Amy and Ben are bargaining over a business opportunity that

Amy and Ben are bargaining over a business opportunity that is worth $100,000. Amy has an outside option that will give her $10,000 if she does not reach an agreement .  Ben\'s outside option is also $10,000. Bargaining proceeds as follows: First Amy proposes a division, then Ben accepts or rejects. If Ben accepts, the division is implemented (and the game ends). If Ben rejects, then the business opportunity drops to $50,000 in value and  Ben himself gets to propose a division. Then  Amy accepts or rejects. If she accepts then the division is implemented (and the game ends). If she rejects then the business opportunity drops to $25,000. Amy makes one final proposal. If Ben rejects then each player obtains their outside option (and the game ends). Assume that if a player is indifferent between accepting or rejecting a proposed division, then the player always accepts the division. Using backward induction, the prediction is that

A)Amy proposes $45,000 for herself and $55,000 for Ben.

B)Amy proposes $50,000 for herself and $50,000 for Ben.

C)Amy  proposes $65,000 for herself and $35,000 for  Ben .

D)Amy  proposes $90,000 for herself and $10,000 for  Ben .

Solution

We start with the last stage where they rejects all the offers hence get outside option of $10,000 each but if Ben accepts the offer before the last stage then he can make offer of anything more than $10000 to $15000

Now Ben can improve his payoff by offereing between $10000 to $40000

hence similarly Amy also think of inmprvoing his chances to earn higher payoffs therefore it is always beneficial for both the players to offer exact half as it is the Nash Equilibrium of above game

Option B is correct response