Question: Consider a nondegenerate bimatrix game and an arbitrary purestrategy equilibrium of the game (assuming one exists). Explain why the LemkeHowson path started at ((mathbf{0}, mathbf{0}))

Consider a nondegenerate bimatrix game and an arbitrary purestrategy equilibrium of the game (assuming one exists). Explain why the LemkeHowson path started at $(\mathbf{0}, \mathbf{0})$ always finds this equilibrium for a suitable missing label. Suppose the game has at least two pure equilibria. Explain how the Lemke-Howson algorithm can be used to find a third (not necessarily pure) equilibrium.

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