1. (15 points) A professional baseball team determines a new player s mitting a salary offer to an arbitrator. salary request to the arbitrator without knowing the team's offer. Assume that both the salary offer and the request will be either $20 (million) or $10 (million). If the offer is at least as much as the request, then the arbitrator chooses the average (that is the midpoint) of the two as the salary, which determines the payoff. For example if both the offer and the request are $20 million then the payoffs are (-20, 20) to (T, P) where T denotes the team and P denotes the player. If the offer is less than the request then the arbitrator simply chooses the amount of the offer as the salary, which, if not appealed, yields a payoff of (-10, 10). (Note that the first element in the vector is the payoff to T and the second the payoff to P). However the player P has the right to appeal in the case when the offer is less than the request. WE will make the following simplifying assumption: if there is an appeal then P is awarded the requested $20 million, but only after a costly arbitration process which costs both parties $1 million in fees. Consequently in such a scenario, the net final payoff vector is (-21, 19). (a) Provide an extensive form representation of this 2-player game. Choose the rep- resentation where T decides at the initial node. (5 points) (b) Write the game in normal form. (Let T be the row player and P the column player). (5 points) (c) What strategies are rationalizable strategies (5 points)