Equilibrium Learning, Uncertainty, and Dynamics: Novel Approaches for Analyzing Games and Automated Markets

Game theory is essential for studying central problems in economics and management such as auctions, contests, oligopoly, and platform competition. However, deriving equilibrium strategies in such games with incomplete information is notoriously challenging. For instance, analytical solutions are available only for simple auction models under restrictive assumptions. The lack of numerical methods for solving equilibrium problems impedes advancements in theory and practice. Building on insights from my recent research, ELUD develops online optimization and learning methods to solve equilibrium problems in single- and multi-stage Bayesian games that have previously been deemed intractable. These new methods are designed to accommodate a variety of distributional assumptions and utility functions allowing to incorporate behavioral motives and asymmetries among agents. Importantly, learning algorithms also serve as models for artificial agents in real-world agentic markets, such as those for bidding in display advertising auctions and pricing on online retail platforms. Such agents cannot play equilibrium strategies from the start, but they adapt to the market and learn profitable strategies over time. However, learning algorithms do not necessarily converge to an equilibrium in games; they can instead lead to cycles or even chaotic behavior and such phenomena have been observed experimentally in some environments. ELUD allows us to understand the properties of market models under which classes of algorithms lead to an efficient equilibrium and when they do not. This is highly ambitious because ELUD needs to develop new mathematical methods to study the constrained dynamical systems resulting from the interaction of learning algorithms. An extensive set of experiments will complement and aid the theory development. After ELUD, there will be widely applicable equilibrium solvers for important classes of games, and a theoretical framework to analyze automated markets.