Solution
Traveler's Dilemma
Show the problem again
An airline loses two travelers' identical antiques. Each independently claims an integer value from $2 to $100. Both are paid the lower claim; additionally, the lower claimant gets a $2 bonus and the higher claimant pays a $2 penalty. How many dollars do rational players claim in the unique Nash equilibrium?
Worked solution
The answer is $2. Against any claim x > 2, claiming x − 1 yields more than matching x (you get x − 1 + 2 = x + 1 instead of x). This undercutting logic unravels every pair of claims above the floor, so the unique equilibrium is ($2, $2). Like the ultimatum game, real players claim near $100 and do far better than equilibrium: a standard talking point on the limits of backward-induction reasoning.
Source: Introduced by Kaushik Basu (1994). Statement written for AxiomIQ.