Learning to Avoid Tragedies: Boundedly Rational Agents in Feedback-Evolving Games

Abstract

Many populations of individuals interact with a common pool of resources. Examples include fishermen and their fisheries and herders and their common land for pasture. The framework of feedback-evolving games incorporates this game-environment feedback, in which a population’s actions affect a shared environment, and in turn, the changing environment shapes incentives for future behaviors. A primary assumption in these models is that agents employ imitative learning processes, leading to the replicator equation describing their behavior. In this article, we investigate the dynamics when agents follow the logit protocol, a boundedly rational and information-based learning process. The primary question we seek to address is whether this more sophisticated learning process can avert tragic outcomes in scenarios where simpler, imitative learning cannot. To do so, we fully characterize stability properties for all two-strategy evolutionary games with environmental feedback, and find that there are regimes where logit learning can avoid tragedies where imitation learning cannot. Interestingly, this can only occur for intermediate levels of rationality. Then, we propose optimal incentive policies that a system operator could implement to promote the health of the environment. We identify cases where, counterintuitively, raising the population’s rationality level leads to worse environmental outcomes when applying the optimal incentive policy.