  The recent framework of performative prediction is aimed at capturing
settings where predictions influence the target/outcome they want to predict.
In this paper, we introduce a natural multi-agent version of this framework,
where multiple decision makers try to predict the same outcome. We showcase
that such competition can result in interesting phenomena by proving the
possibility of phase transitions from stability to instability and eventually
chaos. Specifically, we present settings of multi-agent performative prediction
where under sufficient conditions their dynamics lead to global stability and
optimality. In the opposite direction, when the agents are not sufficiently
cautious in their learning/updates rates, we show that instability and in fact
formal chaos is possible. We complement our theoretical predictions with
simulations showcasing the predictive power of our results.
