The incentive is you say you have a lost dog. Plenty of people say they have lost a dog and they get people looking for a lost dog because people feel bad for you.

The only reason you saw reward is to motivate a movement to look for the dog, but you don't need to. There are many kind people out there who will look without need of a reward.

Further, a reward will not motivate a thief. They know if you say stolen, you likely have talked to cops. If cops are involved, they'd rather stay unarrested than get $1000. Truth is, they can probably sell the dog for more without involving having to explain how they got the dog.

You already had cops go do some talking, so the word is out. Did you get the dog back? Nope.

You say you won't ask questions if they return him, but you definitely would once you have the dog back. You'd get angry. Thieves know this. They won't ever give the dog back if the police are involved.