The Kakutani Fixed Point Theorem is a fundamental result in mathematical analysis and game theory. It states that in a compact, convex set in a Euclidean space, any upper hemicontinuous function that maps this set into itself has at least one fixed point. A fixed point is a point that remains unchanged when the function is applied. This theorem generalizes the Brouwer Fixed Point Theorem by allowing for multi-valued functions, which can assign multiple outputs to a single input. It is particularly useful in economics and optimization, where it helps to find equilibrium points in various models.