Hypothetical Situation: Euthanizing someone else's dog?

Imagine the following situation: You're driving along one day and happen to come accross (or hit) a dog. The dog is not killed, but severly injured. You rush the dog to an emergency vet, only to find out that the treatment for the injury has a very small chance of recovery, will be very stressful on the dog, and will cost you thousands of dollars. The humane thing to do would be to put the dog down. If you cannot contact the owner, is this your descision to make or is the dog made to suffer until the owner can be reached?