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Resonance: Transaction Fees for Heterogeneous Computation

Maryam Bahrani, Naveen Durvasula

TL;DR

Resonance is introduced: a new kind of transaction fee mechanism for the general two-sided market setting, where both sides of the market exhibit a high degree of heterogeneity, and shows that at pure Nash equilibria, Resonance finds an efficient outcome and minimizes the need for strategization by users and nodes.

Abstract

Blockchain networks are facing increasingly heterogeneous computational demands, and in response, protocol designers have started building specialized infrastructure to supply that demand. This paper introduces Resonance: a new kind of transaction fee mechanism for the general two-sided market setting (with users on one side and nodes on the other), where both sides of the market exhibit a high degree of heterogeneity. We allow users submitting transactions to have arbitrary valuations for inclusion, nodes responsible for executing transactions to incur arbitrary costs for running any bundle of transactions, and further allow for arbitrary additional constraints on what allocations are valid. These constraints can, for example, be used to prevent state conflicts by requiring transactions that utilize the same part of the network's state to not be executed in parallel. They also enable support for new transaction types, such as transactions that require multiple nodes for execution (e.g. to run multi-party computation for better transaction privacy). Resonance's design utilizes competition among sophisticated brokers to find individualized prices for each transaction and node. We show that at pure Nash equilibria, Resonance finds an efficient outcome and minimizes the need for strategization by users and nodes. It is also budget-balanced, individually rational for all parties, and computationally tractable.

Resonance: Transaction Fees for Heterogeneous Computation

TL;DR

Resonance is introduced: a new kind of transaction fee mechanism for the general two-sided market setting, where both sides of the market exhibit a high degree of heterogeneity, and shows that at pure Nash equilibria, Resonance finds an efficient outcome and minimizes the need for strategization by users and nodes.

Abstract

Blockchain networks are facing increasingly heterogeneous computational demands, and in response, protocol designers have started building specialized infrastructure to supply that demand. This paper introduces Resonance: a new kind of transaction fee mechanism for the general two-sided market setting (with users on one side and nodes on the other), where both sides of the market exhibit a high degree of heterogeneity. We allow users submitting transactions to have arbitrary valuations for inclusion, nodes responsible for executing transactions to incur arbitrary costs for running any bundle of transactions, and further allow for arbitrary additional constraints on what allocations are valid. These constraints can, for example, be used to prevent state conflicts by requiring transactions that utilize the same part of the network's state to not be executed in parallel. They also enable support for new transaction types, such as transactions that require multiple nodes for execution (e.g. to run multi-party computation for better transaction privacy). Resonance's design utilizes competition among sophisticated brokers to find individualized prices for each transaction and node. We show that at pure Nash equilibria, Resonance finds an efficient outcome and minimizes the need for strategization by users and nodes. It is also budget-balanced, individually rational for all parties, and computationally tractable.

Paper Structure

This paper contains 38 sections, 10 theorems, 45 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Summary of Results
  3. The Heterogeneous Setting
  4. Agents and Their Types.
  5. Allocations.
  6. Validity and Conflicts.
  7. Routings.
  8. Utilities.
  9. Efficient Routings.
  10. Desired Properties in a Mechanism
  11. The Resonance Mechanism: Description
  12. Information Structure.
  13. Action Spaces.
  14. The Mechanism.
  15. Payments and Utilities.
  16. ...and 23 more sections

Key Result

Lemma 5.1

Fix an action profile $(\boldsymbol{\theta}',\boldsymbol{\sigma})$, and let $R^*=(\alpha,\pi,\phi)$ be the routing output by the mechanism and $b^*$ the winning broker. We have

Figures (1)

  • Figure 1: Nonexistence of Collusion-Resistant Routings. Consider the above example where there are two transactions and two nodes. The first transaction (shown on the top left) requires both nodes to execute, and the second transaction (shown on the bottom left) only requires one node, and can be executed with either node. Nodes however only have capacity to execute one of the two transactions. There are therefore three valid (non-empty) allocations: one in which the first transaction is allocated to both nodes, and two more corresponding to the second transaction being allocated to either the first or second node. The surplus maximizing allocation maps the first transaction to both nodes, yielding a surplus of $6-1-1 = 4$. However, if the first transaction pays one of the nodes less than $4 = v_2$, then that node and the second transaction would prefer to collude, since the second transaction is willing to pay up to $4$. Because $4 + 4 > 6 = v_1$, the first transaction cannot pay both nodes at least four, whence no routing is collusion resistant.

Theorems & Definitions (29)

  • Lemma 5.1
  • proof
  • Lemma 5.2: Individual rationality for transactions and nodes
  • proof
  • Lemma 5.3: Individual rationality for brokers
  • proof
  • Definition 5.1: PNE
  • Theorem 5.1: Efficiency with one broker
  • proof
  • Claim 5.1
  • ...and 19 more