Let's say, two players are playing extended version of tic-tac-toe on 10X10 board (who first has 5 tiles next to each other, wins). Should both players play Nash equilibrium strategy, would it mean, that there would never be a winner?
If this claim is true, could it be shown based on the argument that the situation, when none of the players is willing to change her strategy given her oponent's strategy, can only occur when none of the players is going to lose, but neither of them is able to win?
Sorry, if the question seems vague or makes no sence. I am a newbie to GT. Edit suggestions welcome.