Here is the AEA account, opening bit:
Yuliy Sannikov is a theorist who has developed new methods for analyzing continuous time dynamic games using stochastic calculus methods. His work has not only broken new ground in methodology, it has had a substantial influence on applied theory. He has significantly altered the toolbox available for studying dynamic games, and as a result of his contributions, new areas of economic inquiry have become tractable for rigorous theoretical analysis. The areas of application include the design of securities, contract theory, macroeconomics with financial frictions, market microstructure, and collusion.
Here is excellent coverage from A Fine Theorem, here is part of the opening bit:
The JBC has, in recent years, been tilted quite heavily toward applied empirical microeconomics, but the prize for Sannikov breaks that streak in striking fashion. Sannikov, it can be fairly said, is a mathematical genius and a high theorist of the first order. He is one of a very small number of people to win three gold medals at the International Math Olympiad – perhaps only Gabriel Carroll, another excellent young theorist, has an equally impressive mathematical background in his youth.
Sannikov is at Princeton…congratulations to him and them!