The Priam of Myth ...

Priam was the son of Laomedon and was the king of Troy. He became king after Laomedon and all of Priam's brothers were killed by Heracles in the first sack of Troy. Priam himself was the father, by his wife Hecuba and other women, of fifty sons and many daughters, including Hector, Paris, and Cassandra. He unsuccessfully defended his city during the Trojan War, at the end of which Troy was sacked a second time and was finally destroyed.

During the Trojan War, Priam's son Hector was killed by the Greek hero Achilles. In one of the most moving scenes of the Iliad, Priam courageously entered the Greek camp by night and pleaded with Achilles to return Hector's body for burial. Priam himself was finally killed by Achilles' son, Neoptolemus, upon an altar of Zeus in the center of Troy.

The Agamemnon of Myth ...

Agamemnon was the son of Atreus and the brother of Menelaus. He was the king of either Mycenae (in Homer) or of Argos (in some later accounts), and was the leader of the Greek forces during the Trojan War. He married Clytemnestra and had several children by her, including Orestes, Electra, and Iphigenia.

When the Greeks sailed for Troy, their fleet was trapped by unfavorable winds at Aulis. The seer Calchas revealed that their misfortune was due to Agamemnon, who had boasted that he equalled Artemis in hunting; the winds would only change if Agamemnon's daughter Iphigenia was sacrificed. Agamemnon reluctantly agreed to the sacrifice, but Artemis herself whisked Iphigenia away from the altar and substituted a deer in her place.

During the seige of Troy, Agamemnon offended the greatest of the Greek warriors, Achilles, when he took the girl Briseis from him. Achilles' anger with Agamemnon furnished the mainspring of the plot in the Iliad. After the sack of Troy, Agamemnon acquired Cassandra, the daughter of King Priam, as his concubine, and took her home with him to Greece.

Agamemnon had an unhappy homecoming. He was either blown off course and landed in the country of Aegisthos, or he came home to his own land to find Aegisthus waiting for him. In either case, Aegisthus had become the lover of Clytemnestra, and the two together murdered Agamemnon and Cassandra shortly after their arrival. Aegisthus and Clytemnestra then ruled Agamemnon's kingdom, but were eventually killed by Agamemnon's son, Orestes (or by Orestes and Electra in some accounts). The homecoming of Agamemnon and its aftermath were favorite subjects for Greek tragedy.