One-dimensional vs. Multi-dimensional Pricing in Blockchain Protocols

TL;DR

This paper compares one-dimensional and multi-dimensional resource pricing in blockchains, showing multi-dimensional pricing is better at equilibrium but less efficient during transient states, highlighting a key trade-off.

Contribution

It provides a theoretical analysis of the welfare and convergence properties of both pricing schemes and proposes mechanisms to address transient challenges.

Findings

Multi-dimensional pricing outperforms in stable conditions.

One-dimensional pricing converges faster during system transitions.

Trade-offs exist between efficiency at equilibrium and during transient states.

Abstract

Blockchain transactions consume diverse resources, foremost among them storage, but also computation, communication, and others. Efficiently charging for these resources is crucial for effective system resource allocation and long-term economic viability. The prevailing approach, one-dimensional pricing, sets a single price for a linear combination of resources. However, this often leads to under-utilization when resource capacities are limited. Multi-dimensional pricing, which independently prices each resource, offers an alternative but presents challenges in price discovery. This work focuses on the welfare achieved by these two schemes. We prove that multi-dimensional pricing is superior under stable blockchain conditions. Conversely, we show that one-dimensional pricing outperforms its multi-dimensional counterpart in transient states, exhibiting faster convergence and greater computational tractability. These results highlight a critical trade-off: while multi-dimensional pricing offers efficiency gains at equilibrium, its implementation incurs costs associated with system transitions. Our findings underscore the necessity for a deeper understanding of these transient effects before widespread adoption. Finally, we propose mechanisms that aim to mitigate some of these issues, paving the way for future research.