Kakutani Fixed-Point Theorem

Michiko's dad, Shizuo passed away last week. He was 92 years old. It just so happens that Dr. Kakutani was a brilliant mathematician. One tool he developed, known as the Kakutani fixed-point theorem, was a key component of the original proof of the existence of Nash equilibria. Kakutani's theorem is also used to prove a famous theorem developed by Arrow and Debreau, which says there are prices for goods that balance supply and demand in a complex economy.