I've thought about Game Theory and Information Literacy for quite a while (see notes below). One useful avenue may be "search theory" from economics. Here's the quote from wikipedia: 

"In economics, search theory (or just search) is the study of an individual's optimal strategy when choosing from a series of potential opportunities of random quality, given that delaying choice is costly. Search models illustrate how best to balance the cost of delay against the value of the option to try again.

Two common settings for these models (and their empirical applications) are a worker's search for a job, in labor economics, and a consumer's search for a product they wish to purchase, in consumer theory. From a worker's perspective, an acceptable job would be one that pays a high wage, one that offers desirable benefits, and/or one that offers pleasant and safe working conditions. From a consumer's perspective, a product worth purchasing would have sufficiently high quality, and be offered at a sufficiently low price. In both cases, whether a given job or product is acceptable depends on the searcher's beliefs about the alternatives available in the market."

This may be a useful example for matching a student with a piece of information. Students may have criteria for what counts as a "good source" so they are making a similar decision making process as that outlined in economic search theory. 

Look at these notes from Bryan Caplan at George Mason University. 

Game Theory

While you are thinking about this, think about games of moral hazard. These are asymmetric games where one player has a limited amount of risk compared to another. The classic example of this is insurance. If I have my car insured, I might do stupid things because I do not carry the risk. The insurance will pay for my repairs. This is why we have deductibles and why we pay higher rates following accidents. In general, the person carrying the least risk has more knowledge and freedom to act than the person carrying more of the risk. So, games of moral hazard are about actions and information as well as risk.

I wonder if research could be thought in these terms? It's not quite the same, but you could think about the instructor as the insurance company. The goal for the instructor is to get the students to follow assignments and make particular decisions that achieve learning objectives. Depending on how assignments are structured, there are strategic incentives and actions that the students will take. This is very similar to the insurance model in that the car owner has much more information about their actions and the history of the car than the insurance company. Students have more freedom to act and they have more information about their actions. The instructor only gets to know what he/she can observe in classes or from assignments.

The math

Fallis, D. (2004). On verifying the accuracy of information: philosophical perspectives. Library Trends. 52,3 p.463-487.

Fallis (2004) takes Wilson’s discussion into the twenty-first century by introducing game-theory, among other factors, to the information selection process. He notes that information evaluation can be seen as a game of “asymmetric information” where the information consumer is an uninformed player and the information creator is an informed player. The information creator has a benefit to communicating the value of the information to the consumer, and, often, there is a cost involved in this communication. The more experienced player can recognize the outcomes of these costs such as no recognizable errors, quality presentation, or inclusion in various publications and use them to select one piece of information over another.

\"Game Theory\" from Stanford's Encyclopedia of Philosophy

"Suppose first that you wish to cross a river that is spanned by three bridges. (Assume that swimming, wading or boating across are impossible.) The first bridge is known to be safe and free of obstacles; if you try to cross there, you will succeed. The second bridge lies beneath a cliff from which large rocks sometimes fall. The third is inhabited by deadly cobras. Now suppose you wish to rank-order the three bridges with respect to their preferability as crossing-points. Your task here is quite straightforward. The first bridge is obviously best, since it is safest. To rank-order the other two bridges, you require information about their relative levels of danger. If you can study the frequency of rock-falls and the movements of the cobras for awhile, you might be able to calculate that the probability of your being crushed by a rock at the second bridge is 10% and of being struck by a cobra at the third bridge is 20%. Your reasoning here is strictly parametric because neither the rocks nor the cobras are trying to influence your actions, by, for example, concealing their typical patterns of behaviour because they know you are studying them. It is quite obvious what you should do here: cross at the safe bridge. Now let us complicate the situation a bit. Suppose that the bridge with the rocks was immediately before you, while the safe bridge was a day's difficult hike upstream. Your decision-making situation here is slightly more complicated, but it is still strictly parametric. You would have to decide whether the cost of the long hike was worth exchanging for the penalty of a 10% chance of being hit by a rock. However, this is all you must decide, and your probability of a successful crossing is entirely up to you; the environment is not interested in your plans.

However, if we now complicate the situation in the direction of non-parametricity, it becomes much more puzzling. Suppose that you are a fugitive of some sort, and waiting on the other side of the river with a gun is your pursuer. She will catch and shoot you, let us suppose, only if she waits at the bridge you try to cross; otherwise, you will escape. As you reason through your choice of bridge, it occurs to you that she is over there trying to anticipate your reasoning. It will seem that, surely, choosing the safe bridge straight away would be a mistake, since that is just where she will expect you, and your chances of death rise to certainty. So perhaps you should risk the rocks, since these odds are much better. But wait … if you can reach this conclusion, your pursuer, who is just as rational and well-informed as you are, can anticipate that you will reach it, and will be waiting for you if you evade the rocks. So perhaps you must take your chances with the cobras; that is what she must least expect. But, then, no … if she expects that you will expect that she will least expect this, then she will most expect it. This dilemma, you realize with dread, is general: you must do what your pursuer least expects; but whatever you most expect her to least expect is automatically what she will most expect. You appear to be trapped in indecision. All that might console you a bit here is that, on the other side of the river, your pursuer is trapped in exactly the same quandary, unable to decide which bridge to wait at because as soon as she imagines committing to one, she will notice that if she can find a best reason to pick a bridge, you can anticipate that same reason and then avoid her."

1. Putting yourself in other people's shoes (strategy & Nash Equilibrium)

2. Dating Game (coordination)

3. Games of Moral Hazard

4. Duels