Se ajudar um pouco, encontrei algumas definições:
Dog-eat-dog describes a world in which people fight for themselves only and will hurt other people. Example: "I have been in this business for twenty years. It's dog-eat-dog. The competition is always trying to steal your customers."
Dog-eat-dog means that a person is like a dog that will eat another dog. Sometimes people say, "It's a dog-eat-dog world", as an excuse when they have hurt another person. Example: "I can't believe you sold him your motorcycle for so much money!" Reply: "Hey, it's a dog-eat-dog world."
It's a dog-eat-dog world means that you must first watch out for your own interests, because other people will be watching out for theirs. There is no letter s at the end of any of the words in dog-eat-dog. "Example: "That school is dog-eat-dog. The students cheat and even destroy each other's work to get better grades."http://www.goenglish.com/DogEatDog.asp
Nem sempre tem uma tradução do inglês para o português. Tem vezes em que eu quero me expressar de uma forma no Brasil mas eu não lembro a palavra/frase em português, mas eu lembro em inglês!