  A game starts with the empty graph on $n$ vertices, and two player alternate
adding edges to the graph. Only moves which do not create a triangle are valid.
The game ends when a maximal triangle-free graph is reached. The goal of one
player is to end the game as soon as possible, while the other player is trying
to prolong the game. With optimal play, the length of the game (number of edges
played) is called the $K_3$ game saturation number.
  In this paper we prove an upper bound for this number.
