Games of Artificial Intelligence: A Continuous-Time Approach

This paper studies the strategic interaction of algorithms in economic games. We analyze games where learning algorithms play against each other while searching for the best strategy. We first establish a fluid approximation technique that enables us to characterize the learning outcomes in continuous time. This tool allows to identify the equilibria of games played by Artificial Intelligence algorithms and perform comparative statics analysis. Thus, our results bridge a gap between traditional learning theory and applied models, allowing quantitative analysis of traditionally experimental systems. We describe the outcomes of a social dilemma, and we provide analytical guidance for the design of pricing algorithms in a Bertrand game. We uncover a new phenomenon, the coordination bias, which explains how algorithms may fail to learn dominant strategies.