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The replicator equation in evolutionary game theory describes the change in apopulation's behaviors over time given suitable incentives. It arises whenindividuals make decisions using a simple learning process - imitation. Arecent emerging framework builds upon this standard model by incorporatinggame-environment feedback, in which the population's actions affect a sharedenvironment, and in turn, the changing environment shapes incentives for futurebehaviors. In this paper, we investigate game-environment feedback whenindividuals instead use a boundedly rational learning rule known as logitlearning. We characterize the resulting system's complete set of fixed pointsand their local stability properties, and how the level of rationalitydetermines overall environmental outcomes in comparison to imitative learningrules. We identify a large parameter space for which logit learning exhibits awide range of dynamics as the rationality parameter is increased from low tohigh. Notably, we identify a bifurcation point at which the system exhibitsstable limit cycles. When the population is highly rational, the limit cyclecollapses and a tragedy of the commons becomes stable.

The madness of people: rational learning in feedback-evolving games