Y or n not defined when trying to play game again

import random

secret_num = random.randint(1, 10)

guesses = []

def game():
    while len(guesses) < 5:
        try:
            guess = int(input("Pick a number between 1 and 10: "))

        except ValueError:
            print("{} isn't a number!".format(guess))

        else:

            if guess == secret_num:
                print("You got it! My number was {}".format(secret_num))
                break


            elif guess < secret_num:
                print("My number is higher than {}".format(guess))


            else:
                print("My number is lower than {}".format(guess))

            guesses.append(guess)

    else:
        print("You didnt'get it! My number was {}".format(secret_num))


    play_again = input("Do you want to play again? Y/n ")

    if play_again.lower() != 'n':
        game()

    else: 
        print("Bye!")

game()