Too often after a car accident, one of the drivers will readily admit to be at fault and offer to pay you out of pocket. They will beg you not to call the police promising to repair your car for you. It is the biggest mistake you can make because once you leave the scene of the accident you will discover all the contact information you received was fake. Even if you can track them down, without any police report it becomes an uphill task proving they are at fault for the accident.
Always call 911 after an accident even if there is no damage to any vehicle and no one appears injured.