Research summary: Past inquiry has found that implementing complex competitive repertoires (i.e., diverse and dynamic arrays of actions) is challenging, but firms benefit from doing so. Our examination of the antecedents and outcomes of complex competitive repertoires develops a more nuanced perspective. Data from 1,168 firms in 204 industries reveal that complexity initially harms performance, but then becomes a positive factor, except at high levels. We use agency and tournament theories, respectively, to examine how key governance mechanisms—ownership structure and executive compensation—help shape firms' competitive repertoires. We find that the principals of agency theory and the pay gap of tournament theory are both important antecedents of competitive complexity, and an interaction exists wherein firms build especially complex repertoires when both influences are strong. Managerial summary: In boxing, the fight does not always go to the bigger or stronger person, or even to whomever throws the most punches—the fight is sometimes won by the boxer who is unpredictable, such as throwing an uppercut when the opponent expected a right hook. Similarly, when companies compete in the marketplace, advantage is afforded not only to those with more resources or who engage in more competitive activity, but also to those whose actions are unpredictable. In this study, we develop the notion of “competitive complexity,” which describes the diversity and changing nature of a company's competitive moves. Implementing complex competitive repertoires can be painful in the short term but, if done correctly, can help company performance in the long run. Copyright © 2016 John Wiley & Sons, Ltd.