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Section C: Answer ALL questions Question C1. Consider the following game played between two players, A and B. The players take it in turns to remove 1, 2 or 3 flags from a pile of 17 flags, with player A moving first. The player who takes the final flag, leaving none for the next player wins the game receiving a nominal payoff of 1, the other player receiving nothing. a) Define the concept of sub-game perfect equilibrium and explain how this differs from the Nash Equilibrium. b) In the game outlined above, derive the sub-game perfect equilibrium. c) Explain how the equilibrium outcome changes if the initial number of flags was changed from 17 to 16. (13.33%) Question C2. Consider the two player game depicted in the payoff matrix below: Player 2 А в X (6,2) (0,6) Y (1,0) (-1,3) z (2,6) (10,0) Player 1 a) Explain what a mixed strategy Is and provide an example of a real-life game in which we might observe players adopting such strategies. b) Determine all pure and mixed Nash Equilibria for this game. c) Suppose that the payoffs in the game changed such that X and A became dominant strategies for players 1 and 2 respectively, would this change the result from part (b)? Explain your answer.