Meanwhile, in the Greek camp, the great general and king Agamemnon is conversing with his lieutenants and fellow kings. He asks why they seem so glum and downcast—for although their seven-year siege of Troy has met with little success so far, they should welcome the adversity that the long war represents, since only in difficult times can greatness emerge. Nestor, the oldest of the Greek commanders, echoes Agamemnon's argument, citing examples of how heroism emerges from hardship. In response, Ulysses expresses his deep respect for what they have said, but points out that the Greek army is facing a crisis not because of the duration of the war, but because of a breakdown in authority within the Greek camp. Instead of being united, they are divided into factions—and at the root of this crisis is the greatest of the Greek warriors, Achilles, who refuses to fight and instead sits in his tent while his friend (and male lover) Patroclus makes fun of the Greek commanders. Others, like Ajax and his foul-mouthed slave, Thersites, follow this example, and so the entire army is corrupted.
The others agree that this is a great problem, and as they discuss what is to be done, Aeneas appears under a flag of truce, bringing a challenge from Hector. The Trojan prince offers to fight any Greek lord in single combat, with the honor of their respective wives as the issue. The Greeks agree to find a champion and offer Aeneas hospitality. As Aeneas is led away, Ulysses tells Nestor that this challenge is truly directed at Achilles, since only Achilles could match the great Hector in battle. But to have Achilles fight Hector would be dangerous, because if Achilles lost, it would dishearten the entire army. Therefore, Ulysses suggests, they should have Ajax fight Hector instead; even if Ajax loses, they can still claim that Achilles would have won in his place. At the same time, by choosing Ajax as their champion, they will infuriate Achilles and perhaps goad him into rejoining the war, bringing with him all his soldiers. Nestor, impressed with Ulysses's intelligence, agrees to the plan.
Having established the play's personal drama in the first scenes with Troilus and Cressida, Shakespeare now turns to the political drama, which is dominated by the figure of Ulysses. In classical Greek tradition, Ulysses (the King of Ithaca) is the hero of Homer's Odyssey; he is also credited with devising the Trojan Horse ruse that enabled the Greeks to finally take Troy. In every source, he is the wisest and most cunning of the Greeks, and Shakespeare follows this tradition, making his Ulysses a clever politician who easily manipulates the stubborn, foolish warriors around him—especially the play's two great thugs of warriors, Ajax and Achilles.
Ulysses is also a political philosopher (indeed, Troilus and Cressida is notable for the large number of philosophical speeches from various characters), and in this scene he delivers one of the most famous political speeches in all of Shakespeare. Diagnosing the ills of the Greek army, he traces it all to a neglect of the importance of "degree," which, he declares, is the glue that holds society together. If people do not "observe degree, priority, and place" (I.iii.86), he insists:
Then everything include itself in power, Power into will, will into appetite, And appetite, an universal wolf, So double seconded with will and power, Must make perforce a universal prey And last eat up himself. (I.iii.119-24)
In other words, when the respect for authority disappears, anarchy results. The speech is a perfect encapsulation of conservative politics, and it also touches on themes that Shakespeare develops in tragedies like Macbeth and (especially) King Lear, in which the death or failure of a monarch results in the triumph of evil. Macbeth in MacBeth, and Goneril, Regan, and Edmund in King Lear, are perfect examples of the triumph of Ulysses's "universal wolf" in the human heart.
The other Greek kings, including Agamemnon, are strictly second-rate compared with Ulysses, and so it is appropriate that in this scene, as throughout the play, they follow his lead. Achilles has not yet appeared, but the conversation between the kings serves to introduce him to us—"the great Achilles," Ulysses calls him—but the long account of how he and Patroclus sit around mocking the Greek commanders instead of fighting immediately undermines that description. In the Iliad, Homer gives Achilles a reason for sitting out of the fight—he is upset because Agamemnon has taken a slave girl from him. Perhaps Shakespeare assumed that his audience would know the story, and so does not bother repeating it, but in Troilus and Cressida Achilles is never given a real motive for his refusal to fight—and the absence of a motive makes him appear that much more ridiculous. He is Homer's hero, but in Shakespeare's play he becomes an unpleasant, even villainous, figure.
I just finished reading Troilus and Cressida in my effort to read all Shakespeare by his 450th birthday. It wasn't a favorite play, and I probably could have had a very happy life without ever reading it. But in case you're interested, here's my take: