Matches marks total) Imagine an innite population of players, that pair up randomly and play matches against one another. A match oonsists of a n rounds {where n is a nite positive integer]. In each round, the players play the following stage game: The payoff to a player for a match is the sum of their payoffs over the n. rounds of that match (Note: you do not need to discount future payoffs in this question). We dene the following three strategies: In 'Always Cooperatel (denoted ('3'): Play c in every round. It 'Always Defect' [denoted D}: Play d in every round. a "I'it-for-tat" [denoted T}: Play c in the rst round. In all subsequent rounds, play whatever your partner played the round before. {a} (2 marks) Construct a payoff matrix for a match. Your answer should be a symmetric 3 X 3 matrix. {b} {2 mark] Can you eliminate any strictly dominated strategies? Can you eliminate any weekly dominated strategies? How do your answer to these questions depend on n? [c] {4 marks] Find all evolutionarily stable strategies. If applicable, explain how they might depend on n. [d] (2 marks) Suppose that the population begins with an equal frequency of each type of strategy {i.e. 1f3 play C, 1 f 3 play D and 1f3 play T]. Towards which ESS do you expect the population will evolve? Does your answer to the previous question change as it changes