In A Midsummer Night's Dream what is Egeus and Hermia's relationship throughout the play?
Egeus is Hermia's father and they have what might today be termed intergenerational conflict. Egeus believes he has the paternal right to tell Hermia who to marry and wants her to marry Demetrius. Hermia argues for her right to marry Lysander, the man she is in love with. Both father and daughter are strong willed and unwilling to bend.
Egeus drags Hermia before Theseus, the duke of Athens, to compel her to marry Demetrius. Egeus is willing to use all the power of the state to get his way. Hermia naturally rebels against being told what to do and runs off with Lysander.
Egeus's attitude does not change. Near the conclusion of the play, at the end of Act IV, when he, Hippolyta and Theseus come across the lovers, Egeus still insists that Hermia marry Demetrius. Demetrius, however, states that he is now in love with Helena. At this point, Theseus overrules Egeus, saying "I will overbear your will." Egeus shows no more understanding of his daughter than he did before the start of evening's madness: it is Theseus, perhaps with a more nuanced understanding of love or perhaps happy in his own love situation, who decrees she be allowed to marry Lysander.