Antisthenes (c. 455–360) was an Athenian, a pupil of Socrates and the founder of the Cynic school of philosophy. Numerous surviving fragments, most of them witty ripostes, echo his cynical views, but we have no complete work or even substantial fragment except for this pair of speeches. They are in the tradition of Gorgias' Helen and Palamedes, and Antiphon's Tetralogies, and are probably early works of Antisthenes. The character of Odysseus prefigures several of the qualities valued by the Cynics.

The contest for the armor of Achilles was a well-known episode of the Trojan War. After the death of Achilles at Troy, the Greeks decided to give his armor to the next best warrior. The choice was between Ajax, clearly the strongest and most powerful fighter, and Odysseus, who was not as mighty but was more intelligent and resourceful. When the vote came out for Odysseus, Ajax felt (with some justification) that he had been cheated of what was rightly his, and feeling disgraced he committed suicide. In a famous scene in the Odyssey (11.543–567) Odysseus sees the ghost of Ajax in Hades and makes a friendly overture toward him, but Ajax turns away in scornful silence. Sophocles' play Ajax portrays the madness and suicide of Ajax after he has been denied the armor. Aeschylus also wrote a play, now lost, entitled The Decision about the Armor.