Question

Eddy and Amy were two travelers on vacation. They did not know each other but they both took a tour on a sightseeing bus the same day. During the trip, the both bought a local painting that was exactly the same and cost the same amount

. Each paid with cash and were not given a receipt. The tour guides offered to store the paintings for both Eddy and Amy. However, the tour guides lost the paintings. The tour company policy for lost items is to reimburse the amount of the lost item from a minimum of 2 dollars up to maximum of 100 dollars. However, since Eddy and Amy did not have a receipt the tour company

manager could not verify the amount they each spent on the painting. So, the company manager separated Eddy and Amy into different rooms and asked them to write down how much they paid for the painting. The manager told them if they write the exact same amount for the painting as the other traveler, then they will be reimbursed that amount of money. If one of them writes a number smaller than the other, then the smaller number will be used as the reimbursement value. In that case, the person who wrote the smaller number will receive that reimbursement plus a 2 dollar bonus and the person who wrote the larger number will receive the smaller number as reimbursement minus 2 dollar.

•Assume that both Eddy and Amy only care about their own payoffs.

Find the Nash equilibrium strategy for Eddy and Amy.

Answer 1