I heard this tale in India. A hat seller, on waking from a nap under a tree, found that a group of monkeys had taken all his hats to the top of the tree. In exasperation he took off his own hat and flung it to the ground. The monkeys, known for their imitative urge, hurled down the hats, which the hat seller promptly collected.

我在印度听说过这个故事。一名帽商，在一棵树下打盹，醒来后发现，一群猴子早已把他的全部帽子都戴在树顶。恼怒中，他脱下自己的帽子，并把它扔在地上。这群因强烈的模仿冲动而闻名的猴子也扔下帽子，帽商立即把帽子收起来。

Half a century later his grandson, also a hat seller, set down his wares under the same tree for a nap. On waking, he was dismayed to discover that monkeys had taken all his hats to the treetop. Then he remembered his grandfather's story, so he threw his own hat to the ground. But, mysteriously, none of the monkeys threw any hats, and only one monkey came down. It took the hat on the ground firmly in hand, walked up to the hat seller, gave him a slap and said, "You think only you have a grandfather?"

半个世纪后，他的孙子也卖帽子，孙子把货物搁在同一棵树下打个盹。醒来时，他惊愕地发现，一群猴子早已把他的全部帽子都戴在树梢。那时，他想起他祖父的故事，也就同样把自己的帽子扔在地上。可是，令人难以理解的是，没有一只猴子扔掉帽子，接着，只有一只猴子从树上下来。它把地上的帽子牢牢抓在手里，走近这位帽商，给了他一记耳光，还说：“你以为只有你才有爷爷？”

This story illustrates an important distinction between ordinary decision theory and game theory. In the latter, what is rational for one player may depend on what is rational for the other player. For Lucy to get her decision right, she must put herself in Pete's shoes and think about what he must be thinking. But he will be thinking about what she is thinking, leading to an infinite regression. Game theorists describe this situation by saying that "rationality is common knowledge among the players." In other words, Lucy and Pete are rational, they each know that the other is rational, they each know that the other knows, and so on.

这个故事说明了普通决策理论和博弈论之间的一个重要区别。在后一种理论中，对游戏一方什么是合理的可能取决于对游戏另一方什么是合理的。对于露西来说，要得到正确的决策，她就必须置身皮特的处境，考虑他一定会想到的事情。但他也总是考虑她正在想什么，从而导致无限回归。博弈论工作者用这样的说法描述这种情况：“理性是游戏各方的常识。”换言之，露西和皮特是理性的，他们各自知道另一方是理性的，他们每人都知道别人知道的事情，等等。

The assumption that rationality is common knowledge is so pervasive in game theory that it is rarely stated explicitly. Yet it can run us into problems. In some games that are played over time, such as repeated rounds of Prisoner's Dilemma, players can make moves that are incompatible with this assumption.

理性是常识这一假设在博弈论中无处不在，以致人们难得明确指出。然而，这可能使我们遇到问题。在一些随时间推移进行的游戏中，如反复几轮囚徒困境，游戏各方都可能采取与这一假设不相容的行动。

I believe that the assumption that rationality is common knowledge is the source of the conflict between logic and intuition and that, in the case of Traveler's Dilemma, the intuition is right and awaiting validation by a better logic. The problem is akin to what happened in early set theory. At that time, mathematicians took for granted the existence of a universal set-a set that contained everything. The universal set seemed extremely natural and obvious, yet ultimately several paradoxes of set theory were traced to the assumption that it existed, which mathematicians now know is flawed. In my opinion, the common knowledge of rationality assumed by game theorists faces a similar demise. -K.B.

我相信，理性是常识这一假设是逻辑和直觉之间冲突的来源，而在旅行者困境的案例中，直觉是正确的，并且期待一个更好逻辑的验证。这个问题类似早期集合论发生的情况。在那个时候，数学家认为，存在一个包罗万象的全集是理所当然的。全集似乎极其自然且显而易见，但是最终，人们从集合论的几个悖论追溯到全集存在的假设，数学家现在知道，这一假设是有瑕疵的。依我的看法，博弈论工作者假定的理性是常识也面临同样的消亡。-K.B.