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# Traveler’s Dilemma – Definition

### Traveler’s Dilemma Definition

In game theory, the traveler’s dilemma is a non-zero-sum game (a game where one’s gain doesn’t lead to another’s loss like a win-win situation or a loss-loss situation) in which the participants are looking to maximise gains without regard for each other. This game displays the research that making irrational choices often produces a better result in game theory, and is termed the “paradox of rationality.”

### Understanding Traveler’s Dilemma

Traveler’s Dilemma was formed in 1994 by game theorist Kaushik Basu, where he illustrated this concept using an example of two airline passengers. For conciseness, let us assume that two travelers Peter and Paul, after returning from a journey in Caribou found out that one of their antiques got ruined. In this case, Peter’s antique is similar to that of Paul’s, and both are of the same quality and price. Now the airline manager is willing to compensate them for their loss, but has no idea about the actual price of these antiques. The airline manager, being a smart individual knows that if he asks both of them to come up with a price, they’ll inflate it, and so he decides to use another means. He simply asks both fellows to come up with a price between \$2 and \$100 without consulting each other. He makes it known that the person with the lowest price gets a \$2 bonus, while the one with a higher price gets a \$2 penalty for being dishonest. However, if the prices are the same, each participant won’t incur a bonus or a penalty, and the agreed sum will be released to both of them.

Mathematically, if Peter comes up with \$68 and Paul comes up with \$62, then the manager will take \$62 as the actual amount, and pay both participants this amount. However, Peter will have to go home with \$60, and Paul with \$64 (penalty and bonus). According to Traveler’s dilemma, the rational choice is \$2, which is also the Nash Equilibrium. \$2 is the rational choice, because Peter, at first, will come up with \$100, and this would work only if Paul is as greedy as he is. However, Peter knows that there is a chance that Paul might write \$99 to get \$101 (plus \$2 bonus), so he goes on to write \$98, thus spiraling all the way down to \$2, which is the least they can go. At \$2, each participant has nothing to lose, thus it is called the Nash Equilibrium.

### References for “Traveler’s Dilemma”

https://en.wikipedia.org/wiki/Traveler%27s_dilemma

https://www.investopedia.com › Economy › Economics › Behavioral Economics

https://www.quora.com/Game-Theory-What-is-the-travelers-dilemma

### Academic research for “Traveler’s Dilemma”

Anomalous behavior in a traveler’s dilemma?, Capra, C. M., Goeree, J. K., Gomez, R., & Holt, C. A. (1999). Anomalous behavior in a traveler’s dilemma?. American Economic Review, 89(3), 678-690.

The traveler’s dilemma, Basu, K. (2007). The traveler’s dilemma. Scientific American, 296(6), 90-95.

Experiments with the traveler’s dilemma: welfare, strategic choice and implicit collusion, Basu, K., Becchetti, L., & Stanca, L. (2011). Experiments with the traveler’s dilemma: welfare, strategic choice and implicit collusion. Social choice and welfare, 37(4), 575.

Stochastic evolutionary dynamics resolve the Traveler’s Dilemma, Manapat, M. L., Rand, D. G., Pawlowitsch, C., & Nowak, M. A. (2012). Stochastic evolutionary dynamics resolve the Traveler’s Dilemma. Journal of Theoretical Biology, 303, 119-127.

How to play well in non-zero sum games: Some lessons from generalized traveler’s dilemma, Tošić, P. T., & Dasler, P. (2011, September). How to play well in non-zero sum games: Some lessons from generalized traveler’s dilemma. In International Conference on Active Media Technology (pp. 300-311). Springer, Berlin, Heidelberg.

Behavior in one-shot traveler’s dilemma games: model and experiments with advice, Cabrera, S., Capra, C. M., & Gómez, R. (2007). Behavior in one-shot traveler’s dilemma games: model and experiments with advice. Spanish Economic Review, 9(2), 129-152.

[PDF] The effects of common advice on one-shot traveler’s dilemma games: explaining behavior through an introspective model with errors, Capra, C. M., Cabrera, S., & Gomez, R. (2003). The effects of common advice on one-shot traveler’s dilemma games: explaining behavior through an introspective model with errors. Documento de trabajo, 17.

[PDF] Unraveling the Traveler’s Dilemma Puzzle-A Level-k Approach, Baghestanian, S. (2014). Unraveling the Traveler’s Dilemma Puzzle-A Level-k Approach. Goethe Universität Frankfurt am Main, Working Paper.

The rationality of irrationality for managers: returns-based beliefs and the traveler’s dilemma, Velu, C. K., & Iyer, S. (2009). The rationality of irrationality for managers: returns-based beliefs and the traveler’s dilemma. Available at SSRN 1334909.

The traveler’s dilemma: Paradoxes of rationality in game theory, Basu, K. (1994). The traveler’s dilemma: Paradoxes of rationality in game theory. The American Economic Review, 84(2), 391-395.