A competition authority introduces the following leniency programme. The first firm to come forward to reveal a cartel receives a fine reduction of L > 0. All other involved firms that are convicted pay a fine of F > L. If two firms apply at the same time, each is getting the fine reduction with probability 1/2. Now consider an industry in which two firms have formed a cartel. The cartel has stopped its activities. However, there is still a probability p that, in the absence of any leniency application, the competition authority discovers the cartel and imposes the fine F on both firms. (a) [10 marks] Write down the pay-off matrix of the leniency application game in which both firms simultaneously decide whether to apply or not. (b) [10 marks] Find all pure-strategy Nash equilibria. If applicable, find the Pareto- dominant equilibrium