Rethinking Scaling Laws for Learning in Strategic Environments

The deployment of ever-larger machine learning models reflects a growing consensus that the more expressive the model$\unicode{x2013}$and the more data one has access to$\unicode{x2013}$the more one can improve performance. As models get deployed in a variety of real world scenarios, they inevitably face strategic environments. In this work, we consider the natural question of how the interplay of models and strategic interactions affects scaling laws. We find that strategic interactions can break the conventional view of scaling laws$\unicode{x2013}$meaning that performance does not necessarily monotonically improve as models get larger and/ or more expressive (even with infinite data). We show the implications of this phenomenon in several contexts including strategic regression, strategic classification, and multi-agent reinforcement learning through examples of strategic environments in which$\unicode{x2013}$by simply restricting the expressivity of one's model or policy class$\unicode{x2013}$one can achieve strictly better equilibrium outcomes. Motivated by these examples, we then propose a new paradigm for model-selection in games wherein an agent seeks to choose amongst different model classes to use as their action set in a game.