There will be many posts summarizing the modern market design aspect of Roth and Shapley, today’s winners of the Econ Nobel. So here let me briefly discuss certain theoretical aspects of their work, and particularly my read of the history here as it relates to game theory more generally. I also want to point out that the importance of the matching literature goes way beyond the handful of applied problems (school choice, etc.) of which most people are familiar.
Pure noncooperative game theory is insufficient for many real-world problems, because we think that single-person deviations are not the only deviations worth examining. Consider marriage, as in Gale and Shapley’s famous 1962 paper. Let men and women be matched arbitrarily. Do we find such a set of marriages reasonable, meaning an “equilibrium” in some sense? Assuming that every agent prefers being married (to anyone) to being unmarried, then any set of…
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Utopia, you are standing in it! 
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