Variables in positive reinforcement in human beings I've been thinking about positive reinforcement occasionally, and I've always found myself wondering about various things that can influence it.

So, I'm looking for information (results of empirical studies) about the variables affecting positive reinforcement, in hopes of finding answers to my questions and questions that I haven't even thought of, such as:


How does knowing what the positive stimulus is for affect the change? What happens if I did two things, and I don't know which one of them led to the positive stimulus? e.g. I solved a math problem and won some game, and then I received a prize, and I don't know for which one of these things


What happens If (as far as I'm concerned) I did nothing, and then I receive a prize?


If I receive a prize for something I did an hour earlier, for example, will it still change my behavior?
Does receiving a prize while I do a task has a stronger effect? weaker?


Any other interesting questions (as well as answers to them) are welcome 

(And since someone is probably going to make a few changes and add tags - thank you and forgive me. English is not my native language, and I don't have much of a background in psychology)
Your question is, in essence, a request for a mathematical model of Temporal Difference Reinforcement Learning.  In a nutshell, temporal difference models add a notion of time to reinforcement learning models, which describe reinforcement learning as a comparison between what was expected and what actually occurred.

I think most of your answers can be found in the article above.  =)

Edit re: my insistence on mathematical models providing the answer to your question:

Just to be clear, mathematical models don't exist in a vaccuum.  Good models are:


built from constraints imposed by experimental observation
tractable; that is, they reflect the (presumed) underlying implementation


Case and point, the Rescorla-Wagner model's1 delta (prediction error) parameter has been correlated to the phasic activity of dopaminergic neurons.  This is precisely why the model is so hugely successful; it describes not only the experimental data, but the apparent neurological underpinnings, at least superficially.

Note that this is a very important kind of validity for neurological models, so much so, in fact, that there is an entire class of neuroimaging papers dedicated to finding functional activations that correspond to various parameters in such high-quality models.  Exhibit B.

I think your confusion arises from a lack of familiarity with the modelling approach to cognitive neuroscience (and that's okay! It's not obvious!), as well as a non-trivial distinction between the questions "what happens", "how does it happen" and "where does it happen".  You specifically asked what happens, which is the realm of formal mathematics.  What happens, as best we can tell, is that learning is driven by updating a prediction about what will happen concomitantly with (or shortly after) a stimulus, with what actually happens when that stimulus is sensed.  The models describe the exact nature of this interaction.  If you want to be more specific than this, you need to dive into the math.  If you want to know where or how these computations are performed, then that's another question entirely.

1.  this model doesn't integrate any notion of time, contrary to the above TDRL model