On Robot Games of Degree Two

摘要: Robot Game is a two player vector addition game played in integer lattice \(\mathbb {Z}^n\). In degree \(k\) case both players have vectors and each turn the chosen by added to current configuration of game. One players, called Attacker, tries play from initial origin while other player, Defender, avoid origin. The decision problem decide whether or not Attacker has winning strategy. We prove that decidable polynomial time for games any dimension \(n\).