Does PoS make the rich richer? A detailed comparison of the economies of scale profitability under PoW and PoS mechanisms

Written by: Just a Doggie, SecurEth Edited and translated by: Perry Wang

A common criticism of the Proof of Stake (PoS) formula is that it “makes the rich richer”, which can be simply translated as: “the rich benefit more from economies of scale, and the poor do the opposite”.

We can easily see this happening by looking at any industry operating at scale: over time, companies that can operate more efficiently and at greater scale are able to leverage their influence and size to approach monopoly over their industry. We can even see this at the nation-state level: larger, more resource-rich countries attract greater political influence, strike larger trade deals, and directly push international affairs toward their own interests at the expense of poorer countries.

In the context of cryptocurrency consensus algorithms, it’s easy to see how this would play out. Participants with more assets are able to invest more capital into their operations, increasing their overall share of the blockchain’s security system and generating more returns for themselves. In turn, they are able to reinvest these gains into larger operations, earning more return potential indefinitely.

But these are continuous zero-sum games, because the rewards on offer are fixed, but in a publicly accessible and unrestricted cryptocurrency security mechanism, the number of participants is potentially infinite, and the timeline is never-ending. If one competitor can effectively exploit the economies of scale in their operations, they can gain market share at the expense of other competitors, and over time they can leverage this scale differential to build an insurmountable lead. It’s easy to see how the rich can get richer in these systems, and why this is a dangerous thing to do.

But enough of this discussion about PoS, I want to talk about the differences between the two economies of scale of Proof of Work (PoW) and PoS systems.

PoS Economic Security

The idea behind PoS is that individuals pledge their assets, usually in the native cryptocurrency used for security mechanisms, and have that collateral held in escrow by the cryptocurrency protocol itself. In return, they gain the responsibility of producing new blocks and participating in the consensus on the final ordering of those blocks in the cryptocurrency's history. They are rewarded for these activities, in the form of block rewards (usually in the native token) for producing blocks, incentivizing their participation.

In a permissionless consensus system, participation in consensus is essential in order to finalize these rewards, otherwise other participants can just as easily "steal" these benefits for themselves. The goal of consensus on history is to "finalize" these rewards (as well as transaction fees and other benefits such as miner extractable value/MEV) and ensure that they cannot be taken away by others.

The concept of "Finality" is particularly noteworthy in the design of PoS algorithms like Ethereum. It is particularly noteworthy that it is entirely possible to reach "finality" on a part of history, or that participants cannot change it without violating the rules of the protocol (and suffering the consequences). This is a unique feature of the PoS mechanism, because PoW does not have this property, at least not explicitly stipulated. This property is valuable, especially for global transaction settlement networks, because this can determine a clear timeline in which transactions can be considered "finalized" - they cannot be changed without violating the consensus rules.

We should note that there are feasibility limits to this property. For example, if an attacker is able to take away the vast majority of collateral in the protocol (> 66.6%) and is willing to burn it for some extra-protocol goal (such as causing disruption or reversing high-value transactions). Since there are tens of billions of dollars of value invested in Ethereum's PoS protocol, the cost of such behavior is very high, so the value of a single transaction is far from worthwhile for an attacker to invest such a large amount of resources to violate the rule set, but this possibility still exists.

There are still similarities between PoS and other consensus systems such as PoW. Fundamentally, their structure is usually the same: participants are required to invest the resources required to participate in block proposals and consensus, and are rewarded for doing so. However, different consensus protocols and even specific implementations of specific cryptocurrencies vary in every detail: the relative share of rewards obtained for performing these duties, the available amount of extra-protocol benefits that participants can obtain, the opportunity cost of investing resources, and other external factors for participating in such work.

Barriers to entry and economies of scale

I want to delve deeper into the details of these implementations in this post, and how specific choices drive emergent behavior in this protocol. These subtle differences can lead to very different results, and it is important that we conduct academic analysis so that we can identify potential problems in their structure and build better systems.

For example, the Bitcoin blockchain currently offers a reward of 6.25 BTC per block every 10 minutes (about 900 BTC per day), while the transaction fees collected from users sending transactions average about 6% of this amount. The blockchain has an annualized revenue of about $20 billion.

