Iterated reasoning (level-k)

Strategic reasoning is thinking through what others will do — and, crucially, what they think you will do — before you choose. Classic game theory assumes this goes all the way: everyone is perfectly rational and knows everyone else is, reasoning to the logical endpoint. Real people don't. The Keynesian beauty contest makes this vivid: ask everyone to pick a number closest to two-thirds of the group's average, and pure logic drives the answer to zero, yet the winning guess is usually well above it. The reason is level-k thinking: a level-0 player picks at random, a level-1 player best-responds to level 0, level 2 to level 1, and so on — and most people stop after a step or two. So winning isn't about being the most rational; it is about correctly judging how many steps of reasoning others will actually take. It explains why markets and crowds turn on beliefs about others' beliefs, not just fundamentals.