It was narrated from 'Adiyy bin Hatim that: he asked the Messenger of Allah about hunting. He said: "When you release your dog, mention the name of Allah over him, and if you catch up with him and he has not killed (the game), then slaughter it and mention the name of Allah over it. If you catch up with him and he has killed (the game) but has not eaten any of it, then eat, for he caught it for you. If you find that the has eaten some of it, then do not eat any of it for he caught it for himself. If there are other dogs with your dog and they have killed (the game) but have not eaten any of it, then do not eat any of it, because you do not know which of them killed it".
This hadith also teaches us about fairness and justice in hunting; even though our own dog may be involved in killing an animal or catching a prey first does not mean that all rights over that animal belong solely to us; rather there is still an element of fairness involved in this process which requires us to consider other animals or people who may also be involved in this process before claiming full ownership over what was hunted down by our own pet or ourselves alone.
Overall this hadith encourages Muslims to practice hunting while being mindful about their actions and respecting Allah's laws at all times; thus ensuring justice is served fairly among all parties involved in such activities regardless whether those parties include humans or animals alike.
