Optimal fee strategies for miners

[albin]

In academic micro, I think the most applicable model for the assumptions stated is that this is an example of third-degree price discrimination. A good reference is Varian, Intermediate Microeconomics, chapter 25.

The profit-maximizing condition is where the marginal cost of producing an extra unit of output is equal to the marginal revenue in each market. Because the marginal cost is exactly the same in each market, the good should produce the same increase in revenue regardless of which market it is sold in.

I haven't done any serious work in this particular area, but here are some dodgy photos of the textbook sections that I think are relevant:

 

[venij]

I think mining cartels put stress on the bitcoin ecosystem in other ways that simple fee control. For that reason, it's not worth much effort for consideration in this theorycraft.

Given this, and assuming zero marginal cost for transaction inclusion as Gavin mentioned in post #10 (surprised he didn't wait for one more reply), miners would all become "selfish" and maximize block size.

In that case, the supply curve is flat. The demand curve is still variable based on competition with other payment / wealth storage systems. Fees may vary slightly over short periods of time, but they would otherwise increase til near competitive systems as users move into / out of the bitcoin network.

 

[JVWVU]

The video in the third link I believe Craig S. Wright discusses this. (Yes I am in the small group that thinks we alienated a very bright mind in bitcoin with whatever happened for Aussie police to show up)

 

[Joseph Woolfridge]

Having a tiered service is probably only possible with miner cooperation. This is not a hostile thing at all because all it means is that miners would be including transactions that normally wouldn't meet minimum fee requirements because they have passed some priority threshold. Example: transactions starts at a counter of 0. When a block is found and it's not included, count increases to 1 and so on until it reaches a maximum such as 10. You can account for poisson distribution by simply not increasing count if the block is found too soon after an earlier block. A tiered service *might* maximize profit because some people will move to another means of monetary transfer once the cost passes their own personal threshold.

 

[Tron]

I'm hoping for less armchair speculation and more "I studied a similar problem for my PhD thesis in micro, here's a spreadsheet that calculates optimal strategy given blah blah blah...."

I studied a similar problem for my Master's thesis on the economics of software pricing. Sorry, no spreadsheet forthcoming. The problem has too many variables including the motivation of miners.

The reason the problem is similar is that the marginal cost of one additional unit sold is near zero. From a purely rational point of view, and according to the economics books, one should sell additional copies for anything over 0 as it will add to your profit - assuming 0 variable cost for selling/distribution. But setting the price at 0.0001 (for example) will not maximize your profit. Segmenting the market will, but there are reasons that will not work here -- see below. Absent segmenting the market, there is a profit maximization curve. Selling many at 0.0001 will not maximize profit. Selling 0 at 1000 will not maximize profit. In the middle is the price even if you have an infinite number of units to sell.

In short, if the miners collude, they could find that price. If the miners don't collude, then rational self-interest will set the fee, and it is likely to trend towards the marginal cost of adding the transaction.

The marginal cost of adding a transaction is near 0. From a rational point of view, each miner (pool), acting independently should add all transactions with a fee, and ignore all others. However, no-fee transactions are added because the motivations of most miners are pro-Bitcoin and adding those transactions benefits the network.

Brian raises the important point. "One miner or many competing miners?" With competing miners it is not possible to reliably segment the demand into slow, medium, fast without restricting block size. Those advocating for keeping the status quo likely understand this. Once block size limit is raised, any independent miner can add all the mempool transactions with fees to maximize the reward.

I personally think increasing the block-size is necessary. Rewards should come from more transactions at fee X rather than fewer transactions at fee 5X. I think the block size should adjust to upward pressure automatically. The only question is how far and how fast?

I've talked with Jeff Garzik about BIP 100, and I think it's a balanced approach that gives the miners a voice, and prevents extreme movements. There are other proposals I like, including XT. We have an immutable history of transactions, shouldn't we use it to make adjustments to the block size?

 

[hodl_man_sux]

The behavior of miners is determined by a behavior of the users they serve. Claim: if fees are high, a group of frequent users who know ahead they will use btc heavily may as well get into mining. Because this way even mining with loss, they get back their own fees (over a long period).

Next a patriotic miners. For example Chinese may give priority to Chinese users, Chinese merchants, and fill the rest sorted by fee/KB. Finding block means there is now less Chinese tx in pool etc. So users can get ahead in the queue not just by raising fees but mining their own txs or being "friends" with miners/pool ops.

Actually merchants may need good relations with miners anyway. The reason is not only to get confirmed faster, but catching or preventing doublespends.

 

[Peter R]

"What would be the profit-maximizing dynamic block size limit?" -- @Gavin Andresen

I'm going to answer a slightly different question: what would be the profit-maximizing block size limit holding each miner's hash rate constant.

Answer: it's the block size that maximizes the producer surplus, as depicted in (b) below:

Of course, this hurts the consumer and reduces total economic activity. This is monopoly market conditions.

This analysis is simplistic because I didn't consider the fact that there is more than a single demand curve for block space. There's a demand curve for "next block service," a demand curve for "next hour confirmation," a demand curve for "next day," and so on and so forth (as Gavin already noted).

I will consider this question in a follow-up post....

 

[Gavin Andresen]

I'm interested in the answer to this question because it would be a very good default policy for miners who don't want to change defaults.

