Cardano Foundation Research: Serial Monopoly on Blockchain with Quasi-patient Users
A research paper exploring a transaction fee mechanism and its impact on blockchain validator incentives
As part of the Foundation’s mission to advance Cardano as a public digital infrastructure across diverse sectors, we conduct academic research to provide new insights and approaches to examining the blockchain’s utility. Our latest research paper, co-authored with Paolo Penna (IOG Research), was accepted for publication and presentation at the 29th International Financial Cryptography and Data Security 2025 conference, which will take place in April 2025.
With an acceptance rate of just 15%, this achievement underscores the strength of collaborative efforts between the Cardano Foundation and IOG Research. The paper, titled “Serial Monopoly on Blockchain with Quasi-patient Users,” analyzes a specific transaction fee mechanism that we briefly summarize in this article.
Transaction fee mechanisms
Transaction fee mechanisms (TFMs) constitute an integral part of a blockchain system. An effective TFM incentivizes miners (validators) to act honestly and uphold the blockchain's security. Different blockchains employ different transaction fee mechanisms tailored to their unique structures and goals. For example, Ethereum employs its EIP-1559, Bitcoin a first price auction, and Cardano a fixed fee per byte. A deeper understanding of these TFMs will help determine which works best for a particular blockchain.
For instance, miners who operate in a blockchain network with a limited block size (e.g. Bitcoin) prioritize transactions with the highest bids as those transaction fees increasingly constitute a larger portion of their revenue. However, if block size increases sufficiently (e.g. through a protocol upgrade), all transactions could be accommodated, potentially driving bids down to zero or a fixed minimum. Without an adequate incentive to mine, the blockchain’s network security could be significantly impacted as usage and necessary transaction activity decrease in response to a diminished financial incentive.
Some approaches have already been studied to address this challenge, including Lavi et. al (2022) who introduced what is known as a “monopolistic pricing mechanism.” In this mechanism, miners may not fill the entire block but only include transactions (“transaction inclusion”) that pay a minimum price set by the miner (“minimum admission price”). Instead of paying their own bids, all included transactions pay a fee equal to the smallest bid among the included transactions. Lavi et. al (2022) consider a myopic setting where users only care about immediate transaction inclusion. Expanding upon this mechanism, Nisan (2023) proposed a model whereby users are classified as “patient”. Unlike scenarios where delayed transactions can incur opportunity costs, this model assumes users wait without cost until inclusion prices drop, potentially waiting indefinitely. Notably, Nisan (2023) finds wildly fluctuating inclusion prices even when demand is stable.
Bridging the gap with quasi-patient users
Our research paper aims to bridge the gap between impatient (Lavi et. al (2022)) and patient users (Nisan (2023)) via “quasi-patient” users, whose interest in transaction inclusion diminishes over time due to costs. As such, impatient and patient users are extreme cases in our model.
Our work advances the understanding of how (strategic) users can optimize transaction fee decisions by considering the patience levels of others, striking a balance between cost efficiency and timely inclusion. Specifically, we provide upper and lower bounds on the minimum transaction fee (admission price) users must pay to guarantee that their transaction is eventually included. We further analyze price fluctuations under a monopolistic pricing mechanism with quasi-patient users and provide general bounds on the dynamics of minimum admission prices.
By contributing to the understanding of TFMs, this paper supports ongoing research aimed at developing more effective mechanisms. Special attention to TFMs will be required for Cardano in the future, as transaction fees alone must provide sufficient incentives for block producers.
The Cardano Foundation encourages everyone to read the paper in full and for free.