Multi-learner risk reduction under endogenous participation dynamics

Most of the study of endogenous shifts has focused on the single decision-maker setting, where there is one learner that users either choose to use or not. This paper studies participation dynamics between sub-populations and possibly many learners. We study the behavior of systems with risk-reducing learners and sub-populations. A risk-reducing learner updates their decision upon observing a mixture distribution of the sub-populations in such a way that it decreases the risk of the learner on that mixture. A risk reducing sub-population updates its apportionment amongst learners in a way which reduces its overall loss. Previous work on the single learner case shows that myopic risk minimization can result in high overall loss and representation disparity. Our work analyzes the outcomes of multiple myopic learners and market forces, often leading to better global loss and less representation disparity.