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(i) Consider the following payoff matrix for a two-player game where players move simultaneously. Using only the three numbers 1,5, and 8, depict the payoff matrix for a two-player simultaneous move game such that \{Bottom, Right } is the payoff dominant equilibrium while { Top, Left } is the risk dominant or secure equilibrium. Your payoff matrix should not involve dominated or weakly dominated strategies on the part of either player. (2 marks) (ii) Assuming players are risk-neutral and make their decisions based on maximizing expected values of game payoffs, what is the mixed strategy equilibrium for the game you have depicted in Part (i)? Briefly explain how you arrive at your answer. You must show the work you did to arrive at this answer. (4 marks) Part B: (4 marks) Consider a sequential move game played by three players, 1,2 and 3. Player 1 moves first and chooses Left or Right. If Player 1 moves Left, then the game ends. Player 1 gets $60, Player 2 gets $30, and Player 3 gets $20. If Player 1 moves Right, then Player 2 gets to move. Player 2 can choose Top or Bottom. If Player 2 chooses Top, then the game ends. Player 1 gets $50, Player 2 gets $30, and Player 3 gets $20. If Player 2 chooses Bottom, then Player 3 gets to move. Player 3 can choose Up or Down. If Player 3 chooses Up, then Player 1 gets $40, Player 2 gets $40, and Player 3 gets $20. If Player 3 chooses Down, then Player 1 gets $90, Player 2 gets $60, and Player 3 gets $10. What is the Nash equilibrium of this game via backward induction? Clearly explain how you arrive at your answer. In answering this, you should draw the game tree for the game. However, you do not need to reproduce the game tree in your answer. But you must clearly articulate what strategy each of the three players will choose and what the resulting equilibrium is. (i) Consider the following payoff matrix for a two-player game where players move simultaneously. Using only the three numbers 1,5, and 8, depict the payoff matrix for a two-player simultaneous move game such that \{Bottom, Right } is the payoff dominant equilibrium while { Top, Left } is the risk dominant or secure equilibrium. Your payoff matrix should not involve dominated or weakly dominated strategies on the part of either player. (2 marks) (ii) Assuming players are risk-neutral and make their decisions based on maximizing expected values of game payoffs, what is the mixed strategy equilibrium for the game you have depicted in Part (i)? Briefly explain how you arrive at your answer. You must show the work you did to arrive at this answer. (4 marks) Part B: (4 marks) Consider a sequential move game played by three players, 1,2 and 3. Player 1 moves first and chooses Left or Right. If Player 1 moves Left, then the game ends. Player 1 gets $60, Player 2 gets $30, and Player 3 gets $20. If Player 1 moves Right, then Player 2 gets to move. Player 2 can choose Top or Bottom. If Player 2 chooses Top, then the game ends. Player 1 gets $50, Player 2 gets $30, and Player 3 gets $20. If Player 2 chooses Bottom, then Player 3 gets to move. Player 3 can choose Up or Down. If Player 3 chooses Up, then Player 1 gets $40, Player 2 gets $40, and Player 3 gets $20. If Player 3 chooses Down, then Player 1 gets $90, Player 2 gets $60, and Player 3 gets $10. What is the Nash equilibrium of this game via backward induction? Clearly explain how you arrive at your answer. In answering this, you should draw the game tree for the game. However, you do not need to reproduce the game tree in your answer. But you must clearly articulate what strategy each of the three players will choose and what the resulting equilibrium is