We add sophistication (some players guess, correctly, that others are learning according to the general EWA rule) to learning theories. Our approach nests QRE and Nash (hyperresponsive QRE) as special cases and also allows the true proportion of sophisticated players and the perceived proportion to differ (allowing asymmetry as in level-k approaches). We show that adding sophistication improves fit and predictive accuracy in p-beauty contests. The amount of sophistication also increases as a 10-period session is repeated, evidence of "learning to learn". We also estimate a model in which sophisticated players "teach" adaptive ones in multistage trust games and entry deterrence (chain store) games. The teaching model fits reasonably well and provides a learning-based account of reputation formation which can be distinguished from equilibrium belief learning (types-based) approaches in several ways. Most regularities in the data go in the direction predicted by teaching rather than equilibrium updating.

Joint w/ Teck Ho and Juin Kuan Chong