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.

翻译：最近的实绩预测框架旨在捕捉预测影响他们想要预测的目标/结果的环境。在本文中,我们引入了这一框架的自然多试剂版本,让多个决策者试图预测同样的结果。我们展示了这种竞争能够通过证明从稳定向不稳定和最终混乱阶段过渡的可能性而产生有趣的现象。具体地说,我们展示了多试剂预测的设置,在充分条件下,其动态导致全球稳定和最佳性。相反,当代理人在学习/更新速度方面不够谨慎时,我们表明不稳定和事实上正式混乱是可能的。我们用模拟来补充我们的理论预测,展示我们结果的预测力。