Trembling Hand Perfect Equilibrium

Remember learning that every square is a rectangle, but not every rectangle is a square? Well, we’re going to take that concept and apply it to game theory, like so: every trembling hand perfect equilibrium is a Nash equilibrium, but not every Nash equilibrium is a trembling hand perfect equilibrium. Boom. Minds blown, right?

What this means outside the game theory lexicon is pretty much this: in a situation with two actors, we understand that there is a chance—a small one, but a chance—that the other guy might make a mistake and unintentionally make the decision he didn’t want to make. Knowing this, we adopt a “trembling hand perfect equilibrium,” which means we base our own decision on the fact that the other person will probably act the way they’re supposed to act, but then again...they might not. We make a decision that protects us regardless of whether or not the other person trembles—that’s what that unintentional action is called, BTW—and they usually end up being better off for it anyway.