Level-k Thinking: New modeling possibilities?

有趣的觀點:

Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins.

Obviously, picking a number over 50 would be silly. Based on this, picking a number over 25 would be silly. Similarly, picking a number over 12.5 would be silly. Continuing this line of thought, picking any number other than 0 would be silly. These thoughts show the level of thinking of those involved, from level-1 to level-infinity.

Level-k thinking analyzes such games. In actual experiments, players never pick 0, which would be suggested by a Nash equilibrium. Instead, they utilize many different levels of thinking.

使用 Level-k 來 model 不外乎就是讓均衡符合實際的狀況。但是他有一個很強的假設，level-2 的 player 一定要假設他認為其他的 player 是 level-1 或更低，他不能認為有其他 player 是 level-3 或以上的。因為若他認為有人是 level-3，則理性的他，就不再是 level-2 了。

所以為了讓結果更符合實際狀況，level-k thinking 使用了同樣不合理的假設。