The traveler's dilemma

Question

Two travelers lose identical items and must each privately claim a value, an integer from $\$ 2 $to$ $100 $. The airline pays **both** travelers the **lower** of the two claims. As an anti-cheating twist, the traveler who claimed lower also gets a$ $2 $bonus, and the higher claimant pays a$ $2$ penalty. If the claims tie, both simply receive that amount.

What do you claim? Give the game-theoretic answer and what people actually do.

Accepted Answer

The equilibrium is \2, the floor. Suppose you expect your opponent to claim \100. Then claiming \99 pays you 99 + 2 = \101, beating the \100 you would get by matching. But your opponent reasons the same way and undercuts to \98, so you undercut to \97, and the logic of "always claim one dollar below what you expect" cascades all the way down. Formally, for any claim x you expect, claiming x - 1 yields (x-1) + 2 = x + 1 x, so every claim above 2 is dominated. The only place the undercutting stops is the floor: both claim \mathbf{\2} and each receives \2. That is the unique Nash equilibrium. Wh…

The traveler's dilemma

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