Consider a market with two large firms. The demand function is estimated as P=100-10Q and firms have a constant Marginal Cost of 20. Firms have discount factor <1. They compete on prices and they interact only in 2 periods.

The antitrust authority (AA) is considering the introduction of a leniency program. In this program, firms can report in period 2 that they engaged in collusion during period 1. When any firm reports, the AA intervenes in the market and it takes any profit that firms make. On top of removing any profits, the program establishes the following penalties:

• if only one firm report, the reporting firm gets immunity ( profits =0) but the other firm gets a fine of 200.
• if both firms report, each firm gets a fine of 100.

a) discuss why this leniency program could end up inducing firms to collude in period 1. Explain under which condition this would happen. You need to discuss if collusion in period is sustainable as a SPE with some strategy. Hint: In period one firms have 2 actions, collude or not. In period two, they have 3 actions. {Collude and don't report, Don't Collude and don't report, Report}.

b)Suppose that =0.9 and propose a modification to the program's fines such that collusion is not sustainable for these firms.