  In this paper, we utilize results from convex analysis and monotone operator
theory to derive additional properties of the softmax function that have not
yet been covered in the existing literature. In particular, we show that the
softmax function is the monotone gradient map of the log-sum-exp function. By
exploiting this connection, we show that the inverse temperature parameter
determines the Lipschitz and co-coercivity properties of the softmax function.
We then demonstrate the usefulness of these properties through an application
in game-theoretic reinforcement learning.
