game theory

6. You are the bargaining coordinator for Sun Car Manufacturers.  At present you are renegotiating the labor contract with the union representative.  You are bargaining over an expected 20 percent increase in earnings over the next three-year contract period.  You are trying to decide whether to offer one-third, one-half, or all of the increase in earnings to the union.  The union rules are such that all contracts must be voted on.  The additional earnings are contingent on getting started on the new contract next week.  If an agreement isn't reached on the first round of negotiations the firm will go out of business.  The union representative tells you that if you do not give the union all of the additional profits, the union members will not vote for the agreement.

a. Show the extensive form of this game.
b. What will you offer the union?  Why?