From Imitation Games to Kakutani
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Economic Theory Workshop (2005-2010)
University of Pennsylvania
3718 Locust Walk
395 McNeil
395 McNeil
Philadelphia, PA
United States
Joint with: Andrew McLennan
We give a full proof of the Kakutani (1941) fixed point theorem that is brief, elementary, and based on game theoretic concepts. This proof points to a new family of algorithms for computing approximate fixed points that have advantages over simplicial subdivision methods. An imitation game is a finite two person normal form game in which the strategy spaces for the two agents are the same and the goal of the second player is to choose the same strategy as the first player. These appear in our proof, but are also interesting from other points of view.
For more information, contact Jan Eeckhout.