The word agent comes from the present participle agens, agentis ('the one doing') of the Latin verb agere, to 'do' or 'make'.
For many people, the notion of agency is easy to grasp intuitively but difficult to define: typical qualities that a grammatical agent often has are that it has volition, is sentient or perceives, causes a change of state, or moves.
Even Dowty's solution fails for verbs expressing relationships in time: (1) April precedes May.
The grammatical agent is often confused with the subject, but the two notions are quite distinct: the agent is based explicitly on its relationship to the action or event expressed by the verb (e.g. "He who kicked the ball"), whereas the subject is based on a more formal title using the theory of the information flow (e.g. "Jack kicked the ball").
The use of some transitive verbs denoting strictly reciprocal events may involve a conflation of agent and subject.