All the actors on the Greek stage were men. If Athenian drama is a political institution and participation in the Dionysia (as actor, playwright, audience) is a corollary of citizenship, then what can we take away from the fact that some Athenian men performed their citizenship by playing women?
Nancy Sorkin Rabinowitz’s essay from a 1994 issue of Didaskalia: ‘How is it Played?: The Male Actor of Greek Tragedy: Evidence of Misogyny or Gender-Bending?’ is a great place to start thinking about these kinds of questions.
In 2011, Rabinowitz revisted the concept of gender as a performance and its relationship to Athenian drama with an essay in the journal, Helios, which you can access through the University library:
Rabinowitz, N.S. 2011. ‘Male Medea’, Helios 38.2, 149-164.
Didaskalia‘s supplementary issue from 1994, entitled ‘How is it Played?: Genre, Performance and Meaning’, has a number of useful essays that you should look at that come at practical issues of performance from various perspectives (actor, director, playwright, audience member).