We will discuss some famous fixed point theorems, such as Banach fixed point theorem (aka contraction mapping principle), Brouwer fixed point theorem, Schauder fixed point theorem, and Kakutani fixed point theorem. These theorems show up in unlikely areas in social sciences, such as in game theory, social choice theory, and economics. One example would be the proof of existence of Nash equilibrium in game theory, or existence of general equilibrium in market economies, using Kakutani fixed point theorem. 

Our discussion will be based on the notions of convexity, completeness, compactness, and continuity in metric and topological spaces, which was covered in an earlier workshop. These concepts will be briefly reviewed for the sake of completeness.