爱华网博弈论挑战普通决策理论：我知道你知道我知道…
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.
我在印度听说过这样一个故事。有一个卖帽子的人在一棵树下午睡，等他醒来后，他发现一群猴子把他所有的帽子拿到了树稍上。盛怒之下，他取下他自己的帽子然后狠狠地摔在地上。人们知道猴子们非常喜欢模仿，因此这些猴子们也纷纷把帽子掷到地下，这个卖帽子的人然后就迅速拾起了这些帽子。
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?"
过了50年，这个人的孙子也成为一个卖帽子的人，一天他把帽子放在那棵同样的大树下，然后打起盹儿来。等他醒来后，他沮丧地发现猴子们把他所有的帽子都拿到了树梢。这时候，他想起了他祖父的故事，他就把他自己的帽子掷到地上。但是，奇怪的是，没有一只猴子模仿他扔掉帽子，只有一只猴子从树上爬下来，它拾起地上的那只帽子，牢牢抓在手中，并走到这个卖帽者的面前，给了卖帽者一个耳光然后说：“你以为只有你有爷爷么？”
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的区别。在博弈论看来，对一个玩家来说决策的理性可能依赖于另外一个玩家决策的理性。Lucy如果想要得到正确的决策，她必须把自己置于Pete的位置上，并思考他是怎样想的。但是Pete也会想着Lucy是如何思考的，这样一来就导致了无限“回归”。博弈论者把这种情形称为“在玩家看来理性是常识。”换言之，Lucy和Pete是理性的，他们相互之间也知道对方是理性的，他们也知道对方知道这一点，这样一直下去。
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.以上是用户分享关于博弈论挑战普通决策理论的资料希望对您有所帮助了，感谢您对爱华网的支持！
