When you outsmart someone, you use your cleverness or intelligence to defeat them in some way. The roadrunner will always outsmart the coyote, at least according to Saturday morning cartoons.
When two countries are negotiating with each other, they're often each trying to outsmart the other — to maneuver in a way that gives them the better deal. A game of chess is all about which player can strategize better, or who can outsmart their opponent. And classic TV detectives use their wit to outsmart the bad guys by the end of each episode.