In this talk, I will introduce a recently constructed extension operator, called the "Shapley extension". This operator gives a Lipschitz extension for a function defined on a discrete subset of metric space to the whole space. The extension is based on the Shapley theorem, which comes from the Nash equilibrium in the game theory. We will give an application of the Shapley extension in 1-Wasserstein robust optimization problem. This is a joint work with Gao and Zhang.