In some systems, the characters are rewarded for things the players do. Take Exalted, for example. At the end of each session, the GM is instructed to award around 4 XP to everyone. This encourages attendance, but has nothing to do with character actions. Stunts in Exalted are another pretty good example. Bonus dice are awarded for flashy descriptions of combat actions. The player did the describing, the character gets the reward.
My conjecture comes in two parts. First, character advancement should be a reward for actions taken by the characters. Second, Players can be rewarded with metagame currencies, such as scene framing powers and narrational authority. So, character actions like accomplishing character goals or reaching the end of a scenario or situation, as well as taking action to improve one’s skills, should be rewarded with the currency of character advancement or another in-game reward. Desirable player actions, such as attending sessions, initiating roleplays, and so on, should be rewarded with a currency that allows them to take further player actions to improve the game.
As somewhat of an example, let me throw one bit of technology out there, based on a situation I’ve seen. In one game I played, being involved in roleplaying scenes was rewarded with experience. A reasonable question to ask is “Is this the behavior we want to reward?” I would have to say no, since players may be passively involved in roleplays with the group or NPCs without adding much to the game. To put a finer point on it, the behavior I think is more appropriate to reward here is “initiating roleplaying scenes,” because doing so promotes involvement in the game and pushes the story forward.
One method for doing that would be to award Narration Points. An NP allows the player to specify some background action that’s going on in the vicinity of the characters. If they’re in a city, they might decide that a festival is going on. If the campaign focuses on an ongoing war between two nations, they might decide that an important battle has been won or lost. These sorts of background events aren’t intended to have an immediate impact on the story, but they certainly could, since they provide more details to work with.
This is only one possible reward, and there may be more appropriate rewards for this sort of action. This was the first that came to mind for me.