Multinational War is Hard

Abstract

War is a card game so simple that only a child could love it. In this game, the deck is divided into piles, one for each player. At the beginning of each round, each player reveals the top card of her deck. Then, whoever has the best card wins all the revealed cards and places them at the bottom of her deck. War is usually played between two players, but this chapter considers a multiplayer version, called Multinational War. The game works exactly as it does with two players, except it tends to take longer. The tools of computational complexity are used to analyze the questions: Does War have any interesting strategic properties? Is there genuinely a game to play? The chapter establishes that finding the best strategy in Multinational War is a hard problem, and shows that, in this sense, playing Multinational War strategically is at least as hard as playing other classic games.