Traveler's Dilemma

The Scenario

You and another traveler lose identical antiques. An airline manager, unable to determine the true value, asks you both to secretly write down a value between **$2 and $100**.

If you both write the same value, you both get that amount.
If you write different values, the lower value is used as the base. The person who wrote the lower value gets that amount **PLUS a $2 bonus**. The person who wrote the higher value gets that same amount **MINUS a $2 penalty**.

The logical choice seems to be to undercut your opponent slightly, but how far does that logic go?

Conclusion: A Race to the Bottom

This dilemma is a powerful example of how pure, iterative logic can lead to a seemingly irrational outcome:

The Temptation to Undercut: No matter what value the other player chooses (e.g., $100), it's always slightly better for you to choose $99. You would get $99 + $2 = $101, while they get $99 - $2 = $97.
A Cascade of Logic: Your opponent, knowing this, realizes they should claim $98. But then you should claim $97... and so on.
The Nash Equilibrium: This "race to the bottom" logically continues until both players claim the minimum value: **$2**. This is the only point where neither player can improve their outcome by changing their claim.
Rationality vs. Reality: In practice, most humans do not claim $2. They claim much higher, showing that our decision-making involves trust and an intuitive grasp that hyper-rationality can be self-defeating.

Traveler's Dilemma ✈️

The Scenario

Play the Game!

Conclusion: A Race to the Bottom