Game Theory

[1] Consider the following game. Two travelers took a flight to Pittsburgh. The two travelers happen to have the exact same type of luggage with the same contents. Fur- ther, the airline lost both of their bags. The airline representative says that the airline is willing to compensate each of them for the lost luggage. The airline is worried, though, that the travelers will over-represent the value of the bag. Thus, the airline represen- tative asks each traveler (independently) what the value of the lost bag is. Since the travelers have the same bag, the airline is willing to pay each of them if they each an- nounce the same value for the bag. To incentivize honesty, if they announce different values, then the airline will pay the traveler who announces the lower value twice the amount s/he stated and the other traveler receives zero. How much will each traveler announce is the value of the bag in the Nash Equilibrium