= 1. [Ch.17 U3] Consider two players who bargain over a surplus initially equal to a whole number amount V, using alternating offers. That is, Players 1 makes an offer in round 1; if Player 2 rejects this offer, she makes an offer in round 2, if Player 1 rejects this offer, she makes an offer in round 3; and so on. Suppose that the available surplus decays by a constant value of c = 1 each period. For example, if the players reach agreement in round 2, they divide a surplus of V-1; if they reach agreement in round 5, they divide a surplus of V-4. This means that the game will be over after V rounds, because at that point there will be nothing left to bargain over. In this problem, we first solve for the rollback equilibrium of this game, and then solve for the equilibrium of a generalized version of this game in which the two players can have BATNAs. (a) Let's start with a simple version. What is the rollback equilibrium when V=4? In which period will the players reach agreement? What payoff x will Player 1 receive, and what payoff y will Player 2 receive? y (b) What is the rollback equilibrium when V=5? (c) What is the rollback equilibrium when V=10? (d) What is the rollback equilibrium when V =11? (e) Now we're ready to generalize. What is the rollback equilibrium for any whole-number value of V? (Hint: You may want to consider even values of V separately from odd values.) Now consider BATNAs. Suppose that if no agreement is reached by the end of round V, Player A gets a payoff a and Player B gets a payoff of b. Assume that a and b are whole numbers satisfying the inequality a+b