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 a family of hedonic games ensuring a Nash-stable coalition partition? We propose the Nash-stable set which determines the family of hedonic games possessing at least one Nash-stable partition, and analyze the conditions of non-emptiness of the Nash-stable set. Besides, we deal with the decentralized clustering. We formulate the problem as a non-cooperative game and prove the existence of a potential game.
翻译:激励机制的设计对于促进联合学习至关重要。 我们处理有助于联合学习环境的代理商的集群问题。 假设代理商自私行事,我们用介质和组群分别是玩家和联盟的超音速游戏来模拟他们的互动作为稳定的联合分配问题。 我们处理的一个问题是: 是否有一套超音速游戏来确保纳什稳定的联合分割? 我们提出一套纳什稳定模式,用以确定至少拥有一个纳什稳定分区的超音速游戏的组合,并分析纳什稳定组合的非空性条件。 此外,我们处理分散的集群。我们把这一问题发展成一种不合作的游戏,并证明存在一种潜在的游戏。