isn't a great equilibrium so to start looking at exactly how this works we're going to do another exercise where we're going to analyze a minimax game and see what gradient descent does for this game we have a scalar variable X at a scalar variable Y and we have a value function x times why and basically the one player controls X and would like to minimize this value function the other player controls Y and would like to maximize it and the exercise is to figure out if this value function has an equilibrium anywhere if so where is at equilibrium