Do dominant or less dominant firms innovate more? There is considerable research on this question, with theoretical studies based on game theory and empirical evidence often divided. We provide a new theory that the decisions that concern strategic choice in innovation may be influenced by expected relative returns. Our approach, which we call the returns-based beliefs approach, is based upon subjective probabilities. It combines a decision analytic solution concept and Luce's (Individual Choice Behavior, Wiley: New York, 1959) probabilistic choice model. We show that the returns-based beliefs approach provides support for the thesis that dominant firms invest more in research and development (R&D) within an asymmetric mixed-strategy game. Consequently, the returns-based beliefs approach accords better with recent empirical studies of innovation. Using R&D data across a range of industries in the UK from 2001 to 2006, we show that firms’ spending on R&D is related more to their own profitability than to that of their competitors, which is consistent with the returns-based beliefs approach. Copyright © 2011 John Wiley & Sons, Ltd.