What is the main conflict in The Cocktail Party by T. S. Eliot?

The play mainly follows the story of Edward and Lavinia Chamberlayne, a British couple who have been married for five years. The story opens in the drawing room of the Chamberlaynes’ apartment, where Edward is entertaining a group of friends. Lavinia is absent, and he explains that she is away tending a sick aunt. As the guests leave, one man named Peter remains behind to ask Edward to intervene for him with a woman named Celia, for whom he has feelings. Edward agrees. He asks one man—the “unidentified guest”— to remain behind, and reveals to the stranger that his wife has left him. The stranger says that he can bring Lavinia back to Edward if Edward will promise that he will ask her no questions and expect no explanations. Edward agrees and the unidentified guest leaves, though not before the conversation is interrupted a few times by returning party guests, most of whom the audience will later discover have ulterior motives.