Abstract

$$ \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\E}{\mathbb{E}} \newcommand{\Csmooth}{\bar{C}} \newcommand{\Craw}{C} \newcommand{\tasktype}{\tau} \newcommand{\bps}{\mathrm{BPS}} $$

Streaming payment protocols enable continuous monetary flows between AI agents, yet none provide flow control: when a downstream agent reaches capacity, payments accumulate with no mechanism to reroute, buffer, or throttle—unlike data networks where packets can be dropped or queued. We introduce Backpressure Economics (BPE), a cryptoeconomic mechanism that adapts the Tassiulas–Ephremides backpressure routing algorithm from communication networks to monetary flows in multi-agent economies.

We make four contributions. (1) Formal model. We define a capacity-constrained monetary flow network where agents declare processing capacity through commit-reveal signals, and flow weights are set proportionally via EWMA-smoothed capacity. (2) Throughput optimality. We prove, via Lyapunov drift analysis, that BPE achieves throughput-optimal allocation: every stabilisable demand vector is served with bounded overflow buffers, matching the classical backpressure guarantee in the monetary domain. (3) Protocol design. We implement BPE as five Solidity smart contracts on Superfluid’s General Distribution Agreement (GDA), providing permissionless pool creation, concave-sqrt stake-weighted Sybil resistance, and multi-stage pipeline composition with upstream congestion propagation. (4) Evaluation. Simulations over 1,000-step horizons show BPE achieves 95.7% allocation efficiency versus 93.5% for round-robin under steady load, recovers from 20% node-kill shocks within 50 steps, and reduces buffer stall rates from 73% to under 9% with overflow escrow sized at one period of peak demand. A Sybil-cost analysis confirms that stake fragmentation yields strictly negative net profit for all split counts \(n > 1\). All contracts compile on Base Sepolia with 40 passing unit tests.