Cryptocurrencies have caught the attention of industry, academia, and the public at large. This column analyses an economic model of a cryptocurrency system featuring user-generated transaction fees, focusing on Bitcoin as the leading example. The Bitcoin system requires significant congestion to raise revenue and fund infrastructure or risk collapse in the long term. Moreover, the current design of the system – specifically the processing of large but infrequent blocks of transactions – makes it less efficient at raising revenue.
By Gur Huberman, Jacob Leshno and Ciamac C. Moallemi*
A cryptocurrency is a digital currency stored on an open and decentralised electronic payment system. Following Nakamoto (2008), cryptocurrencies have caught the attention of industry, academia, and the public at large, with Bitcoin being the most prominent. There are hundreds of cryptocurrencies, many running on large and reliable decentralised computer networks. An innovative computer science design called the blockchain has enabled this wave. The blockchain supports the creation of a decentralised electronic payment system that can be trusted in aggregate, although none of the system’s servers is individually trusted. This novel blockchain design relies on a combination of cryptography and game-theory based incentives. These incentives should be of interest to economists, especially those focusing on market design.
The blockchain design enables Bitcoin and other cryptocurrencies to function similarly to conventional electronic payment systems such as PayPal, Venmo, FedWire, Swift, and Visa. Each of them is owned and operated by an organisation that determines the system’s rules and modifies them as circumstances change. The governing organisation ensures the system is trusted, and it is responsible for maintaining the required system infrastructure. It also decides how, and how much, participants pay for using the system. These electronic payment systems are natural monopolies in that they enjoy economies of scale and network effects. Consequently, they are often regulated (or outright owned by government agencies) in order to mitigate the welfare loss associated with their monopolistic positions.
The innovation in Bitcoin’s blockchain design is its ability to operate an electronic payment system without a governing organisation. Rather, a protocol sets the system’s rules, by which all constituents abide. Absent is a central entity that maintains the infrastructure. Bitcoin’s infrastructure instead consists of computer servers (called ‘miners’) which enter and exit the system at will, responding to perceived profit opportunities. Any internet-connected computer with enough memory and processing capacity can serve as a miner. Participating miners need to exert computational efforts, and are rewarded for their service to the system. Miners follow the rules of the protocol because it is in their self-interest to do so; when they believe others follow the protocol they will maximize their expected profits by following it as well. Thus, the protocol is difficult to change as changes require collective agreement on a new protocol.
A two-sided platform
Unlike other payment systems, Bitcoin is a two-sided platform with pre-specified rules. Its two main constituencies are the users who hold balances and engage in electronic transactions, and miners who maintain the system’s infrastructure.
A simplified description of the system is as follows. Coin owners broadcast messages in which they announce payments they wish to make. Each transaction is a cryptographically verified message. The miners vet newly received transactions for legality (they verify conformity with syntax rules, ownership, absence of double spending, etc.) and organise them into blocks of newly received transactions. Each miner maintains the ledger of all past transactions (the blockchain) where transactions are arranged in blocks. Every ten minutes, on average, the Bitcoin system randomly selects one miner to add a block of transactions to the ledger, processing all the transactions within that block. To participate in the selection process, a miner must exert computational effort, which is referred to as ‘proof of work’. The probability of being selected is proportional to a miner’s computational effort. When the selected miner adds a block to the ledger, he is said to have mined the block. Equilibrium between many small miners ensures that all miners are in consensus, and only legal transactions are processed. The Bitcoin protocol limits the block size to 1MB, and thereby the number of transactions within a block. Therefore, the system’s throughput is bounded, and does not depend on the number of miners.
To provide proper incentives, the system compensates miners for their effort by rewarding miners when they are selected to mine a block. The reward consists of newly minted coins and the transaction fees paid by the transactions processed in the block. The protocol specifies how many newly minted coins are awarded in each block. This number is cut in half approximately every four years. In contrast, transaction fees are not fixed by the protocol; users choose the transaction fees they pay.
Thus, the blockchain design carries an economic innovation in that no participant has the power to set or modify fees or rules of conduct or otherwise control the system. Users and miners are price-takers. Users are provided protection from monopoly pricing: even if the system becomes a monopoly, there is no monopolist who charges monopolist fees. However, for the system to function properly it must raise sufficient revenue from the users to fund the required infrastructure.
In a recent paper, we translate the above description to an economic model that allows the analysis of the long run behaviour of the system, when miners are compensated solely from transaction fees (Huberman et al. 2017). The analysis aims to answer two sets of seemingly disparate questions:
- In the long run, who will pay the miners—and why will they pay them?
- If the system becomes popular, how will it manage its limited throughput? That is, how will service priority be assigned?
The absence of a Bitcoin-controlling organisation renders both questions non-trivial. The model asserts a single answer to both questions: the system’s congestion due to its limited throughput leads users to pay transaction fees to gain processing priority. These very fees fund the miners. This answer raises follow-up questions regarding social efficiency, stability, robustness and parameter choice.
Features of the model
The equilibrium behaviour of users and miners creates the distinctive features of the transaction fees, revenue, and infrastructure level.
