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"Agreeing on Strategies," by Ivar Ekeland. Nature, 12 August 1999, pages 623-624.
In a situation where two companies are racing for a patent, each uses a strategy based on its own position and the position its executives believe the other to be in. Without knowledge of the actual position and strategy of the other company, it may seem impossible for leaders of one company to always make the best decision. Game theory is the branch of mathematics which models such situations. This article in Nature describes a new theorem by Reny, which describes circumstances under which it is possible for all players to make the best possible decision---acting in their own best interest and correctly anticipating the actions of everyone else. The theorem doesn't establish a way to determine this best possible decision, but it does guarantee that a best decision exists in some situations.
--- Elizabeth Moisan
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