Robust Identification in Repeated Games: An Empirical Approach to Algorithmic Competition

We develop an econometric framework for recovering structural primitives---such as marginal costs---from price or quantity data generated by firms whose decisions are governed by reinforcement-learning algorithms. Guided by recent theory and simulations showing that such algorithms can learn to approximate repeated-game equilibria, we impose only the minimal optimality conditions implied by equilibrium, while remaining agnostic about the algorithms’ hidden design choices and the resulting conduct---competitive, collusive, or anywhere in between. These weak restrictions yield set identification of the primitives; we characterise the resulting sets and construct estimators with valid confidence regions. Monte~Carlo simulations confirm that our bounds contain the true parameters across a wide range of algorithm specifications, and that the sets tighten substantially when exogenous demand variation across markets is exploited. The framework thus offers a practical tool for empirical analysis and regulatory assessment of algorithmic behaviour.