King Lear: How does familial conflict reveal the protagonist's character?

King Lear is the quintessential story of betrayal and loyalty, centering on two families: the Earl of Gloucester and his sons, Edgar and Edmund, and King Lear and his daughters Regan, Goneril and Cordelia. Familial interactions are basically the theme of this Shakespearian play.

Edmund is the bastard son of Gloucester, and he takes this title to heart-- his schemes to gain power are driven by his status as "outcast" among his family. Edmund is smart, sly, and charming, as evidenced by the affections of Regan and Goneril. His good looks and suave manner are a stark contrast to his betrayal of his own father. Edmund is easy to sympathize with, as his opening monologue talks about his ostracism and how he deserves all of the opportunities afforded to his brother, Edgar. He responds by framing Edgar and driving Gloucester to his eventual death, proving him to be treacherous. However, Edmund almost seems to repent for his misdoings at the end of the play, conceding that he ordered Cordelia's death; this suggests that his exile from acceptable society may have caused his actions instead of him being truly evil. 

Edgar is pretty much functionless at the beginning of the play, other than as Edmund's pawn. After being framed in a scheme to overthrow his father, Edgar must disguise himself as a poor beggar ("Tom O'Bedlam") in order to escape persecution. Instead of leaving the country, Edgar stays and ends up helping his own father, Gloucester, after he is blinded, including warning him off of a suicide attempt. Though Edgar seems weak or dull at first, he reveals a keen intelligence and creativity that serves him well. His loving nature allows him to give mercy to a father that believed him to be disloyal, and he is one of the heroes at the end of the play.

Goneril and Regan are the elder, less favored daughters of King Lear; they are also the most despicable of people. When their aging father gives them his land in return for their professed "love", they drive him out of his own kingdom simply because they find him annoying and want the rest of his power. Throughout the play, Regan and Goneril ignore all loyalty, betraying spouses and each other. Their characters are cruel and witchy from the start, supported by their waspish tendencies.

Cordelia, on the other hand, is Lear's favorite daughter, who refuses to publicly proclaim her love and is thus exiled. Even after this banishment, she continues to love her ailing father, even though her return home results in her death. Cordelia risks everything for her true love of her family, revealing a self-sacrificing and devoted character.