It's generally frownded upon in civilized society to make your pets fight other peoples pets for entertainment. Their are a few exceptions, like pokemon, or when you have multiple suitors. Another exeption is Kabuto Sumo. 

In Kabuto Sumo, you battle for supremacy in the ring with your own pet bettle wrestler. The gameplay of Kabuto Sumo resembles the coin-pusher arcade games in which you strategically drop quarters and anxiously anticipate coins cascading off the platform. This game features a similar experience, with you trying to strategically slide pieces onto the board and push the other players out of the ring. It's an exciting combination of dexterity, strategy, and luck.