A company is negotiating wages with its union. The firm's profits are E = 10 where is the salary. The objective function of the union union is U = 10  (^2)  5. The rules of wage bargaining are as follows: The company makes a salary offer that the union must accept or reject. In case of acceptance, the negotiation ends and each party takes the payments described above, given the agreed salary. In case of rejection, the union makes a counter offer that the company must accept or reject. In case of rejection, each party takes zero. In case of acceptance, each party takes the payments described above according to the agreed agreement. The company and the union do not value the present the same as the future, in particular, the discount factor is  = 0.8. Finally, assume that if an agent is indifferent between accepting or rejecting the proposed salary, he accepts.

 

d.1) Graph the extensive form of the game indicating the actions of each player in each set of information, as well as the payments of each player. Also, for each player, specify which elements make up a strategy.

d.2) If we reached the second stage of the game, what salary would the union offer in that stage? What would be the payments for each party, firm, and union? Justify each step.

d.3) Find the unique subgame perfect equilibrium of this bargaining game. It indicates the salary that is agreed as well as the payments of each party. It also indicates when the agreement will be reached and the benefits for the company and for the union. Justify each step.

d.4) Study how the strategies that make up the subgame perfect equilibrium would be affected when initially = 0.8 and we let tend to zero. Could you give an interpretation of this result? Justify each step