Question

2. (25) My sons (“Boy 1” and “Boy 2”) are negotiating over how to divide a pile of 20 chocolates. Boy 1 will engage Boy 2 in up to three rounds of negotiations. The order of events is:

FIRST ROUND: Boy 1 makes Boy 2 an initial offer. Boy 2 accepts or rejects. If he accepts, the game ends and the two boys get their chocolates. If Boy 2 rejects, I punish them for not working together by eating 5 chocolates myself. The game then continues with 15 chocolates to be divided.

SECOND ROUND: Boy 2 makes an offer. Boy 1 accepts or rejects. If he accepts, the game ends and the two boys get their chocolates. If Boy 1 rejects, I eat 5 chocolates myself and the game continues with 10 chocolates to be divided.

THIRD ROUND: Boy 1 makes a final offer. Boy 2 accepts or rejects. If he accepts, the two boys get their chocolates. If Boy 2 rejects, the game ends and I eat all the remaining chocolates. Note that I am expecting you to make an assumption of spiteful players, all else equal. Said another way, I assume that “reject” will break the indifference of getting zero either way...

(a) (5) If we reach the third round of the game, what would be Boy 1’s offer?

(b) (5) Given that my sons know (a) in round 2, what would be Boy 2’s 2nd Round offer?

(c) (5) Given that my sons know (b) in round 1, what would be Boy 1’s 1st Round offer?

(d) (10) What is Boy 1’s first-round strategy? What is Boy 2’s first-round strategy? What is the equilibrium outcome of the game?

Answer 1

a) inside the third round:

Kid one and Boy a couple of catch that on the off chance that the give is rejected, at that point they'll get zero doughnuts, that is also the tie-breaking reason. in this way Boy one can give at least one friedcake to Boy a couple of and keep fifty nine doughnuts.

On the off chance that Boy a couple of rejects the give she will get zero. along these lines she is going to make due with the give.

Balance result are Boy one fifty nine friedcakes and Boy a couple of one doughnut.

(b) Second round;

Since every one of them square measure caution to the final product inside the third circular. conjointly amid this round, Boy a couple of necessities to give. thusly something yet fifty nine doughnuts won't be adequate by Boy one. Also, at fifty nine doughnuts Boy one are detached.

Henceforth, balance sum are Boy one fifty nine doughnuts and Boy a couple of twenty one doughnuts.

(c) inside the first round:

Presently amid this round, Boy one needs to give to Boy a couple of and each square measure caution to the second circular results.

So amid this situation, something however twenty one doughnuts won't be worthy to Boy a couple of. Also, Boy a couple of are unconcerned at twenty one doughnuts.

Thus, balance sum are Boy one seventy nine doughnuts. also, Boy a couple of twenty one doughnuts.

(d) Boy one system are to supply Boy a couple of the amount that Boy a couple of couldn't cannot, so diversion doesn't move to second round.

Kid a couple of methodology are to it diversion shouldn't move to the third circular.

Harmony result is Boy one seventy nine doughnuts and Boy a couple of twenty one doughnuts