1 Signaling - Reputation Game Consider the following duopoly consisting of Firm 1 (The Incumbent) and Firm 2 (The Entrant) that operate on a market with two time periods. Profits are denoted in thousands of dollars (K). In period 1: Both firms are on the market, but only Firm 1 takes an action. Firm 1 (the Incumbent ) can either "prey" or "accommodate". In period 2: Only Firm 2 takes an action: Firm 2 (the Entrant) can either "stay" in the market or "exit " the market. Information problem: Firm 1 has either a sane or crazy CEO, which is a priori not known to the CEO of Firm 2. The probability that Firm 1's CEO is sane is 20% (with the remaining 80% the CEO is crazy). Payoff of Firm 2: In period 1, Firm 2 makes $100K profits if Firm 1 accommodates, but -$50K if Firm 1 preys. In period 2, if Firm 2 stays, it gets a payoff of $100K if Firm 1's CEO is sane, but -$50K if the CEO is crazy (assuming that in period 2 a crazy CEO at Firm 1 remains hostile toward Firm 2). If it exits, Firm