2.1 Game Theory (21 points): Consider a differentiated products duopoly game in which firms have three possible price strategies: C= collusion, B=Bertrand, and W=price war. Pay-offs for the two firms are given below in (1,12) order: Firm 2 Strategies Firm 1 Strategies: C B W C 4.4 0,5 -1,5 B 5,0 2,2 -1,1 W 5,-1 1,-1 0,0 a. What are the possible pure strategy Nash equilibrium/equilibria to the one-shot play of this game? If firms play the game only once, what strategy do you expect each firm to play? What will their pay-offs be? Explain. Now consider a two-period game with the pay-offs given above for each period. Suppose firms have the following beliefs: (i) If both firms play collusive in period 1, both will play Bertrand (B) in period 2. (ii) If either firm cheats (plays P