In a new paper, Timing Games: Probabilistic backrunning and spam, co-authored with Bruno Mazorra and Christoph Schlegel, we look into equilibrium strategies of capturing backrunning opportunities when transaction ordering policy is First-Come First-Serve (FCFS) with state update happening at fixed block times or Priority Gas Auction (PGA). A distinctive feature of these settings is that the state is not observed until the (block) time is up. Hence, the players can not learn and react to opportunity capture by themselves or counterparties.
We show that in a unique symmetric equilibrium, all expected value drains to chain (gas) fees creating mostly spam transactions and the expected utility of all players is zero, independent of the number of players. The unique symmetric equilibrium can be computed constructively: only the first transaction in time is randomized, the rest of transaction times are deterministic after the first transaction is sampled. The analysis can be easily generalized to multiple independent opportunities.
Any feedback is welcome.