The strongly time consistent in a cooperative game with perfect information

Under the optimality principle in the multi-stage cooperative game , we have discussed the strong time consistency in cooperative games with perfect information. Strong time consistency requires that if players can obtain higher rewards at a future time point, they should take actions at the current time point to maintain time consistency and maximize their rewards. We have found that in certain specific cases, the general core of cooperative games belongs to its strong dynamic stable core. To this end, we proposed a theorem and used a proof by contradiction to theoretically demonstrate the strong time consistency in cooperative games with perfect information. This finding has a positive impact on the study of cooperative games with specific relations of benefits.