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In a carrot game for a player, that player must help his opponent to get a desired response. In a stick game for a player, that player must hurt his opponent to get a desired response. We show that most all smooth monotonic two player games can be classified as: carrot for both, carrot for one and stick for the other, or stick for both. We transform carrot and stick games into sequential move games and incentive games. A carrot game for a player implies mutual benefits will come from his moving first. A stick game for a player implies that if he moves first, the other player will suffer. Incentive games based on a carrot game for each player bring mutual gains. Those based on a stick game for each player bring harm to at least one and possibly both.