Eddie and May compete ruthlessly with one another to end up on top in their personal and years long power struggle. Both Eddie and May want the other to desire them. However, neither one wants to lose the position of admitting they desire the other. They both want to remain powerful enough to resist the other's desire. Eddie tries to seduce May by telling her how much he sacrificed to come see her. Eddie admits to missing May desperately. May is partly moved by Eddie's words but cannot get past the idea that Eddie has been having a relationship with the Countess. Eddie's defense is weak against her accusations. Eddie offers to leave instead of admitting to his affair. The thought of Eddie leaving again makes May upset. She tells Eddie about her date who is arriving shortly. This spins Eddie into jealousy. Both May and Eddie are jealous of the other's new relationships, and May will not take Eddie back. She does kiss him but then knees Eddie in the groin.
Eddie feels the need to prove his manhood to May throughout the play. He attempts to win May back while simultaneously keeping alive his affair with the woman they call the Countess. Eddie shows off his rodeo skills to May by lassoing his rope around the bedposts. He is an egoist who becomes even more boastful when he drinks. Eddie carries in a bottle of tequila and a shotgun at one point in the play. Attempting to show May how strong his tolerance is he drinks a lot of the bottle by himself and threatens May and her mysterious date who has yet to arrive. Being a man's man—full of bravery, taking risks and having one's way with women is Eddie's ideal. He expects May's date to be nothing but "a punk chump in a two dollar suit or something." Or at least this is what he hopes. Even when Eddie sees that Martin is harmless he continues to threaten and intimidate him. Eddie shares many traits with the stereotypical western man or cowboy though his personality and past make him a more complicated character whose depth and strivings go beyond the archetype he puts up on a pedestal and emulates.
May and Eddie's differ in their interpretation of their past and present relationship. The way these individuals remember the past and the way that each one interprets these events contributes to the shaping of their identity. May refuses to take Eddie back because she does not want to repeat the mistakes her mother made and mistakes that she herself has made again and again. She also feels ashamed about her blood relation to Eddie and wants to put those thoughts behind her. On the other hand, Eddie tries to juggle both May and the Countess because, like his father, he does not view a wandering, two-timing identity as negative. He is not bothered much anymore by his blood relation to May and he sees the repeated acts of abandonment as May's fault not his own.
May and Eddie's relative ability to move on with their lives relates to the interpretation of their memories. Their painful, complicated past plagues their present with the version of the story they happen to remember or believe in. Their memories and sense of history defines them as individuals. Their contradictory interpretation of their memories of their shard past colors their present conflict. Shepard seems to be saying that individuals' traumatic memories shape each person differently and each person's tolerance for pain varies from individual to individual and is not always compatible.