# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"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 astrategy based on its own position and the position its executives believe theother to be in. Without knowledge of the actual position and strategy of theother company, it may seem impossible for leaders of one company to always makethe best decision. Game theory is the branch of mathematics which models suchsituations. This article in *Nature* describes a new theorem by Reny,which describes circumstances under which it is possible for all players tomake the best possible decision---acting in their own best interest andcorrectly anticipating the actions of everyone else. The theorem doesn'testablish a way to determine this best possible decision, but it does guaranteethat a best decision exists in some situations.

*--- Elizabeth Moisan*