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—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 ZeroDeterminant (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. Since the MMZDstrategy can be adopted by all organizations, we further study the scenario where multiple organizations jointly adopt the MMZD strategy and form an MMZD Alliance (MMZDA). We prove theoretically that the MMZDA strategy strengthens the control of the maximum social welfare. Experimental results validate that the MMZD strategy is effective in maximizing the social welfare and the MMZDA can achieve a larger maximum value.



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