Traveller’s Dilemma, formulated by Kaushik Basu in 1994, is a game theory paradox that shows the gulf between the rational choice (the Nash equilibrium) and real-life behaviour. The description of the game is as follows:
Two travellers, A and B, find their bags damaged by the airline when returning from a vacation. The bags and the artefacts inside are identical. The airline manager mentions that the policy allows a minimum of $2 and a maximum of $100 reimbursement. Since she does not know the value of the objects, the manager separates the travellers and asks them to write down the value. But, on a few conditions.
1) They can write a number between 2 and 100
2) They receive the same amount if they write the identical numbers.
3) If they are different, both will get the lower amount. In addition, the person with the lower quote gets $2 as a bonus, and the person with a higher one loses $2. For example, if A quotes 45 and B 80, A gets 47 (45 +2), and B gets 43 (45 -2).
Nash Equilibrium
The rational process goes like this. A first thinks of writing $100. A then changes her mind, thinking B could also write $100. In that case, both will receive $100. On the other hand, if A writes $99 (and B $100), A will get $101, including the bonus amount for being a lower quote. But A knows B can also think in similar logic, thereby changing her quote to 98, and so on. The Nash equilibrium is where both players write down $2!
The theory has been tested in web-based experiments by Ariel Rubinstein. The players had the task of writing a number between 180 and 300. The results, however, did not match the rational expectation. Most participants (55%) chose to write the maximum number. 17% wrote numbers between 295 and 299, 14% between 181 and 294, and only 13% wrote the Nash equilibrium of 180.
Reference
The Traveler’s Dilemma: Scientific American
