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, and in order 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 game theory, the Nash equilibrium for the game 'The traveler's dilemma' is for each player to guess $2. What I find interesting --and please, correct if I am wrong -- is that if we alter the rules of the game slightly by removing the $2 minimum (and let the players choose negative values), then it becomes a game very similar to the dollar auction where there is no equilibrium, where the iteration escalates causing great loss to both players.
If player A guesses $2, then player B should guess $1, which means player A should guess 0 and so on...
So I guess the rational strategy would be to not play at all?
0 comments:
Post a Comment