To get a piece of the Bitcoin blockchain revenue, you need to buy specialized ASIC miners from a handful of hardware manufacturers that offer Bitcoin mining machines with the efficiency levels needed to profit from Bitcoin mining without losing money. The true cost of such machines is difficult to estimate for large buyers, as sales data for these companies is hard to come by and they tend to offer more favorable deals to large buyers. However, the biggest cost of Bitcoin mining by far is not the money needed to buy these machines, but the electricity required to run these machines 24/7 in large mining pool configurations.

While anyone can theoretically mine Bitcoin, we can begin to see that due to the structure and parameters of the network, there are extremely high barriers to entry, such as purchasing ASICs and the space to store and run them, reasonable electricity costs, and the cost and capital expenditure of purchasing these assets at scale to compete with other companies that have similar economies of scale. Not everyone has access to these opportunities, and a considerable degree of capital is required, and that’s before we even take into account the political costs of running a large operation and the differences in electricity costs between different regions.

On the other hand, there are limits to these kinds of economies of scale. For example, you are unlikely to be able to buy up “all” the available electricity in a particular region to run mining rigs, which would attract the attention of the government, which wants to ensure that other citizens have fair access to electricity. You also cannot find an infinitely large building to house the mining rigs, or build a cooling system powerful enough to keep the mining rigs cool.

The ultimate limiting factor is that these manufacturers can only produce so many rigs per year, and you can’t buy them all (at least not without driving the price above the break-even point for mining profits). For every potential advantage that a competitor can optimize, there is a limit to their optimization potential.

However, given these inherent limitations, the scale of the Bitcoin mining business continues to grow every year, and over time, as more mining machines are created, miners have access to more negotiated electricity, mining machine efficiency increases, and participants reduce their operating costs through innovation, the scale ceiling of Bitcoin mining economics continues to rise.

Comparing the PoW and PoS mechanisms, it can be seen that there are big differences in these parameters, as well as restrictions and barriers to entry. For example, the PoS design of Ethereum 2.0 stipulates that the block reward (currently about 400,000 ETH per year) decreases as the number of participating validators increases. Currently on the Ethereum mainnet (currently still the PoW consensus mechanism), the transaction fees paid by users to miners are about 4,000 ETH per day. After the merger (Merge) of the current PoW network upgrade to PoS occurs, the transaction fees should theoretically be the same or greater. Lastly, more than $5 billion of detectable MEV has been extracted from the Ethereum network in the past year, and this number is growing every day as we find more sophisticated measurement methods. The total annualized revenue of Ethereum validators is about $6.4 billion.

Ethereum 2.0 Reward Curve

To become a validator in Ethereum 2.0, you must own 32 ETH (about $100,000 at current prices) to get a validator slot, after which you have a one in ten chance of being randomly selected to participate in the protocol. However, due to the structural design of the protocol, validators are actually equivalent to joining a mining pool locally, and the variability of block rewards received by validators is greatly reduced because everyone's income is roughly the same. This does not affect the transaction fees or potential MEV that validators receive when they are selected to publish a block. These are still rewarded specifically to the block proposer, which means that it is very important for validators to stay online and responsive so as not to miss the opportunity to earn these fees. In fact, transaction fee income and MEV account for an increasing proportion of Ethereum protocol revenue, so it is crucial to ensure that they are always online.

The specific costs associated with downtime in PoS are higher, and are not limited to the potential loss of reward opportunities. For example, there is a leakage rate, where your staked assets are partially deducted due to unresponsiveness. If enough validator pools are unresponsive, the penalties will increase exponentially to avoid consensus deadlocks that lead to uptime losses. This drives the diversification of validator geography and software setups to ensure the highest possible uptime. Block production becomes easier because the cost of hosting mining hardware in different locations is almost the same. Finally, more complex validator setups with software and hardware redundancy (capable of handling more validator slots) increase engineering costs, resulting in lower overall profitability.

Calculating entry threshold

In a permissionless cryptocurrency security system, anyone can theoretically meet the necessary entry and profitability thresholds to ensure that you can participate in the protocol's continuous zero-sum game. However, in practice there are real limitations, both implicit and explicit, that prevent individuals with fewer resources from participating.

It’s easy to calculate the barrier to entry in a PoS mechanism. For a future PoS Ethereum, this barrier is access to 32 ETH (~$100k at current prices), (minimum) hardware specs (~$1-2k to buy, ~$200/month to rent), and a reliable internet connection (~$100/month).

For an 18-month pledge period, these costs equate to approximately $105,000, most of which is funding costs.

