On the persistence of strategic sophistication.

We examine whether the “Level-k” model of strategic behavior generates reliable cross-game predictions at the individual level. We find no correlation in subjects' estimated levels of reasoning across two families of games. Furthermore, estimating a higher level for Ann than Bob in one family of games does not predict their ranking in the other. Direct tests of strategic reasoning generally do not predict estimated levels. Within families of games, we find that levels are fairly consistent within one family, but not the other. Our results suggest that the use of Level-k reasoning varies by game, making prediction difficult.