Number game - calling a function from within itself

I'm working on creating this number game (guess the computer's number) with my own little touches. I've created a function that prompts the user to enter 'y' or 'n' based on whether they want to play again. Since I've added a few extra things (like a "give up" option), I want to call this function in a few different places. Within the function, I want to have an option to start the function again if the user doesn't enter 'y' or 'n' (for example, if they enter 'yes' or something totally wrong). This is the "else:" at the bottom... but I get an error when I run it (it appears to be going back into the game() function). Is there a way I can call the function from within itself?

def play_again():
    play_again = raw_input("Would you like to play again? Enter 'y' for yes, 'n' for no.")
    if play_again.lower() == 'y':
        print "Alright! Let's get started!"
        game()
    elif play_again.lower() == 'n': 
        print "Thanks for playing. Have a nice day!"
    else: 
        print "Error: please enter 'y' to play again or 'n' to quit."
        play_again()