Plugging in our numbers above, that's about $45,000 in revenue over that 18 month period (assuming no significant slashing, or leak penalties for inactivity, and ignoring the human resource costs of running this setup), for an annualized total return of about 28% in ETH (in USD, there's obviously more variation). Once we factor in these costs, the annualized profit above is likely to be much lower, and the Ethereum merger happening will make participation less risky. A more reasonable estimate would be closer to 5% annualized, assuming these future conditions.

For PoW, calculating this number is much more difficult. First, there is no in-protocol limit on the number of validator slots available, and capital costs vary widely (ASICs, electricity, real estate, rig maintenance, etc.). The ecosystem is also much more opaque, preventing similar profitability comparisons from being drawn, but we will do our best to draw conclusions from hash rate charts and the public costs of ASICs. ASICs have a profitability window of about 18 months before they start to fail or are replaced by newer models, so we hope to justify choosing the above profitability window for our PoS calculations. PoW mining is also a much more mature and larger industry, and annualized returns (in BTC) are likely much less than what we calculate here.

First, let’s do some more direct comparisons. The maximum amount of ETH determines the upper limit of the total number of slots that can be staked. If the total supply of ETH is limited to 120 million (there is no upper limit in theory, but in practice it will be this much), about 3.75 million validator slots can be filled (each slot requires 32 ETH). Bitcoin’s hashrate is currently 1.15 EH/s, and the Antminer S9 miner has a hashrate of about 13 TH/s and costs about $500. To have 1/3.75 million of the Bitcoin network hashrate, you would need to have 2,375 Antminer S9 miners, with a hardware cost of about $1.19 million. The more efficient Antminer S17 Pro miner costs about $2,000 and has a hashrate of about 53 TH/s, so you would only need to have about 583 Antminer S17 Pro miners, with a miner cost of about $1.17 million, to have the same percentage of the network share as one Ethereum 2.0 validator slot.

However, if we make a more detailed comparison, the market capitalization of the Ethereum network is only about 42% of the Bitcoin network, so the equivalent expenditure of the Bitcoin network to have the same network share as an Ethereum 2.0 validator slot is only US$495,000 (10.75 BTC), or 248 Ant S17 Pro miners.

An Antminer S17 Pro lasts about 4 years (with electricity costs remaining constant at $0.11/kWh), so mining Bitcoin with that miner costs about $15,600 (0.35 BTC) in electricity, so we can extrapolate that using an Antminer S17 Pro to mine 248 BTC over 4 years costs $3.87 million (84 BTC). Normalizing this to the 18 month period used above, that equates to 93 BTC mined at $1.45 million (31.5 BTC) in electricity costs, for an annualized return of 47% (in BTC)! This number has been much higher recently due to China’s crackdown on cryptocurrency mining, and other structural changes to Bitcoin’s hash rate, but we can assume that at least half of this number is guaranteed to be achieved in practice.

To make a more like-for-like comparison, assuming we only have the ability to spend $105,000 on mining equipment and electricity costs for 18 months, what would the benefits be in practice? We could buy about 6 Antminer S17 Pro miners ($12,000, or the equivalent of about 0.26 BTC) and mine about 2.25 BTC in 18 months using $39,600 in electricity (equivalent to 0.86 BTC), for an annualized return of about 33% (in BTC terms).

This is very similar to the rewards we calculated for Ethereum validator slots! But we can start to see how economies of scale come into play here, with a well-resourced actor (the miner mentioned earlier who can afford 248 Antminer S17 Pros) receiving a 42% higher reward than a less resourced actor (the miner who can afford 6 Antminer S17 Pros). As you can see, PoW economies of scale are where the rich get richer!

Summarize

We can see that if we do a specific one-to-one comparison in terms of operating and capital expenditures, there really isn’t a huge difference in profitability between mining and staking mechanisms.

Putting aside the discussion of “decentralization” for the moment, we can see that the argument that PoS can make the “rich richer” is fundamentally flawed.

The argument above is that any capital-intensive investment will allow participants who can invest more capital to obtain better returns than those who can invest less capital. Hopefully, the arguments in this article will convince you that this argument is just intellectual laziness and does not withstand the simplest scrutiny.

Additionally, I hope you learned more about comparing the economic security of cryptocurrencies through profitability, and how economies of scale affect the barriers to entry for permissionless security systems.

Source link: medium.com