1. These results are all about finding good solutions to allocation problems without using money or in cases where money isn't or can't be applied.
2. These results do tend to show that a "centrally planned" solution can be better for everyone than a "free market" solution. But as you say, by central planning I really just mean that some entity takes in everyone's preferences and outputs a global allocation, with the nice property that everyone is happy with what they got and nobody can find a way to deviate from their assignment and be better off. One might argue that a "free market" would find the same solution eventually, but it might be slower.
These two results are sort of the opposite of the Invisible Hand stuff as well as the common assumption that, for instance, everyone values money the same (which underlies the justification for much of economics). So I think they're really cool in that respect.
FYI - Here's a link to an interactive illustration of the deferred acceptance algorithm that I posted a few years back on HN: http://mathsite.math.berkeley.edu/smp/smp.html
http://www.amazon.com/Two-Sided-Matching-Game-Theoretic-Econ...
It is readable if you're interested in the problem. This book on the same subject is also good, although not by any Nobel prize winners:
http://www.amazon.com/Stable-Marriage-Problem-Algorithms-Fou...
http://www.alternet.org/economy/there-no-nobel-prize-economi...
And I don't see that in the first 2 pages. Or was that about the math nobel prize ?
In this case, it is simply the post title being misleading, as it's not the Nobel prize these folks won, but the Nobel memorial prize in economics, which is a relatively new prize which is not part of the 5 Nobel prizes which had been given by Nobel's estate for more than a century.
Edit: oh I see they didn't reward a dead in this case, misread your comment..
This one seems to be given for work that could be said to claim that central planning really can work after all.
Shapley and Roth deal with topics that fall, at the highest level, under the field of game theory, but more specifically market design. Market design relies heavily on mechanism design, which can also be called reverse game theory. In game theory, you're interested in determining the best strategy given a set of conditions (the players, their strategies, the timing of their moves, their payoffs and the information they have [or don't have]). On the other hand, mechanism design is concerned with what the conditions have to be in order to achieve a specific objective or outcome. Hence, mechanism design problems map well onto many problems of regulation.
For example, let's say there is a Senator, call her Mrs. X, who is interested in passing a bill that achieves outcome Y. The mechanism design solution is then the set of rules that lead to outcome Y occurring. Setting the right rules refers to Mrs. X drafting a bill that includes mechanisms such that every actor in the game HAS AN INCENTIVE to play the strategy/strategies that lead to outcome Y.
How does this fit in with market design? Well, besides generally using mechanism design to align the incentives of both the buyers and sellers, there is a deeper point to be made about market design here. All so often in economic theory it is assumed that a market already exists, and the analysis is then on understanding the inner functions of that market. However, what that type of analysis leaves out is how that market even came into existence in the first place. In what ways were incentives aligned such that both buyers and sellers found a match for one and other to begin with? In other words, why is this market here and how did it get here? These are the nature of the questions that market design tries to answer. By understanding how and why the actors in the market are doing what they are doing, you begin to understand how markets form. And if you understand how markets form, you can apply that know-how to the formation of new markets, or to improve old ones.
The study of "non-economic" (ie, meta) activity that has (determinant) economic impact is most properly referred to as Political Economy. Although many trained "economists" avoid this. The illusory notion that veracity lies in 'scientific' objectivity (and so with it, government funding), has something to do with it.
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[1] ie, It is only defined directly by identification of a contractual exchange between N parties (agents), or 'archeologcally' through recipt, contract, or other record. But such an exchange directed by fiat, for example, would not qualify.
[2] For the definitional seperation of Hierarchy from Market, see for example Coase or Williamson.