Miners prefer to process transactions with higher fees, but cannot affect the transaction fees chosen by users. Therefore, in equilibrium a miner selected to process a block will choose to process the transactions with the highest fees. The total revenue from fees paid by users is equal to the total payment to miners. Because miners can freely enter or exit the system, each miner’s expected profit is zero, and the amount of revenue determines the number of miners. Thus, even if the system as a whole is a monopolist, it provides its service at cost.
Users compete for service priority by paying transaction fees, as if processing priority was auctioned by the miners. Because of the stochastic nature of the system, even if the system has sufficient capacity on average, some transactions will suffer from delays. Higher fees secure higher priority and therefore less delay. Analysis of the implied congestion-queueing game shows that, in equilibrium, transaction fees are equal to the additional delay costs imposed on others. Thus, absent congestion and delays, users need not pay transaction fees, and transaction fees increase with the level of congestion. Moreover, this trade-off is quite sharp: in the absence of significant congestion, transaction fee revenue will be miniscule. The independence of the system’s capacity of the number of miners implies that the number of miners does not affect congestion.
Although the model focuses on the long run, its insights apply also to today’s minting-heavy environment. Namely: (i) miners’ expected profit is zero; (ii) the higher the congestion, the higher the transaction fees; (iii) the higher the transaction fees, the harder is the proof of work performed by the miners. Pertaining to (ii), Figure 1 depicts the theoretical and actual relation between average daily block size and the corresponding average transaction fee; congestion is associated with block size being close to 1MB. Moreover, it is empirically clear that significant congestion is associated with meaningful revenue generation.
Figure 1 Average fee per block and block size, model-based and actual, 1 April 2011 to 30 June 2017
The Bitcoin system offers an alternative to regulating a monopoly or controlling prices via market competition. Bitcoin can be a monopoly in the sense that all potential users are using the Bitcoin system. But even then, its service will not be priced at the monopoly price. Instead, pricing is determined in equilibrium. However, the equilibrium price varies with congestion and is unlikely to be optimal. Significant congestion and costly delays are necessary for raising revenue. In addition, there are additional social costs of running the Bitcoin system. The total social cost of the Bitcoin system can be lower or higher than the dead-weight loss of monopoly.
Absence of sufficient congestion can be disastrous for the system. Without sufficient congestion, users pay almost no transaction fees, generating almost no revenue to fund miners. As miners exit, the system becomes less reliable, leading users to leave the system, thereby reducing congestion further. Because the system’s throughput does not depend on the number of miners, the miners’ entry and exit choices do not help balance the system. Without an alternative way to maintain the miners, the system will collapse.
This point is critical in the context of current debates to scale or increase the capacity of the Bitcoin system in order to ameliorate congestion experienced by users. If the capacity of the system is successfully scaled in a way that eliminates or even significantly reduces congestion, it will also eliminate transaction-fee revenue and imperil the long-term sustainability of the system.
The analysis suggests two simple design modifications to the protocol. First, the system can target an appropriate level of revenue by controlling its capacity. Currently the capacity is fixed (one 1MB block every 10 minutes), and therefore revenue and the cost to users vary with the level of demand. Instead, the system can adjust its capacity according to demand to achieve a consistent level of congestion and revenue.
Second, our analysis shows that raising a target revenue level requires imposing less delay costs on users if blocks are smaller. The parameter choices in both the present design of the Bitcoin system as well as proposed future variants call for the processing of relatively large blocks (many transactions) relatively infrequently (minutes between blocks). Under such parameter configurations, significant delays are necessary for the generation of target levels of fee revenue. Thus, it would be beneficial to redesign the system with the smallest block sizes possible (given engineering constraints), and maintain throughput through frequent small blocks. This would allow the same level of revenue to be generated with much less delay imposed on users.
Finally, we pose the question of characterizing set of feasible revenue-generating mechanisms for distributed blockchain systems and identifying the optimal one. Revenue- generating rules must provide proper incentives for miners to process transactions, and transaction fees must be verifiable by third parties. We discuss some possible mechanisms that can be implemented by the protocol.
At the time of this writing, 657,000 BTC are newly minted and awarded to miners annually. (12.5 BTC per ten minutes.) They are worth almost $3.3 billion at the current (12 October 2017) approximate Bitcoin price of $5,000. In addition, miners earn transaction fees which have been increasing with network congestion, and currently add up to 20% of the miners’ revenue.
The Bitcoin system deploys substantial resources. It, and the blockchain protocol at its core, have inspired multiple imitations and applications. The blockchain protocol presents a novel economic design that would merit an economist’s attention and scrutiny even if it had not been functional. Its apparent functionality and usefulness should further encourage economists to study this marvellous structure and its future and futuristic descendants.
*About the authors:
Gur Huberman, Robert G. Kirby Professor of Behavioral Finance, Columbia Business School; CEPR Research Fellow
Jacob Leshno, Assistant Professor, Graduate School of Business, Columbia University
Ciamac C. Moallemi, Associate Professor of Business, Graduate School of Business, Columbia University
Huberman, G, J D Leshno and C C Moallemi (2017), “Monopoly Without a Monopolist: An Economic Analysis of the Bitcoin Payment System”, CEPR Discussion Paper No. 12322.
Nakamoto, S (2008), “Bitcoin: A Peer-to-Peer Electronic Cash System”.