andidate Two firms (firm R and firm C) compete for customers and are considering improving le Edit their operations. Each firm has one of two options: (i) to invest in a new Al-powered recommendation system, or (ii) to invest in upgrading their Data Management Systems. Investing in the recommendation system carries a cost of 20 for each firm and generates a benefit of v 2 0 but, as this system is patentable, only one firm could reap this reward: if both firms invest in the recommendation system, then each gets, on expectation, v/2 while if only one invests it receives v. Upgrading Data Management Systems generates an individual benefit of 20 but also an individual cost that is increasing in the number of firms upgrading: if only one firm upgrades it bears a cost of 10, while if both firms upgrade, they each incur a cost of 19. Both firms simultaneously decide whether to invest in the recommendation system or upgrade Data Management. a. Write down the 2x2 payoff matrix of this game. What is firm R's best response, as a function of the parameter , to firm C upgrading its Data Management System? What is firm R's best response, as a function of the parameter v, to firm C investing in the recommendation system? (6 marks) b. Find all pure strategy equilibria as a function of the parameter v. (6 marks) c. Critically assess the validity of each of the following statements regarding the concept of Nash equilibrium in a simultaneous game: i."In a Nash equilibrium, there is no other profile of strategies which gives higher payoffs to the players." ii."In a Nash equilibrium, even after watching the rival's choice, a player would not profit from changing his/her intended strategy." (5 marks