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Question C2. Consider the two player game depicted in the payoff matrix below: Player 2 A B Player 1 X (6,2) (0,6) Y (1,0) (-1,3) Z (2,6) (10,0) 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. (13.33%) Question C3. Two flatmates, Amy and Ben, decide each week whether to clean their flat or not. Their payoffs are described below: Ben Clean Don't Clean Clean Amy (30,30) (35,5) Don't Clean (5,35) (6,10) a) Define what the tit-for-tat strategy is in the context of the game outlined above. b) Suppose that the flatmates make their decision in order to maximise their discounted utility with a discount factor of 8. Compute the present value for each player when they follow the tit-for-tat strategy and when that player chooses their best alternative strategy. c) For what values of 8 can the tit-for-tat strategy support an outcome where both flatmates clean every week? (13.33%)