  Many applications of RCTs involve the presence of multiple treatment
administrators -- from field experiments to online advertising -- that compete
for the subjects' attention. In the face of competition, estimating a causal
effect becomes difficult, as the position at which a subject sees a treatment
influences their response, and thus the treatment effect. In this paper, we
build a game-theoretic model of agents who wish to estimate causal effects in
the presence of competition, through a bidding system and a utility function
that minimizes estimation error. Our main technical result establishes an
approximation with a tractable objective that maximizes the sample value
obtained through strategically allocating budget on subjects. This allows us to
find an equilibrium in our model: we show that the tractable objective has a
pure Nash equilibrium, and that any Nash equilibrium is an approximate
equilibrium for our general objective that minimizes estimation error under
broad conditions. Conceptually, our work successfully combines elements from
causal inference and game theory to shed light on the equilibrium behavior of
experimentation under competition.
