The real Greek god of war, Ares, might have a thing or two to say about that. Kratos is a fictional character made up by game creator David Jaffe, not a mythical one. While Kratos is loosely based on the idea of a Greek god and/or a Spartan hero, he is not part of the ancient and official pantheon, though he interacts with them in the game.
There was a spirit (daimon) or minor god of strength called Kratos or Cratus, but he was generally only encountered as part of a guardian of the throne of Zeus, always subservient to his will.
Since Kratos is fictional, created for the purposes of the game, his interactions with the Greek gods and goddesses are only loosely based on mythology.
Kratos's Appearance: Vigorous big muscled man with ash-grey skin.
Kratos' Symbols or Attributes: Double chained swords.
Kratos's Strengths: Powerful, strong, skilled fighter.
Kratos's Weaknesses: Constantly enraged - which can be an advantage in battle.
Major Temple Sites of Kratos to Visit: As a fictional character, there are no sites in Greece legitimately associated with him. However, Mount Oympus frequently features in the game.
Kratos's Birthplace: Sparta
Kratos's Spouse: None known in the game so far
Kratos's Parents: In the game story, Zeus is said to be the father of Kratos. This is certainly consistent with Greek mythology, as Zeus was the father of many.
Kratos's Patrons: Kratos is initially a follower of the real Greek god of War, Ares. In the story, he is also assisted by Athena, Gaia, and other gods and goddesses.
Children: None in the game story so far.
Basic Story: In the game "God of War" Kratos is a Spartan fighter and follower of Ares. Ares eventually tricks him into killing his own family, and Kratos ends up killing Ares and becoming the new God of War on Mount Olympus. He is also called the "Ghost of Sparta" in the game.
Interesting Fact: While not a real Greek god, Kratos does have a typically Greek-sounding name. Actually, the "-os" ending is pre-Greek, and is only found in words which predate the Greek language. Many Minoan words, such as Minos or Knossos, end in -os, but we don't know the ancient Minoan name of their Greek god of war, or if they even had one. Athena or other goddesses may have filled that role for the Minoans. As a Spartan, it's not surprising Kratos has been given a name ending in "-os", as the Minoans had close ties with ancient Sparta and it is believed that Sparta preserved many aspects of the then-vanished Minoan culture.
More Fast Facts on Greek Gods and Goddesses:The 12 Olympians - Gods and Goddesses - Greek Gods and Goddesses - Temple Sites - The Titans - Aphrodite - Apollo - Ares - Artemis - Atalanta - Athena - Centaurs - Cyclopes - Demeter- Dionysos - Eros - Gaia - Hades - Helios - Hephaestus - Hera - Hercules - Hermes - Kronos - The Kraken - Medusa - Nike - Pan- Pandora - Pegasus - Persephone - Perseus - Poseidon - Rhea - Selene - Zeus.
Pictures of other Greek Gods and Goddesses: Greek Deities Clip Art Images