The power of digital platforms is at the center of major ongoing policy and regulatory efforts. To advance existing debates, we designed and executed an experiment to measure the performative power of online search providers. Instantiated in our setting, performative power quantifies the ability of a search engine to steer web traffic by rearranging results. To operationalize this definition we developed a browser extension that performs unassuming randomized experiments in the background. These randomized experiments emulate updates to the search algorithm and identify the causal effect of different content arrangements on clicks. Analyzing tens of thousands of clicks, we discuss what our robust quantitative findings say about the power of online search engines, using the Google Shopping antitrust investigation as a case study. More broadly, we envision our work to serve as a blueprint for how the recent definition of performative power can help integrate quantitative insights from online experiments with future investigations into the economic power of digital platforms.

The power of digital platforms is at the center of major ongoing policy and regulatory efforts.

Digital platforms pose a well-recognized challenge for antitrust enforcement.

The power of digital platforms is at the center of major ongoing policy and regulatory efforts.

Typical measures of market power in economic theory focus on classical pricing markets of homogeneous goods, where a firm's primary action is choosing a price to sell the good or the quantity of This simple relationship allows one to directly reason about participant welfare and profit of firms. In addition, not all participants with accounts on a digital platform are equally active and inactive participants should not factor into the market power of a firm the same way active participants do. Participant behavior plays a critical role in digital market places. As outlined by the Stigler Committee [2019], "the findings from behavioral economics demonstrate an under-recognized market power held Thaler and Sunstein, 2008; Fogg, 2002]--can be exploited by firms in digital economies, but do not factor into traditional measures of market power. Performative power focuses on measuring power rather than harm.

Digital platforms pose a well-recognized challenge for antitrust enforcement.

We introduce the notion of performative power, which measures the ability of a firm operating an algorithmic system, such as a digital content recommendation platform, to cause change in a population of participants. We relate performative power to the economic study of competition in digital economies. Traditional economic concepts struggle with identifying anti-competitive patterns in digital platforms not least due to the complexity of market definition. In contrast, performative power is a causal notion that is identifiable with minimal knowledge of the market, its internals, participants, products, or prices. Low performative power implies that a firm can do no better than to optimize their objective on current data. In contrast, firms of high performative power stand to benefit from steering the population towards more profitable behavior. We confirm in a simple theoretical model that monopolies maximize performative power. A firm's ability to personalize increases performative power, while competition and outside options decrease performative power. On the empirical side, we propose an observational causal design to identify performative power from discontinuities in how digital platforms display content. This allows to repurpose causal effects from various studies about digital platforms as lower bounds on performative power. Finally, we speculate about the role that performative power might play in competition policy and antitrust enforcement in digital marketplaces.