Modern pretrained language models are critical components of NLP pipelines. Yet, they suffer from spurious correlations, poor out-of-domain generalization, and biases. Inspired by recent progress in causal machine learning, in particular the invariant risk minimization (IRM) paradigm, we propose invariant language modeling, a framework for learning invariant representations that generalize better across multiple environments. In particular, we adapt a game-theoretic implementation of IRM (IRM-games) to language models, where the invariance emerges from a specific training schedule in which all the environments compete to optimize their own environment-specific loss by updating subsets of the model in a round-robin fashion. We focused on controlled experiments to precisely demonstrate the ability of our method to (i) remove structured noise, (ii) ignore specific spurious correlations without affecting global performance, and (iii) achieve better out-of-domain generalization. These benefits come with a negligible computational overhead compared to standard training, do not require changing the local loss, and can be applied to any language model. We believe this framework is promising to help mitigate spurious correlations and biases in language models.