Part 1 Equilibrium Selection Consider the following version of the example in section 2 of Kandori et al (1993). " Learn- ing, mutation, and long run equilibria in, games" with students meeting in pairs every period to work together with each using one of two computer systems, 31 or 82. There are 9 students in the group and the payo matrix is 31 52 31 3,3 0,0 82 U,\" 11 1 During each period every student meets every other student once and at the end of each period1 students observe the average payoffs frOm having each computer system. Those who have the system doing worse on average change their systems for the next period. Also at the beginning of each period, before meetings begin, each member of the group exits (mercies) with a probability 5 and is replaced by a student who has computer system 31 with probability m and 32 with probability [1 m). The meetings then take place with no opportunity to change computer systems during the period. Let 2: represent the state of the system which is the number of the nine students with computer system 51 and ads) the average payoff of a student with computer system a; when the state is 2:. (a) What are the three Nash equilibria of this game? (b) Work out the values of z for which the system moves to coordination on 51 and for which it move to coordination on 32 (check this with average payoff calculations). Illustrate the basins of attraction on a line and indicate how many nmtations are required to escape from each equilibrium. (c) Give the intuition for why coordination on .51 is more likely in the long run when the mutation rate is sufciently small and how this result is independent of in. so long as m > 0. (d) Briey discuss how the approach in this paper is an improvement on other ways of addressing the equilibrium selection problem and also comment on any limitations. Please turn over for part 2 Part 2 Backwards Induction Sarah and Mark play the repeated Prisoner's Dilemma for exactly N periods. (8) (f) (g) Explain why the subgame perfect equilibrium is for both to defect every period whatever the value of N. When Sarah and Mark play this game with N = 2 they play the subgame perfect equilibrium. However, when they play with N = 1000, they both start off coop- erating and both defect for the rst time in period 998 and then defect for the remaining two periods. How would you explain their play? What do you predict will happen if they play with N = 1000 a second time? Search the literature for papers that relate to the nitely repeated prisoner's dilemma and the backwards induction solution which is to defect every period. Summarise One or more of the papers you nd. If it is one paper give a more detailed summary and if it is more than one, compare and contrast them. (A reminder that in the class exam information email you were guided to have a minimum of 500 words for this part)