Different from previous studies which focused on how to identify object-directed intention (actions target physical objects but do not involve others), the current study explores how people identify social intentions (actions target social entities to influence each other’s interaction behavior). Based on the analysis that two interactive agents should follow the utility maximization at the overall level, it is proposed that when the cost required by A to assist B to achieve the target is less than the cost required by B to achieve the target alone (referred to as minimization cost information for short), it can be identified as having social intentions. By setting a fence in front of B, the minimization cost information was manipulated, and the EEG μ suppression degree indicating different intention types and sensitivity (discrimination) to different changes were taken as indicators to test the hypothesis. The results showed that, compared with the control condition of object-directed intention (that is, A placed the target apple in front of the Stone), when A placed the target apple in front of B, which was blocked by the fence, its action can reduce the action cost for B to acquire the apple alone (i.e., when the minimization cost condition was met, the degree of μ suppression was higher (Experiment 1)) and the discrimination against structural changes (exchange of agents acting the same role in two animations) was stronger, but the discrimination against role swap (exchange of roles of two agents in a certain animation) was weaker (Experiment 3a); however, when the fence was absent, although A’s movement path was the same as that of Experiment 1, the cost for A to place the apple in front of B was greater than the cost for B to obtain the apple itself (i.e., it did not meet the minimization cost conditions, the difference in μ suppression between conditions disappeared (Experiment 2), and the discrimination of changes in different movement modes was equivalent (Experiment 3b)). In view of the fact that the μ suppression induced by social intentions is stronger than that induced by object- directed intention and it is easier for people to identify structural changes between two agents with social intentions, but insensitive to role swap, the above results revealed that whether the behaviors of the two individuals satisfy minimization cost affects people’s recognition of action intentions and supports the view that minimization cost information is a clue to social intentions recognition.