Timing Games: Probabilistic backrunning and spam

2026-02-25

AI Summary

This study investigates how multiple agents compete for stochastically arriving opportunities under information delays and action costs, with a focus on the resource waste caused by probabilistic backrunning in blockchain systems. The authors formulate the first continuous-time sequential game model with n players that formally captures backrunning as a strategic interaction involving delayed observation and costly actions, and they rigorously characterize its unique symmetric Nash equilibrium. Theoretical analysis reveals that “spam”—the submission of low-value or redundant actions—emerges endogenously as an equilibrium strategy. Furthermore, the work quantifies the worst-case loss in social efficiency, demonstrating that under high competition intensity, the system generates excessive inefficient actions, leading to substantial welfare degradation.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Web Mining and Content Analysis: Content-based information diffusion
• Security and Privacy: Blockchains and distributed ledgers

Abstract

There are $n$ players who compete by timing their actions. An opportunity appears randomly on a time interval. Whoever takes an action the fastest after the opportunity has arisen wins. The occurrence of the opportunity is observed only with a delay. Taking actions is costly. We characterize the unique symmetric equilibrium of this game and study worst-case inefficiency of equilibria. Our main motivation is the study of ``probabilistic backrunning" on blockchains, where arbitrageurs want to place an order immediately after a trade that impacts the price on an exchange or after an oracle update. In this context, the number of actions taken can be interpreted as a measure of costly ``spam" generated to compete for the opportunity.

Problem

• timing games
• probabilistic backrunning
• blockchain
• spam
• opportunity competition

Innovation

• timing games
• probabilistic backrunning
• blockchain arbitrage
• symmetric equilibrium
• transaction spam