The goal of the finite game is to win. Sports, politics, wars, and Monopoly all have strict rules you have to follow. The boundaries are clear – there is a beginning, a middle and an end. It's clear who's playing and who's not.
The goal of the infinite game is to keep playing. It is "any authentic interaction, from touching to culture, that changes rules, plays with boundaries and exists solely for the purpose of continuing the game"
"A finite player seeks power; the infinite one displays self-sufficient strength. Finite games are theatrical, necessitating an audience; infinite ones are dramatic, involving participants"