They should name the teams, but instead of a game, have a series of competitive skills competitions. They could be a mix of traditional contests (speed competitions, accuracy matches) and off the wall things (maybe even a volleyball game or Horse). This wouldn't be for adults, but for kids who would really get into this sort of thing. They could spread it out across a whole day. The winning team might get some money and a patch to add to their uniform or something else that plays into their narcissistic tendencies.