  Feedback-evolving games is a framework that models the co-evolution between
payoff functions and an environmental state. It serves as a useful tool to
analyze many social dilemmas such as natural resource consumption, behaviors in
epidemics, and the evolution of biological populations. However, it has
primarily focused on the dynamics of a single population of agents. In this
paper, we consider the impact of two populations of agents that share a common
environmental resource. We focus on a scenario where individuals in one
population are governed by an environmentally "responsible" incentive policy,
and individuals in the other population are environmentally "irresponsible". An
analysis on the asymptotic stability of the coupled system is provided, and
conditions for which the resource collapses are identified. We then derive
consumption rates for the irresponsible population that optimally exploit the
environmental resource, and analyze how incentives should be allocated to the
responsible population that most effectively promote the environment via a
sensitivity analysis.
