Brouwer fixed-point theorem
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Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. Brouwer. It states that for any continuous function f mapping a nonempty compact convex set to itself, there is
For flows in an unbounded area, or in an area with a "hole", the theorem is not applicable.
John Nash used the theorem in game theory to prove the existence of an equilibrium strategy profile.
Game theory
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Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and comput
Brouwer fixed-point theorem
…deep results about differential equations and is covered in most introductory courses on differential geometry. It appears in unlikely fields such as game theory. In economics, Brouwer's fixed-point theorem and its extension, the Kakutani fixed-point theorem, play a central role in the proof of existence of…
John Nash
Example of a Bayesian game