As one of the typical settings of Federated Learning (FL), cross-silo FL allows organizations to jointly train an optimal Machine Learning (ML) model. In this case, some organizations may try to obtain the global model without contributing their local training, lowering the social welfare. In this paper, we model the interactions among organizations in cross-silo FL as a public goods game for the first time and theoretically prove that there exists a social dilemma where the maximum social welfare is not achieved in Nash equilibrium. To overcome this social dilemma, we employ the Multi-player Multi-action Zero-Determinant (MMZD) strategy to maximize the social welfare. With the help of the MMZD, an individual organization can unilaterally control the social welfare without extra cost. Experimental results validate that the MMZD strategy is effective in maximizing the social welfare.

翻译：作为联邦学习联盟(FL)的典型环境之一,跨SIlo FL允许各组织联合培训最佳机器学习模式(ML),在这种情况下,一些组织可能试图在不提供当地培训的情况下获得全球模式,降低社会福利;在本文件中,我们首次将跨SIlo FL组织之间的互动模式作为公益游戏,并在理论上证明在纳什平衡中无法实现最大社会福利的社会困境存在。为了克服这一社会困境,我们采用多玩家多行动零残疾战略(MMMZD)来尽量扩大社会福利。在MMZD的帮助下,单个组织可以单方面控制社会福利而无需额外成本。实验结果证实MMZD战略在尽量扩大社会福利方面是有效的。