An airline loses two suitcases belonging to two different travelers. 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. The challenge is: what strategy should both travelers follow to decide the value they should write down?
In Nash equilibrium, $2 is what each of the travel will write down. Because if one travel writes $100, while the other writes $99, that person will lose $2 to be $98 while the other will gain $2 to be $101. Writing down $99 is better than $100, and so on. Therefore, the equilibrium is at $2 when each traveler finalizes their price.
Real life application
- suppliers would sell a certain product cheaper than its competitors by secreting cutting corners
- education will take an early shape on a child because it “forces” the children to have early education
Benc Tan 