  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.
