We consider the differential inclusion known as Best Response Dynamics for a bimatrix game (A, B), with A, B - the payoff matrices for two agents. It is known that if (A, B) is equivalent to a zero-sum game and the Nash equilibrium is an internal point of the phase, then it is also stable in the sense of Lyapunov. Hofbauer's conjecture states that the internal Nash equilibrium can be stable only if (A, B) is equivalent to a zero-sum game. We claim that Hofbauer's conjecture is false and so we will present our approach to this problem. This is a joint work S. van Strien and D. Turaev.