Can we use rational economic theory to explain voting, volunteering, giving to charity, helping strangers or even risking life? Behavioral economics often attribute these to altruistic preferences. However, some phenomena cannot be explained by sole presence of individuals with other-regarding preferences, such as the well-documented "crowding-out" effect. For example, when people start to get monetary benefits from donating blood, their actual donation will go down.
In a series of papers (see here and here), Roland Benabou and Jean Tirole attempt to explain this crowding out effect using rational economic models. Put it simply, they have built two different models to capture two such possible mechanisms that would eventually lead to crowd-out. One is the so-called informed principal problem. In this model, the principal wants to motivate the agent to make efforts. However, although the principal knows the critical factors of the task the agent is going to take (e.g., its chance of success, or the ability of the agent in doing the task), the agent doesn't know about it. It turns out that the principal would have more incentive to motivate the agent only if the agent is not that good. This would eventually become a bad signal for the agent to make such efforts.
The other mechanism, often documented in the psychology literature as the "overjustification effect", is called "multi-dimensional signaling" by Benabou and Tirole. They argue, that people don't care only about monetary payoffs, they also care about their self-fulfillment (e.g., intrinsic warm glow when helping others) and their reputation (e.g., what others would say about them when they do good deeds). If all people in the society could be characterized by parameters of intrinsic, extrinsic and reputational motives, and these parameters also follow some kind of distribution, then, as they have shown in their model, when we increase the monetary incentives, part of the population who are initial contributors would be crowded out by new contributors who are more greedy but less altruistic.