On robot games of Degree two

Abstract

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