Problems with your Google account might be blocking the installation of apps. This can be overcome by removing the account from the device and either installing the app with another account or adding the credentials back in after a restart.
Note that following these steps will remove your data completely from the device.
Open Settings, then Accounts and select the problematic Google account(s). Tap the menu button and then the option to remove the account. While it isn’t necessary to reboot, it’s a good idea at the very least so you can be sure you have correctly removed the account.
When you’re ready, add your account details again, as if you’re setting up the phone for the first time. Make another attempt to install the app or game.