A Data-Driven Distributionally Robust Game Using Wasserstein Distance

This paper studies a special class of games, which enables the players to leverage the information from a dataset to play the game. However, in an adversarial scenario, the dataset may not be trustworthy. We propose a distributionally robust formulation to introduce robustness against the worst-case scenario and tackle the curse of the optimizer. By applying Wasserstein distance as the distribution metric, we show that the game considered in this work is a generalization of the robust game and datadriven empirical game. We also show that as the number of data points in the dataset goes to infinity, the game considered in this work boils down to a Nash game. Moreover, we present the proof of the existence of distributionally robust equilibria and a tractable mathematical programming approach to solve for such equilibria.

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