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On the Welfare of EIP-1559 with Patient Bidders

Moshe Babaioff, Noam Nisan

TL;DR

It is shown that with "patient" bidders, this algorithm produces schedules of near-optimal welfare, provided it is given a mild resource augmentation (that does not increase with the time horizon).

Abstract

The ``EIP-1599 algorithm'' is used by the Ethereum blockchain to assemble transactions into blocks. While prior work has studied it under the assumption that bidders are ``impatient'', we analyze it under the assumption that bidders are ``patient'', which better corresponds to the fact that unscheduled transactions remain in the mempool and can be scheduled at a later time. We show that with ``patient'' bidders, this algorithm produces schedules of near-optimal welfare, provided it is given a mild resource augmentation (that does not increase with the time horizon). We prove some generalizations of the basic theorem, establish lower bounds that rule out several candidate improvements and extensions, and propose several questions for future work.

On the Welfare of EIP-1559 with Patient Bidders

TL;DR

It is shown that with "patient" bidders, this algorithm produces schedules of near-optimal welfare, provided it is given a mild resource augmentation (that does not increase with the time horizon).

Abstract

The ``EIP-1599 algorithm'' is used by the Ethereum blockchain to assemble transactions into blocks. While prior work has studied it under the assumption that bidders are ``impatient'', we analyze it under the assumption that bidders are ``patient'', which better corresponds to the fact that unscheduled transactions remain in the mempool and can be scheduled at a later time. We show that with ``patient'' bidders, this algorithm produces schedules of near-optimal welfare, provided it is given a mild resource augmentation (that does not increase with the time horizon). We prove some generalizations of the basic theorem, establish lower bounds that rule out several candidate improvements and extensions, and propose several questions for future work.

Paper Structure

This paper contains 27 sections, 20 theorems, 28 equations.

Table of Contents

  1. Introduction
  2. Background on Blockchains
  3. The EIP-1559 algorithm and its parameters
  4. Our Main result
  5. Lower Bounds
  6. Maximum Block size
  7. Dependence on Range of per-unit Values
  8. Model Extensions
  9. Partially Patient Bidders
  10. Multi-dimensional Fees
  11. Strategic Points of View
  12. Model and Notations
  13. Blocks, Schedules, and Social Welfare
  14. Online Scheduling Algorithms
  15. EIP-1559 has High Welfare for Patient Bidders
  16. ...and 12 more sections

Key Result

Proposition 1.2

Any schedule produced by an EIP-1559 algorithm with parameters $(B, c, \eta, p_{min}, p_1)$ has average block size limit $B$ with slackness $\Delta = \frac{1}{\eta}\cdot \ln \frac{H}{L}+ {(c-1)}$, where $H$ and $L$ are upper and lower bounds on the per-unit value of any input transaction, and on the

Theorems & Definitions (46)

  • Definition 1.1
  • Proposition 1.2
  • Theorem 1
  • Proposition 1.3
  • Proposition 1.4
  • Proposition 1.5
  • Proposition 1.6
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • ...and 36 more