Matching Pennies

Looking for something fun to do this afternoon? Sounds like it’s time to grab two pennies and a friend and sit down for a rousing game of Matching Pennies! Here’s how it works: each person puts down a penny. If they match—if they’re both heads or both tails—then Player One gets a point. If they don’t match, Player Two gets a point. And that’s it. That’s the game. Fun, right? Couldn’t we just do this for hours?

Sure, maybe if we’re four years old. Seriously, no one’s rushing home from work to play Matching Pennies. But the game does illustrate an important concept: in situations where one person’s loss is another’s gain, and each outcome has an equal probability of happening, and nothing we do can influence that probability, we have no incentive to change our game strategy. Put another, more scholarly-sounding way, this zero-sum game has no Nash equilibrium.

Boom. Can’t wait to take those three-dollar words to the next block party.