Traveler's Dilemma

The “traveler’s dilemma” is a fun concept in game theory developed by Kaushik Basu, where two players each try to get the most amount of money for their own antiques. Sound thrilling? Oh, it is.

Here’s the full story: two airline passengers on the same flight happen to have checked identical antique items into their suitcases, unbeknownst to one another. These are our travelers. Let’s call them Roy and Roger, just for giggles. Anyway, as sometimes happens, both of their suitcases were mysteriously damaged during the flight, and both of their antique items—let’s say they’re rotary phones, because those things are practically antiques nowadays anyway—were also damaged. The nice airline manager has offered to compensate each of them for the rotary phones, but here’s the deal: he doesn’t know what they’re worth. And since this dilemma was developed in 1994, he couldn’t just look it up on his smartphone.

So he lays out a little proposal for Roy and Roger. He’s willing to give them each somewhere between $2 and $100 for their rotary phones, but he’s going to attach some rules:

1) Roy and Roger each have to write down what they think their phone is worth, and they can’t talk to each other about it.

2) If they both write down the same amount, that’s what they each get.

3) If one writes down a higher amount, the airline manager will assume he’s exaggerating and accept the lower amount as the true value, and that’s what they’ll each get. In addition to that, he’ll take a $2 penalty from the high bidder for being shady and give it to the low bidder for being honest.

And that, friends, is the traveler’s dilemma. Which dollar amount to choose? According to the Nash equilibrium, Roy and Roger should each write down $2, because that’s the minimum permissible price. But let’s be real—neither of them is likely to write down $2. They’re a lot more likely to choose a value closer to $100, because even if they end up writing down slightly different numbers, they’ll both still walk away with a whole lot more than $2.

So why do we care about Roy, Roger, a somewhat sadistic airline manager, and a couple rotary phones? Because the traveler’s dilemma illustrates something known as the “paradox of rationality”: sometimes, game theory’s totally rational models and outcomes don’t work out as well as good old-fashioned self-interest and illogical-ness.

Deep stuff, right? See? We told you it would be thrilling.