I was reading John Goldingay's OT Theology and came across an interesting story (123-124). In Job 41:5 God asks Job if he could play with Leviathin like a bird; the implication is that Leviathin is God's pet, not Job's. While humans may have birds or whatever else to play with, God has Leviathin and Behemoth to play with. The Talmud recounts that after a hard day of work, God goes to play with Leviathin to wind down.