in the Android Emulator system images. To solve this problem, we now offer versions of Android System Images that include the Play Store app. The Google Play images are available starting with Android Nougat (API 24). With these new emulator images, you can update Google Play Services via the Play Store app in your emulator just as you would on a physical Android device. Plus, you can now test end-to-end install, update, and purchase flows with the Google Play Store.

Quick Boot - Quick Boot allows you to resume your Android Emulator session in under 6 seconds

Android CTS Compatibility

Performance Improvements - With the latest versions of the Android Emulator, we now allocate RAM on demand, instead of allocating and pinning the memory to the max RAM size defined in your AVD.

Virtual sensors

Wi-Fi support

GPS location and Many more...

OR

Update this SDK Build-Tools and Android Emulator to latest and this alert message will not come again,

Settings --> Android SDK --> SDK Tools(tab) --> Android SDK Build-Tools

Use emulator that has Play Store installed. Updating play services would be as easy as in real device.

Since Google introduced Google Play Store images in Android SDK Tools 26.0.0 now emulators comes with installed Google Play Store.

From 26.0.3

• Adds a new tab in the extended window for Google Play Store images that displays the Play Services version and a button to check for updates to Play Services.

You need install Google play image, Android SDK -> SDK platforms --> check show Package details --> install Google play.

Based from Google documentation,

If you want to test your app on the emulator, expand the directory for Android 4.2.2 (API 17) or a higher version, select Google APIs, and install it. Then create a new AVD with Google APIs as the platform target.

Try to navigate to settings--> apps in your emulator and then find Google Play Services. Check the version number and use it in you build.gradle. To update it with the latest version, you can see it in these documentation and SO question.