Replying to Some fender bender help

Just looking for some advice here..

during the weekend when i was backing out of a spot in a parking lot, the person directly behind me started backing out too (after i did) and i rolled into him while he sat there. at the point of collision i was like 15 feet from my spot and like 6 from his, his car being a couple feet out of his spot. he busted his light up a bit and i have a couple okay dents, but we both decided to not involve cops or insurance, BUT he thinks i should pay for his light.

1) who can we use as an arbitrator without getting too involved with cops/paperwork etc? can i just walk into a cop station and ask a "hypothetical" situation without them inquiring further?

2) anyone happen to know the letter of the law here (who is at fault?)? i think we're both obviously at fault but i dont think im responsible for his light

thanks bros