We study a class of distributionally robust games where agents are allowed to heterogeneously choose their risk aversion with respect to distributional shifts of the uncertainty. In our formulation, heterogeneous Wasserstein ball constraints on each distribution are enforced through a penalty function leveraging a Lagrangian formulation. We then formulate the distributionally robust Nash equilibrium problem and show that under certain assumptions it is equivalent to a finite-dimensional variational inequality problem with a strongly monotone mapping. We then design an approximate Nash equilibrium seeking algorithm and prove convergence of the average regret to a quantity that diminishes with the number of iterations, thus learning the desired equilibrium up to an a priori specified accuracy. Numerical simulations corroborate our theoretical findings.

翻译：本文研究一类分布鲁棒博弈问题，其中智能体可异构地选择其对不确定性分布偏移的风险规避程度。通过拉格朗日方法引入惩罚函数，我们在模型中为每个分布施加异构的Wasserstein球约束。随后构建分布鲁棒纳什均衡问题，并证明在特定假设下该问题等价于具有强单调映射的有限维变分不等式问题。我们设计了一种近似纳什均衡求解算法，证明平均遗憾值随迭代次数增加而收敛至可忽略量级，从而以先验指定的精度学习目标均衡。数值仿真结果验证了理论结论。