The word "agon" in Greek is the root of our word "agony", and it means a fight. The Greeks tended to see pretty much everything that happened as a fight between two sides, even things that seem to us like they only have one side. Memorizing your lines for the play, for instance, is an agon, a fight, between you and the play. Getting up in the morning when you are tired is an agon between your nomos and your physis (or an agon between your desire to do well in school and your desire to watch late-night TV). But a war is also an agon, and a game of checkers, and courtship is an agon where one person tries to win the other one's heart.
To find out more about "agon" and its role in Greek thought, check out these books from Amazon.com or from your library:
Philosophy and Science in Ancient Greece: The Pursuit of Knowledge, by Don Nardo (2004). For teenagers. Don Nardo has written many books for young people about the ancient Greeks.
The Cambridge Companion to Greek and Roman Philosophy, edited by David Sedley (1997).
Homo Necans: The Anthropology of Ancient Greek Sacrificial Ritual and Myth, by Walter Burkert (1987). (Homo Necans means Man the Killer). Burkert is one of the great experts in Greek religion.