As shown in research data, to what extent do explicit game mechanical rewards, such as various types of fate points (hero points, willpower, artha, other consumable resources) or experience points, affect player behaviour?
Anecdotally, OSR folk seem to enjoy experience from gold and refer to it as an incentive for good play, while modern D&D often uses milestone experience or just levels whenever the game master says so.
Likewise, I recall reading some people speaking for the beliefs and artha in Burning wheel as finally rewarding them for playing like they want to, while others think of these as artificial and unnecessary crutches. I remember similar discourses around other games with such explicit mechanical rewards.
Since everyone has an opinion and personal experience, those are not very useful answers. Scientific studies would be optimal, but surveys or other larger scale data would also be interesting. I do not remember articles about this in Analog game studies or International journal of roleplaying, but it has been a while since I browsed them. I am not too familiar with the broader game studies literature.
Some credible possibilities might be: Although a vocal minority says something, the trend is that most people change or do not change their behaviour in the presence of mechanical rewards. Or perhaps some personality factor affects this, or perhaps people can toggle it on and off, depending on what they are playing.
The context of roleplaying games is very relevant here - first of all, they are a leisure activity, so research on, for example, avoiding physical pain or earning financial rewards hardly matters. This makes it challenging to apply research on for example Pavlovian conditioning or financial decision making to roleplaying games without serious thought.
Second, they are somewhat distinct from many other games, in that most roleplaying games are not explicitly competitive in the same way that many other social games are, and the nature of goals in roleplaying games is in any case different from those in board games or many electronic games. Hence, it takes some care to apply research on motivation in games in the broad sense. But there might very well be something relevant there.