How does the trophy system work?

Every time you head into battle you have the potential for winning or losing Trophies. The amount of Trophies won or lost depends on 2 things: The difference between your Trophy count and your opponents, and the amount of victory stars won. If you were to defeat someone who has much higher Trophies than you and defeated them with a 3 star victory you would earn much more than if you defeated a lower Trophy count by 1 star.