Mind Your Decisions looks at the game theory of the classic Thanksgiving showdown between Lucy and Charlie Brown.
Time after time, Lucy would bring her football to the park and entice Charlie Brown to practice some place kicks. Lucy would hold the ball, Charlie Brown would run full-steam to kick it only to have Lucy snatch the ball away at the last minute sending Charlie Brown flying, yelling ARRRRGGGHHH and landing in a heap. What a blockhead. Sure you can understand his willingness to trust her the first time, maybe even the first two times, but after that it’s pretty clear what Lucy’s objective is.
You may try to make excuses for Charlie Brown by arguing that subgame-perfection requires a great deal of strategic sophistication. But you don’t need to invoke any refinements here. The unique Nash equilibrium action for Charlie Brown is to say no. Even worse, not yanking the ball is a weakly dominated strategy for Lucy and after that strategy is eliminated, Charlie Brown has a strongly dominant strategy to walk away.
So it is not surprising that in It’s The Great Pumpkin Charlie Brown, he has finally figured this out and flatly refuses to play Lucy’s game. That’s when she goes contract theory on him.
Now we are reaching higher-order blockheadness. First of all, whether or not the contract is valid, its terms are not verifiable to a court. And Charlie Brown should be able to figure out there is something fishy about this contract. Lucy would only offer a contract if she preferred the outcome (run, don’t yank) to the outcome (walk away). But even though Lucy has never directly revealed any preference between these two outcomes, there is pretty good evidence that the worst possible outcome for Lucy would be to see Charlie Brown successfully kick.
Indeed, Lucy knew from the beginning that Charlie Brown would eventually figure out her intention to yank the ball. After that, she knows Charlie Brown will refuse to play. So if Lucy really preferred (run, don’t yank) to (walk away) then she would prevent this evaporation of trust by allowing Charlie Brown to kick the ball at least a few times, but she never did.
The only way to rationalize Lucy’s steadfast insistence on sending him flying is to assume either that (run, don’t yank) is her least-preferred outcome, or that she thinks that Charlie Brown is indeed a blockhead and unable to deduce her intentions. In either case, Charlie Brown should have viewed Lucy’s contract with deep suspicion.