Question

Five dollar bills are to be shared by two players. Ann makes an offer how to share them, which Beth can either accept or reject. If she accepts, the bills are divided as agreed upon. If the rejects, two dollar bills are taken away and only three remain on the board. Then Beth makes an offer how to share them, which Ann can accept or reject. If Ann accepts, the bills are divided accordingly and if she rejects nobody gets anything. Sketch the extensive form of the game and find the equilibrium path. What is the optimal move for Ann and Beth? Remember that you don’t have to draw the whole game tree.

Answer 1

The extensive Game Tree is drawn as below

The first Payout is that of Beth and the second Payout is of Ann.

Ann knows that if she rejects, no one gets anything. So she will accept Beth's proposal.

However, Beth knows that the best case scenario will be for her to get $3

ANd Ann knows that since Beth can get a maximum of $3, so it is best to propose a $3 payout to Beth in the first round and $2 for herself. Beth, since she is getting her best payout, will accept.

So the equilibrium will be Ann proposes a payout of $3 for Beth and $2 for herself in the first round which Beth will accept.

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