Alex Tabarrok does his best on how to explain their work to your grandma. Here's the bottom line:
The basic set-up of agents with private information submitting "bids" which are then fed into a mechanism resulting in outcomes is very general. How to raise taxes, regulate a monopolist, fund a public good (here's my own contribution to mechanism design), allocate organs, assign interns to hospitals, split common costs, allocate electricity across a grid - all can be thought of as mechanism design problems. The tools that Hurwicz, Maskin and Myerson developed and their methods of paying attention to participation and incentive compatability constraints and using the revelation principle helps us to design, at least in principle, the best solutions to all of these problems.
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