In Pride and Prejudice, what is Mr. Wickham's motivation, especially toward Lizzy, and how does it change through the story, if at all?
Mr. Wickham's primary motivation in the novel is to marry for financial security. He is arguably the most selfish character in the novel. When he is first introduced he is presented as a charming man who has definite romantic interest in Elizabeth, but once it becomes clear that she will not have much of an inheritance, he quickly shifts his attentions to Miss King who has a comfortable amount of inheritance in the bank. Lizzy isn't all that interested in Wickham and actually defends this action to her aunt when they talk about what Wickham has done. Lizzy fully understands the necessity of financial security, even if she isn't willing to marry for it. At this point in the novel she still believes Wickham's story that Darcy hasn't been fair in regards to his inheritance from the Darcy estate.
As the novel progresses we learn that the relationship with Miss King has fallen apart and that Lydia is very interested in Wickham. Unfortunately, Lydia is very naive and foolish -- she runs off with Wickham and creates a complete scandal. Wickham has no intention of marrying a Bennet daughter -- they have no money! Wickham only agrees to marry Lydia when Darcy bribes him with an incredible amount of cash and a commission in the military (higher rank). By this time, Elizabeth knows that whole story of Wickham's lies about Darcy, and she is appalled that her sister now has to be married to the man, but she is relieved that a family scandal has been avoided. When she later learns that the marriage came about because of Darcy, her feelings for Darcy are cemented. She ultimately marries him for love and tolerates Wickham as a brother-in-law.
Mr. Wickham is a greedy soldier attempting to secure his financial future through marriage. In the story, he initially pursued Elizabeth, and while she finds his company pleasant, she politely declines his advances, at which point he moves his interest to another potential spouse. He eventually runs off with Lydia, Elizabeth (Lizzy)’s much younger sister, causing a scandal.
While Lizzy thought he was relatively charming and even defended him because she believed his tale about how Mr. Darcy forced him into poverty, the scandal revealed his true colors. When a mysterious benefactor swoops in to finance the marriage and Mr. Wickham’s future, the family is saved from an extended drama, but it doesn’t undo his transgressions. Mr. Wickham was only ever interested in securing his own financial future, even when he courted Lizzy.