  In recent years, federated learning has been embraced as an approach for
bringing about collaboration across large populations of learning agents.
However, little is known about how collaboration protocols should take agents'
incentives into account when allocating individual resources for communal
learning in order to maintain such collaborations. Inspired by game theoretic
notions, this paper introduces a framework for incentive-aware learning and
data sharing in federated learning. Our stable and envy-free equilibria capture
notions of collaboration in the presence of agents interested in meeting their
learning objectives while keeping their own sample collection burden low. For
example, in an envy-free equilibrium, no agent would wish to swap their
sampling burden with any other agent and in a stable equilibrium, no agent
would wish to unilaterally reduce their sampling burden.
  In addition to formalizing this framework, our contributions include
characterizing the structural properties of such equilibria, proving when they
exist, and showing how they can be computed. Furthermore, we compare the sample
complexity of incentive-aware collaboration with that of optimal collaboration
when one ignores agents' incentives.
