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Parallel Execution Fee Mechanisms

Abdoulaye Ndiaye

TL;DR

This paper investigates how pricing schemes can achieve efficient allocations in blockchain systems featuring multiple transaction queues under a global capacity constraint, and finds that revenue maximization tends to allocate capacity to the highest-paying queue, whereas welfare maximization generally serves all queues.

Abstract

This paper investigates how pricing schemes can achieve efficient allocations in blockchain systems featuring multiple transaction queues under a global capacity constraint. I model a capacity-constrained blockchain where users submit transactions to different queues -- each representing a submarket with unique demand characteristics -- and decide to participate based on posted prices and expected delays. I find that revenue maximization tends to allocate capacity to the highest-paying queue, whereas welfare maximization generally serves all queues. Optimal relative pricing of different queues depends on factors such as market size, demand elasticity, and the balance between local and global congestion. My results have implications for the implementation of local congestion pricing for evolving blockchain architectures, including parallel transaction execution, directed acyclic graph (DAG)-based systems, and multiple concurrent proposers.

Parallel Execution Fee Mechanisms

TL;DR

This paper investigates how pricing schemes can achieve efficient allocations in blockchain systems featuring multiple transaction queues under a global capacity constraint, and finds that revenue maximization tends to allocate capacity to the highest-paying queue, whereas welfare maximization generally serves all queues.

Abstract

This paper investigates how pricing schemes can achieve efficient allocations in blockchain systems featuring multiple transaction queues under a global capacity constraint. I model a capacity-constrained blockchain where users submit transactions to different queues -- each representing a submarket with unique demand characteristics -- and decide to participate based on posted prices and expected delays. I find that revenue maximization tends to allocate capacity to the highest-paying queue, whereas welfare maximization generally serves all queues. Optimal relative pricing of different queues depends on factors such as market size, demand elasticity, and the balance between local and global congestion. My results have implications for the implementation of local congestion pricing for evolving blockchain architectures, including parallel transaction execution, directed acyclic graph (DAG)-based systems, and multiple concurrent proposers.

Paper Structure

This paper contains 20 sections, 5 theorems, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. The Problem of Execution in Standard TFMs: An Example
  4. The Problem with Global Ordering and a Uniform Price
  5. A Potential Solution: Market Value-Weighted Ordering
  6. Model
  7. Setup.
  8. User Valuations.
  9. Delay Costs.
  10. Local Equilibrium Demand.
  11. Global Inclusion Constraint.
  12. Results
  13. Revenue Maximization
  14. Revenue.
  15. Welfare Maximization
  16. ...and 5 more sections

Key Result

proposition 1

There exists a threshold capacity $\underline{\kappa} \in (0,+\infty)$ such that for all total capacities $\kappa\leq\underline{\kappa}$, the revenue-maximizing uniform price and the revenue-maximizing relative prices allocate all capacity to the highest price queue, i.e., $\mathcal{S}=\{1\}$.

Figures (4)

  • Figure 1: Example Transaction Queues
  • Figure 2: Global Ordering under Uniform Price. Newly arrived and executed transactions are highlighted in red and starred.
  • Figure 3: Market Value-Weighted Ordering. Each transaction is treated as if its bid is $a_i/\mathbb{E}[v_{a}]$ or $b_i/\mathbb{E}[v_{b}]$
  • Figure 4: Execution under Market Value-Weighted Ordering. Executed transactions from queue B' are highlighted in blue and starred.

Theorems & Definitions (9)

  • proposition 1
  • proof
  • proposition 2
  • proof
  • proposition 3
  • corollary 1
  • proof
  • corollary 2
  • proof