What is the Traveler's Dilemma?

In game theory, the travelers dilemma is a non-zero-sum game (a game where ones gain doesnt lead to another's loss like a win-win situation or a loss-loss situation) in which the participants are looking to maximize 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.

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How does the Traveler's Dilemma Occur?

Travelers 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, Peters antique is similar to that of Pauls, 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, theyll 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 wont 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 Travelers 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.