随机复合博弈模型中的合作与竞争：一个分布式优化与博弈问题的视角

From the perspective of the relationship between the number of groups and players in a random composite game model, problem 1 can also be seen as including two categories: stochastic composite optimization problems and stochastic composite game problems. Specifically, when the number of groups is 1, the competition between groups will disappear, and problem 1 will degenerate into a stochastic composite optimization problem where multiple autonomous entities cooperate to minimize an objective function. Similarly, when the number of intelligent agents within each group is 1, the cooperative relationship within the group will be abandoned, and problem 1 will be transformed into a competitive situation where multiple autonomous entities pursue their own interests, i.e., a composite game problem. Therefore, problem 1 not only models the cooperation-competition relationship among autonomous entities in an uncertain environment but also includes discussions on distributed optimization problems and distributed game problems in general situations.