Describe the incident involving Pip and the younger gentleman in Miss Havisham's garden.  What prompts Pip's actions, and how does he feel about himself later in chapters 11-19?

Pip and the pale young gentleman get into a fistfight in Miss Havisham's yard. As Pip is once again allowed to explore the yard, he runs into a pale, young gentleman who challenges him to fight. Despite the young man's jumping about and expert preparation (bringing some water and explaining the rules), Pip gives him a bloody nose, a black eye, and a general whopping. They end the fight and the boy, cheerful as ever, wishes Pip a good afternoon.