Game theory says "rational" players should claim $2. But real humans claim $97-$100—and earn FAR more! When does being "irrational" actually make you better off?
✈️ The Scenario
An airline lost your suitcase and another traveler's identical suitcase. You must each independently claim a value between $2 and $100. If claims match, you both get that amount. If they differ, both get the lower amount—but the lower claimant gets a $2 bonus and the higher claimant pays a $2 penalty.
Your Claim
$50
Opponent's Claim
???
$2 (Nash)$100 (Max)
Your Payout
$0
Opponent's Payout
$0
Opponent Type
The "Rational" Logic Chain
If opponent claims $100, I should claim $99 (get $101)
But they'll think that, so claim $98
But I know they'll do that, so claim $97
This continues all the way down...
...to $2! The Nash equilibrium.
Nash Equilibrium
$2
Both players "rationally" claim the minimum!
Session Statistics
Games played:0
Your total earnings:$0
Average per game:$0
If you always claimed $2:$0
The Paradox
The Nash equilibrium says both players should claim $2, earning $2 each. But humans typically claim $97-$100 and earn $95-$100 each—50× better! Being "irrational" pays off when everyone else is too.
When Rationality Becomes Absurd
In 1994, economist Kaushik Basu introduced the Traveler's Dilemma to highlight a fundamental problem with classical game theory's notion of "rationality."
The Setup
Two travelers lose identical antique suitcases. The airline asks each to independently claim a value between $2 and $100:
If claims are equal: both receive that amount
If claims differ: both receive the lower amount, but:
Lower claimant gets +$2 bonus
Higher claimant gets -$2 penalty
The "Rational" Death Spiral
Here's the reasoning that leads to disaster:
The Undercutting Logic:
1. If my opponent claims $100, I should claim $99 → I get $101, they get $97
2. But they'll anticipate this and claim $98 to undercut me
3. So I should claim $97 to undercut them
4. But they'll anticipate THAT...
5. This continues until both claim $2—the Nash equilibrium!
The logic is airtight. Each step makes sense. And yet the conclusion—that both players should claim $2 and receive $2—is absurd when they could both claim $100 and receive $100.
What Real Humans Do
In experiments, real people don't play the Nash equilibrium. Instead:
Most players claim between $95 and $100
Average claims are around $97
Almost nobody claims $2
Players earn approximately $95-$100 on average
By being "irrational," players earn 50 times more than the "rational" equilibrium predicts!
"The game's logic dictates that 2 is the best option, yet most people pick 100 or a number close to 100. Furthermore, players reap a greater reward by not adhering to reason in this way."
— Kaushik Basu
Why Nash Equilibrium Fails Here
The problem isn't with the logic—it's with the assumptions behind Nash equilibrium:
Common knowledge of rationality: Each player assumes the other will follow the undercutting logic perfectly
Infinite regress: The reasoning requires going 99 steps deep
Ignoring actual behavior: Real opponents don't undercut to $2
Basu's Purpose
Basu designed this puzzle specifically to challenge economic orthodoxy:
"I crafted this game to contest the narrow view of rational behavior and cognitive processes taken by economists...to challenge the libertarian presumptions of traditional economics and to highlight a logical paradox of rationality."
— Kaushik Basu, American Economic Review (1994)