An airline loses two suitcases belonging to two different travelers, Alice and Bob. Both suitcases happen to be identical and contain identical antiques. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of \( \$ 100 \) per suitcase-he is unable to find out directly the price of the antiques. To determine an honest appraised value of the antiques, the manager separates both travelers so they can't confer, and asks them to write down the amount of their value at no less than \$2 and no larger than \( \$ 100 \). He also tells them that if both write down the same number, he will treat that number as the true dollar value of both suitcases and reimburse both travelers that amount. However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travelers will receive that amount along with a bonus/malus: \( \$ 2 \) extra will be paid to the traveler who wrote down the lower value and a \( \$ 2 \) deduction will be taken from the person who wrote down the higher amount. Find all the Nash equilibrium/equilibria and explain why
