The phrase "bragging rights" means having the satisfaction or pride to boast about one's achievements, possessions, or superiority over others. Full definition
This meant manufacturers like Porsche, McLaren, and Koenigsegg were unable to compete for bragging rights for lap times, a reality Koenigsegg was very vocal about when it was unable to test its new One: 1 «megacar» on the «Ring. (automobilemag.com)
This could be used by players as bragging rights of their PvP accomplishments. (thatvideogameblog.com)
The crew of the No. 4 Compuware Corvette C6.R driven by Oliver Gavin and Olivier Beretta will take on Alex Job Racing for bragging rights in pit stop prowess. (corvetteracing.com)