I decided to have a little fun with this challenge and wrote a few more class definitions. I'm hoping that's not a problem, just wanted to see if I could wrap the entire game in something that would be extensible enough to create other games such as UNO or Poker.
The Deck could be extended, as could the CardGame class to create other types of card decks and card games, as well as the player class, etc. I didn't do anything too fancy, but I think all aspects of the game are covered. One could easily add the ability to increase the number of decks used for the game, or increase the number of players.
Just clone the repository and then:
cd War
php main.php