I received an in-game notification saying, "If you are a 'Good Sport' you will receive periodic rewards". (see picture below)
How do I become a 'Good Sport & what rewards can I receive?
How often will I receive rewards?
I did get a notification when I accidentally blew up someone else's car, saying [something along the lines of]: "You blew up someones car. You are a Poor Sport."
I also saw an in-game message that mentioned [something like] "If you are a Poor sport, you will play with other poor sports"
Best Answer
You'll become a "bad sport" by leaving missions/races/deatchmatches etc. early and destroying other player's personal vehicles.
The "bad sport" designation lasts for about 2 days. So if you want to be a "good sport" again, don't do things that are considered bad for 2 days.
I am not 100% sure what you can get as a reward. I once got a cash bonus of 1000$, but there could be more things (like discounts on ingame items).
Source: IGN