"Lucy and Pete, returning from a remote Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it. Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44. "
What is your choice? What is your reasoning?
People generally make choices at $100 or just a little lower while game theory predicts that a rational player should play $2. See original article in Scientific American and Letters and Responses that give all the details.
Things never get as close to game-theoretic ideal of rationality and "rationality being common knowledge among the players" as when game-theoreticians play against each other. But even game-theory professionals that know that they play against other game-theory professionals still choose values close to $100. And this is not a problem of lack of analytical skills - nobody would suspect that they can't apply backward induction to the problem.
Finally, the question that I was mostly interested in – how would people play if presented with structurally identical problem but with punishment/reward value increased from $2 to some higher value? To my satisfaction, further research shows that people are more likely to come closer to the game-theoretic prediction (the lowest possible choice) in this case.
More links:
- What were they thinking? chart
- Play the game online
- article "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions" by Jacob K. Goeree and Charles A. Holt
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