Question

Anne and Ben are bargaining over how to split the value of a joint venture. Initially the joint venture has a value $100. Bargaining takes place as an alternating offers bargaining game. Ben gets to make two offers for every one that Anne makes. An offer by Ben is simply a suggestion of how much value should go to him and the remainder of the joint venture value will then go to Anne. If an offer is rejected, the bargaining game moves on to the next period. For each period that passes the value of the joint venture is reduced by $1. Hence, in the first period Anne and Ben are bargaining over $100. If they fail to reach agreement they will in period 2 be bargaining over $99, etc. The bargaining potentially goes on until there is nothing left to bargain over. If Anne and Ben fail to reach agreement, they each get a payoff of zero. Ben makes the first offer. If it is rejected, he makes an offer again in round 2. If that is rejected, Anne makes an offer in round 3. If rejected Ben makes an offer in round 4, and so on. Thus, Anne makes offers in rounds 3, 6, 9, . . . . Ben makes offers in the other rounds.

1) If the parties were to reach the last period of bargaining where there is still a strictly positive value to the venture, who would be making the offer in this period? Consider this period effectively the last period of the alternating offers game.

2) What is the Nash equilibrium of the last period subgame?

3) Using backward induction, what is the subgame perfect Nash equilibrium? Is agreement reached and if so, what is the value of the joint venture upon agreement? What is the agreed upon split?

Answer 1

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