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It is a perfect investment of incentives: it is not resolved by running better, but by understanding which horse is best to arrive late.
A sultan promises his inheritance to one of his two sons, but imposes a strange condition: The owner of the horse that arrives the latest in the neighboring city will win it. As soon as they hear the rule, the two princes stop moving.
Neither wants their horse to arrive before the other's. Time passes and, seeing that the race does not start, they consult a wise woman from the desert.
She tells them a single sentence. Immediately, the two mount up and speed away.
What did he tell them?
If each prince rides his own horse, both want that horse to arrive later, so neither has an incentive to advance. But if they exchange horses, each one starts riding the other's horse.
So, to win the inheritance, what is best for each prince is for his own horse—the one his brother is now riding—to arrive later. Therefore, everyone now has an incentive to have the horse they are riding arrive as quickly as possible.
The wise woman's phrase was, in essence: “Exchange horses.”
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