What are the rules for the War card game when played by 2 players?

In the War card game played by 2 players, the deck is divided evenly between the players. Each player reveals the top card of their deck simultaneously. The player with the higher card wins both cards and adds them to their pile. In case of a tie, a "war" occurs where each player places three cards face down, then reveals a fourth card. The player with the higher fourth card wins all the cards. The game continues until one player has all the cards or a predetermined number of rounds is reached.