Bidding for Speed: Modeling the High-Frequency Trading Arms Race as an All-Pay Auction

Abstract

This thesis models the high-frequency trading arms race as a strategic competition through the lens of all-pay auctions, where traders incur costs to gain execution priority in a continuous-time financial market. Building on the conceptual foundation of Budish, Cramton, and Shim (2015), but departing from their model's general framework, we consider a setting in which firms compete to access prized arbitrage opportunities by investing in capital to execute trades before others. Using tools from auction theory and game theory, we characterize equilibrium behavior in both symmetric and asymmetric cases, proving conditions under which pure or mixed strategy equilibria exist. The analysis reveals the scale of the social surplus lost in the current financial market, and how small asymmetries can lead to disproportionate advantages for some firms. These results provide a theoretical basis for understanding the inefficiencies inherent in continuous-time markets and inform discussions of market design.