Timing Games: Probabilistic backrunning and spam

TL;DR

This paper models a timing game where players compete to act quickly on randomly appearing opportunities, analyzing equilibrium behavior and inefficiencies, with applications to blockchain arbitrage and spam strategies.

Contribution

It characterizes the unique symmetric equilibrium in a timing game with delayed observation and applies it to probabilistic backrunning and spam in blockchain markets.

Findings

Identifies the structure of equilibrium strategies in timing games.

Quantifies worst-case inefficiency of equilibria.

Provides insights into blockchain arbitrage and spam dynamics.

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.