  We study fairness through the lens of cooperative multi-agent learning. Our
work is motivated by empirical evidence that naive maximization of team reward
yields unfair outcomes for individual team members. To address fairness in
multi-agent contexts, we introduce team fairness, a group-based fairness
measure for multi-agent learning. We then prove that it is possible to enforce
team fairness during policy optimization by transforming the team's joint
policy into an equivariant map. We refer to our multi-agent learning strategy
as Fairness through Equivariance (Fair-E) and demonstrate its effectiveness
empirically. We then introduce Fairness through Equivariance Regularization
(Fair-ER) as a soft-constraint version of Fair-E and show that it reaches
higher levels of utility than Fair-E and fairer outcomes than non-equivariant
policies. Finally, we present novel findings regarding the fairness-utility
trade-off in multi-agent settings; showing that the magnitude of the trade-off
is dependent on agent skill.
