What it means
In the standard story, an airline damages two identical items belonging to two separate travellers. The manager asks each to write down a claim between $2 and $100 without consulting the other, and promises the following rule: if the claims match, both are paid that amount.
If the claims differ, the airline assumes the lower figure is the honest one. It pays both people the lower amount, then adds $2 as a reward to the person who named it and subtracts $2 from the person who named the higher figure.
The twist is that naming a slightly lower number than your partner is always profitable. If both claim $100, either can claim $99 instead and receive $101 while the other receives $97, so undercutting looks sensible for both.
The argument repeats at each step. After $99, the next undercut is $98, and the process continues down to the lowest allowed claim of $2, which is the Nash equilibrium (a pair of choices where neither player can do better by changing alone).
The puzzle is famous because the equilibrium is so poor. Both travellers could receive $100 by cooperating, yet logic drives them to $2, and in experiments people mostly choose high values, often close to the maximum, especially when the reward for undercutting is small.
The lesson for business is about trust and incentives. Price wars, bidding contests and negotiations can follow the same pattern, in which each side's sensible reaction to the other pushes both towards a worse outcome than if they cooperated.
In practice
Real-world examples.
Example
Two rival bakeries in a town each decide whether to cut the price of a loaf. Each cut wins customers from the other for a short time, but when both cut, margins fall for everyone and neither gains market share.
Example
Two suppliers bid for a contract worth up to $100,000 and know that the buyer will choose the lower bid. Each is tempted to undercut by a small amount, and the process repeats until the bids approach a loss-making level.
Example
Two partners in a joint venture are asked to report the value of their shared assets for a buyout. A small reward for the lower report and a small penalty for the higher report encourage both to understate, even though honest reporting would give a better result.
Formula
Calculation
For claims a and b, the payoffs are:
If a = b, each receives a.
If a < b, the first receives a + 2 and the second receives a - 2.
Take an illustrative case where traveller A claims $100 and traveller B claims $99. The lower claim is $99, so B receives $99 + $2 = $101 and A receives $99 - $2 = $97. If both had claimed $100, each would have received $100, so B gains $101 - $100 = $1 by undercutting, while A loses $100 - $97 = $3. If both then claim $2, each receives only $2.Case study
Seen in the real world.
Harborview Holdings is an illustrative, fictional company that asked two divisions to submit a cost estimate for a shared project. The rule was that the division giving the lower estimate would receive a small bonus, and the other would have its budget trimmed slightly.
The first round produced estimates of $950,000 and $940,000. Each division then reduced its figure to beat the other in later rounds, and by the third round both estimates were below the true cost of the work.
The chief financial officer saw that the incentive was producing unreliable numbers, so the company replaced it with a single agreed estimate reviewed by an independent team. In this illustrative story the project came in on budget, and the lesson was that rewards for undercutting each other can make everyone worse off.
Watch out
Common mistakes.
- Assuming the logical answer is what people actually do, when experiments show many choose high numbers.
- Reading the game as a literal travel problem rather than a model of incentives and trust.
- Believing cooperation never works, when repeated contact, communication and reputation can sustain better outcomes.
Questions
People also ask.
Why is the equilibrium so low?
Each player gains by undercutting the other by one step, and the same reasoning repeats until the minimum claim is reached.
Why do real players choose high values?
They may expect the other player to cooperate, care about fairness, or find the reward for undercutting too small to be worth the risk.
Where does this appear in business?
In price wars, auctions, internal budgeting and any situation where small rewards for undercutting push parties towards worse results.
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