2023/12/18 by Fabian R. Pieroth, Pieroth, Fabian R., Nils Kohring +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Experimental Behavioral Economics Studies #FOS: Computer and information sciences #Sports Analytics and Performance
paper · pdf · doi:10.48550/arxiv.2312.11751
openalex publication_date 2023/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute equilibrium strategies in multi-stage games with continuous signal and action spaces as they are widely used in the management sciences and economics. Examples include sequential sales via auctions, multi-stage elimination contests, and Stackelberg competitions. In sequential auctions, analysts performing equilibrium analysis are required to derive not just single bids but bid functions for all possible signals or values that a bidder might have in multiple stages. Due to the continuity of the signal and action spaces, these bid functions come from an infinite dimensional space. While such models are fundamental to game theory and its applications, equilibrium strategies are rarely known. The resulting system of non-linear differential equations is considered intractable for all but elementary models. This has been limiting progress in game theory and is a barrier to its adoption in the field. We show that Deep Reinforcement Learning and self-play can learn equilibrium bidding strategies for various multi-stage games. We find equilibrium in models that have not yet been explored analytically and new asymmetric equilibrium bid functions for established models of sequential auctions. The verification of equilibrium is challenging in such games due to the continuous signal and action spaces. We introduce a verification algorithm and prove that the error of this verifier decreases when considering Lipschitz continuous strategies with increasing levels of discretization and sample sizes.