Semester One Final Examination, 2018 ECON2070 Introduction to Strategic Thinking 4. Consider the following normal form game. A B C A 5,5 0,6 4,4 B 6.0 1,2 3,1 C 0,0 3,3 2,1 (a) Find a Nash equilibrium in pure strategies. (2 marks) Now, consider the infinitely repeated game where each player evaluates a strategy profile using the average discounted payoff, that is: U,(s) = (1-8) ) 8-14,(8). 1-1 Recall that ET_, 8t-1 - 1-8 and taking the limit as 7 + co, we have ). 81-1 =- (b) Consider trigger strategies that use the Nash equilibrium you found in part (a) and are intended to enforce (A,C) being played in every period. Write down those trigger strategies. (2 marks) (c) Consider an arbitrary sub-game. How high must o be to ensure the trigger strategies you wrote down induce a Nash equilibrium in that subgame? Since the players are not identical in terms of payoffs, give an argument for each player. (8 marks)