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Generalization in reinforcement learning (RL) is of importance for real deployment of RL algorithms. Various schemes are proposed to address the generalization issues, including transfer learning, multi-task learning and meta learning, as well as the robust and adversarial reinforcement learning. However, there is not a unified formulation of the various schemes, as well as the comprehensive comparisons of methods across different schemes. In this work, we propose a game-theoretic framework for the generalization in reinforcement learning, named GiRL, where an RL agent is trained against an adversary over a set of tasks, where the adversary can manipulate the distributions over tasks within a given threshold. With different configurations, GiRL can reduce the various schemes mentioned above. To solve GiRL, we adapt the widely-used method in game theory, policy space response oracle (PSRO) with the following three important modifications: i) we use model-agnostic meta learning (MAML) as the best-response oracle, ii) we propose a modified projected replicated dynamics, i.e., R-PRD, which ensures the computed meta-strategy of the adversary fall in the threshold, and iii) we also propose a protocol for the few-shot learning of the multiple strategies during testing. Extensive experiments on MuJoCo environments demonstrate that our proposed methods can outperform existing baselines, e.g., MAML.