Question 1: Consider the following sequential two-player game with VNM prefer- ences in which player 2 has two information sets: T M B L R L R R 2,3 1,1 5,0 0,2 3,2 1.25,4 1.1 Use a payoff matrix to depict the strategic form of the game. Derive the unique pure-strategy NE. Can this strategy profile form part of a Weak Sequential Equi- librium (WSE)? If no, carefully explain why not. If yes, fully describe such an equilibrium. 1.2 Is there a WSE in which player 1 plays T with probability 1? Is there a WSE in which player 1 plays M with probability 1? Explain your answers. 1.3 Is there a WSE in which player 1 randomizes between T and M but plays B with probability zero? If no, carefully explain why not. If yes, fully characterize such a WSE. Question 1: Consider the following sequential two-player game with VNM prefer- ences in which player 2 has two information sets: T M B L R L R R 2,3 1,1 5,0 0,2 3,2 1.25,4 1.1 Use a payoff matrix to depict the strategic form of the game. Derive the unique pure-strategy NE. Can this strategy profile form part of a Weak Sequential Equi- librium (WSE)? If no, carefully explain why not. If yes, fully describe such an equilibrium. 1.2 Is there a WSE in which player 1 plays T with probability 1? Is there a WSE in which player 1 plays M with probability 1? Explain your answers. 1.3 Is there a WSE in which player 1 randomizes between T and M but plays B with probability zero? If no, carefully explain why not. If yes, fully characterize such a WSE