By its nature, Badgers is a rather peaceful game and can be played just for the fun of hiking around, collecting and trading badges, and for watching badges making their way on the map.
However if you insist on fight, you can have it:
You can fight for Regions. You just have to go to places, remove your strongest opponents badges and drop your own ones.
You can try to climb up one of the Highscores to become the best.
But, if you are looking for trouble, be aware, that the fighting power is connected to the production and collecting game:
The higher your production rate of own badges is, the more offensive you can play: Your own badges double as “amunition”.
The higher your level is, the stronger badges you will produce for offense: A level 20 badge has as much influence as 20 level 1 badges.
The higher your capacity, i.e. the more different badges you hold, the more opponent badges you can remove from a region.