This is a quick primer on “Levels of thinking”. I’ll just spell it out once, and then link back to this post later.
Here’s a simple game called “Matching Pennies“:
Two people each have a penny. They each (secretly) decide to leave the penny either face up or face down on the table. On the count of three they reveal the penny. If they are both face up, or both face down, then Player A gets a point. If they don’t match, Player B gets a point.
Levels
Level 1 – Player A
If you’re Player A, and if you think your opponent is going to play heads, you should play heads.
Level 2 – Player B
You’re player B, and you’re pretty sure Player A has a lick of sense. They’re probably anticipating that you’ll play heads, so they’ll play heads. But since you’re smarter than the average bear, you’ll play tails.
Level 3 – Player A
Aha! You’ve cleverly tricked player B into a false sense of confidence. You’ll out do them by playing tails.
Level 4 – Player B
Ah, the plot thickens. You’ve made your opponent think that they knew, that you knew, that they knew, that you were going to play tails. But they don’t know. They have no idea that you’re actually going to play heads all along. What a twist!
The moral of the story is two fold. One, is to as accurately as you can, anticipate how many levels your opponent thinks on, and then think one more. The second and most important, is to never reveal what level you think on.