Consider two players who bargain over a surplus initially equal to an integer value ofV, using alternating offers. That is, Player 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 one each period. For example, if the players reach agreement in round 2, they divide a surplus ofV1; if they reach agreement in round 3, they divide a surplus ofV2. This means that the game will be over afterVrounds, because if the offer is rejected at that point there will be nothing left to bargain over and both players get nothing.

1. (a)Let's start with a simple version. What is the SPE of this game ifV=2? In which period will they reach agreement? What are the equilibrium payoffs for both players? Does player 1 or 2 get higher payoff?
2. (b)What is the SPE of this game ifV=3? Does player 1 or 2 get higher payoff?
3. (c)Canyoufollowthelogicinpart(a)tofindtheSPEofthisgameifV=4? Doesplayer1or2
4. get higher payoff?
5. (d)Canyoufollowthelogicinpart(b)tofindtheSPEofthisgameifV=5? Doesplayer1or2 get higher payoff?
6. (e)Now we're ready to generalize the above results. What is the SPE for any integer value ofV? In which case is there a first-mover advantage? (Hints: you may consider the case for even values ofVand odd values ofVseparately.)