The original game scenario was formulated in 1994 by Kaushik Basu and goes as follows:[1][2] "An airline loses two suitcases belonging to two different travelers.
However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travelers will receive that amount along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount.
If it is used where there is information asymmetry- the Airline manager does not know the value of the antique- the result will be irrational behavior.
Remarkably, and, to many, counter-intuitively, the Nash equilibrium solution is in fact just $2; that is, the traveler values the antiques at the airline manager's minimum allowed price.
For an understanding of why $2 is the Nash equilibrium consider the following proof: The above analysis depends crucially on (1) imperfect information- the airline manager does not know the true value and (2) irrationality- in particular failure to use the Muth Rational strategy.
[3] When the game is played experimentally, most participants select a value higher than the Nash equilibrium and closer to $100 (corresponding to the Pareto optimal solution).
This paradox could reduce the value of pure game theory analysis, but could also point to the benefit of an expanded reasoning that understands how it can be quite rational to make non-rational choices, at least in the context of games that have players that can be counted on to not play "rationally."
[6] Experimental findings show that groups are always more rational – i.e. their claims are closer to the Nash equilibrium - and more sensitive to the size of the bonus/malus.
(The minimum guaranteed payout is $1, and each dollar beyond that may be considered equivalent to a year removed from a three-year prison sentence.)
These games tend to involve deep iterative deletion of dominated strategies in order to demonstrate the Nash equilibrium, and tend to lead to experimental results that deviate markedly from classical game-theoretical predictions.