Citation

Mazorra, B., Schlegel, C., Mamageishvili, A. “Timing Games: Probabilistic backrunning and spam.” Flashbots / Offchain Labs. arXiv:2602.22032v1 [cs.GT] (Feb 25, 2026).

Core Problem

On FCFS (First-Come-First-Served) blockchains and during inter-block windows, opportunities arrive at unpredictable times. Searchers cannot wait until the opportunity is certain (risk being too late), so they send transactions randomly during the window, hoping to land immediately after the opportunity.

When many searchers do this, the result is not just a speed race but spam — redundant transaction submissions that consume blockspace.

Model Setup

  • n players competing to place a transaction immediately after a target that arrives at a random time
  • Opportunity arrival: random in time interval [0, 1]
  • Observed with a delay (revealed only after the interval ends)
  • Taking an action has cost c per transaction
  • The player positioned immediately after the opportunity (and before competitors) wins

Equilibrium Results

High cost case (c ≥ 1/e):

  • Players submit at most one transaction in equilibrium
  • Mixed strategy: submit at random time T drawn from an equilibrium distribution
  • The distribution ensures strategic unpredictability and capture probability balance

Low cost case (c < 1/e):

  • Players submit multiple transactions (spam) in equilibrium
  • Even though this is individually optimal, it’s socially inefficient

Key equilibrium property:

  • First player wants to submit as late as possible (more information → higher probability opportunity has arrived)
  • But must be early enough that competitor doesn’t preempt them
  • Randomization is essential: pure deterministic timing is always dominated

Spam as Equilibrium Outcome

The main result: spam emerges naturally from probabilistic backrunning equilibrium when costs are low.

On FCFS chains with low transaction fees (most L2s):

  • c is small → multi-transaction equilibrium
  • Searchers submit many transactions “just in case”
  • This is individually rational but collectively wasteful

Quantification: worst-case social inefficiency from spam grows with competition (number of players n). In the limit, almost all blockspace is consumed by spam with only a small fraction resulting in actual trades — consistent with empirical evidence from Base/Optimism (>50% block gas consumed by spam, only 6–12% trades).

Connection to Ethereum L1 Timing Games

This paper formalizes the different structure of timing games on FCFS chains vs. Ethereum L1:

  • Ethereum L1 timing games: proposer delays block reveal to capture more CEX information → AdaptiveSwitch, PoT as solutions
  • FCFS/L2 timing games: searchers randomly submit transactions during windows → spam MEV as equilibrium

Both involve timing, but the strategic structure is different. The Mazorra et al. paper addresses the FCFS case.

Implications for Protocol Design

  • Priority fee ordering (not pure FCFS) reduces spam: spammers must pay more → raises effective cost c → shifts toward single-transaction equilibrium
  • Minimum gas prices achieve similar effect
  • Private mempools reduce the window during which probabilistic backrunning is useful (no public opportunity signal) → but may worsen other forms of spam
  • 2602.11147 (2-Prop): addresses L1 timing games via double-block-proposal mechanism
  • 2604.00234 (Spam MEV): empirical framework for spam on high-throughput chains