Robot Game is a two player vector addition game played

in integer lattice Zn. 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.