  Incentive mechanism design is crucial for enabling federated learning. We
deal with clustering problem of agents contributing to federated learning
setting. Assuming agents behave selfishly, we model their interaction as a
stable coalition partition problem using hedonic games where agents and
clusters are the players and coalitions, respectively. We address the following
question: is there any utility allocation method ensuring a Nash-stable
coalition partition? We propose the Nash-stable set and analyze the conditions
of non-emptiness. Besides, we deal with the decentralized coalition partition.
We formulate the problem as a non-cooperative game and prove the existence of a
potential.
