  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 power, lowering the social welfare. In this
paper, we model the interactions among organizations in cross-silo FL as a
public goods game and theoretically prove that there exists a social dilemma
where the maximum social welfare is not achieved in Nash equilibrium. To
overcome this 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. Since the MMZD strategy can be adopted by all organizations, we
further study the case of multiple organizations jointly adopting the MMZD
strategy to form an MMZD Alliance (MMZDA). We prove that the MMZDA strategy can
strengthen the control of the maximum social welfare. Experimental results
validate that the MMZD strategy is effective in obtaining the maximum social
welfare and the MMZDA can achieve a larger maximum value.
