Noisy Introspection in the “11–20” Game

Arad and Rubinstein (American Economic Review, 102(7), 2012, 3561–3573) recently proposed a simple money-request game designed to trigger level-k reasoning. In an experiment that explores three variants of the game, they find evidence for the level-k model with observed levels of strategic thinking consistently ranging from 0 to 3. Our baseline treatment uses the basic version of the money-request game and replicates their results. We apply the noisy introspection model developed by Goeree and Holt (Games and Economic Behavior, 46, 2004, 365–382) to the baseline-treatment data and use this to predict behavior and beliefs in five other treatments that employ games with a very similar structure. The data from these additional treatments clearly refute the level-k model, which predicts no better than the Nash equilibrium in these games. Our data provide striking evidence that the assumption of best-response behavior underlying the level-k model is untenable. The noisy introspection model, which instead assumes “common knowledge of noise,” predicts behavior remarkably well.