Nash equilibrium

Question Two - One Shot Game and Tit-for-tat Consider two companies that can either cooperate or cheat when they work together. The payoffs of both strategies are given below: Company B Cooperate Cheat Company Cooperate 25, 25 15, 30 Cheat 30, 15 20, 20 a) Find the Nash equilibrium in this one shot game. 4 Marks January 2022 Microeconomics II ECONI153 Page 2 of 10 Approved b) Is the Nash equilibrium you just found Pareto efficient or Pareto inferior? Explain. 2 Marks c) Now consider that a number of companies make their business decisions in a repeating pattern. When two companies match to collaborate for making business, they might follow a tit-for-tat strategy: they cooperate on high prices in the first round and do what their competitor does in the next round. Or they might decide to cheat from the first round. Hence, the returns for the companies become the following: Tit-for-tat Cheat 25/P. Tit-for-tat 15+20(1-Py/P, 25/P 30+20(1-Py/P Cheat 30+20(1-P)/P. 20/P 15+20(1-Py/P 20/P Where P indicates the probability of terminating the high price strategy in each round. Write the payoff functions for tit-for-tat and cheat strategies and find the equilibrium proportion of tit-for-taters (T) in this market. 6 Marks d) For which values of expected number of rounds in the game, will all the players in the long-run certainly follow a tit-for-tat strategy. 4 Marks e) Now consider that P takes a value that would lead to an unstable interior equilibrium in which both tit-for-taters and cheaters exist. Find the impact of rising P on the basin of attraction of the tit-for-tat and explain what this result intuitively means