Rubinstein and Leland have both demonstrated that many observed violations of expected and discounted utility can be explained if people employ similarity judgments to make choices. In this paper, I show that this decision process also explains which equilibria will be selected in single‐shot games with multiple equilibria and implies that play in games will be associated with anomalies in risky choice. Data supporting these predictions are presented. Copyright © 2012 John Wiley & Sons, Ltd.