It is possible lots of miners would override the default for short-term gain, but I think it is also possible miners would find ways to punish defectors. In any case I think it is an interesting puzzle.

 

[Peter R]

Yes, it is a fascinating question. If we assume miners are short-term profit-maximizing agents, then the market is perfectly competitive and all miners will viciously undercut each other even though by cooperating they could increase their revenues (holding the demand curve fixed). In such a case, we get the equilibrium block size depicted in part (a) of my earlier diagram.

But we already have empirical evidence that miners make decisions based on longer-term thinking as well (for example, no miner that I am aware of runs replace-by-fees even though it is the profit maximizing strategy from a short-term perspective). So I do suspect that miners will also cooperate to some extent to raise prices somehow (i.e., the market will not be perfectly competitive). @Pecuniology could add something here I believe.

 

[Erdogan]

I think you can not assume marginal cost of zero. In that case, competition will drive price to zero (until block size meet the limit of physics ).

I think, when only fees are relevant, a miner could try a strategy of including all A-fee transactions, then some B- and C-fee transactions, specially after they have already waited for a while.

In practice, the transaction demand will vary, the strategies will vary, and even high-paying transactions will not always confirm in the first block. The block sizes will vary, and slowly converge to some commonly accepted size, with occasional breakouts downwards and upwards just like any other market.

I have no problems with a cartel of miners trying to agree on a certain fee-maximizing strategy, because the only long time strategy they could possibly agree on and defend, will be a strategy close to maximum value creation for transactors (users) and miners together. Anything far from that will open up for competition (internally and externally) and destroy the cartel.

 

[cliff]

@Peter R - Very interesting stuff. Seems like under the "short-term profit-maximizing agents" assumption, the probability for cooperation between miners is inversely related to bitcoin's marketshare as a currency, store of value, useful cargo ship for sending value, etc. So, while bitcoin is still small potatoes, there is an incentive to cooperate to attract new users. But, as user base grows and the tech integrated in society (and users dependent thereon), the incentive to cooperate is probably less.

 

[solex]

So, while bitcoin is still small potatoes, there is an incentive to cooperate to attract new users. But, as user base grows and the tech integrated in society (and users dependent thereon), the incentive to cooperate is probably less.

@cliff that is a great insight.
At the present time the miners know that it is Bitcoin against the fiat world and will look at the long-term implications of their actions vis-a-vis the BTC price. However, we suspect that once the upper slope of the S-curve of adoption is reached it will be dog-eat-dog to the death.

 

[Peter R]

@Erdogan

We're just considering different lenses through which to view the problem, so that we can make incremental progress in our understanding.

If we assume that perfect competition exists AND that the marginal cost of block space is zero, then indeed fees go to zero and the Blockchain fills with spam. I believe Dr. Nicolas Houy was the first to study the problem through that lens in his 2014 paper "The economics of Bitcoin transaction fees." Although the model was obviously simplistic, this paper revealed the interesting insight that a block size limit is economically-equivalant to a fixed-fee requirement.

If we account for orphaning but still assume perfect competition, then the marginal cost of block space is nonzero and a transaction fee market exists without a block size limit. I believe I was the first to formally analyze this problem in my paper from August 2015.

(If we assume monopoly conditions, then see my chart a few posts up.)

I believe Gavin is suggesting that we assume that marginal cost is zero (if doing so makes it easier to solve the problem) but that market competition is imperfect and ask what we can learn.

 

[jonny1000]

Answer: it's the block size that maximizes the producer surplus, as depicted in (b) below:

Peter, I thought the above charts assume that orphan risk is a marginal cost. I think Gavin says he wants a response to his question with the very reasonable assumption that orphan risk and marginal cost is zero. Please could you respond assuming this.

It is possible lots of miners would override the default for short-term gain, but I think it is also possible miners would find ways to punish defectors.

Gavin, this is a well studied area of economics and is called a cartel. In order for a cartel to work and not break down, it is often said the following conditions are helpful:

1. One dominant producer

2. High barriers of entry and exit

3. No anonymous producers

4. A small number of producers

5 Commoditized product

In order for the threat of punishing defectors to work the industry needs certain characteristics. I would argue these characteristics are unhealthy to have in Bitcoin mining.

At the same time we have seen many cartels break down in recent decades, in areas from oil to diamonds. With improved regulation and better information sustaining cartels is becoming more difficult. I do not think Bitcoin should move in this direction, as otherwise there is always the risk that the cartel breaks down.

By the way I don't think its a good idea to model cartel pricing into mining code by default, one can never get these kinds of things right. This is why BIP100 is so clever, it provides an open framework for cartel like pricing to dynamically form in the market, without an actual cartel.

 

[theZerg]

@Peter R and I are saying the same thing. His supply curve is my cost curve (micro assumes producers will sell products at or above cost).

This curve is mostly flat with a wall at 1 mb or at the BU median excessive block. With core this wall is nearly vertical, it is only not because high fees would convince more miners to turn on. With BU the wall's slope is the likelihood of the miner's whose EAS is larger than the point to mine EAD blocks before the rest of the miners mine a longer chain. So still pretty steep.

It would be interesting to plot the real fee curve in the mem pool and blocks animated by time.

I think the 1mb group's argument is that as fees rise things like on block betting will consolidate. For example instead of betting $5 twice ppl will bet $10 once. I don't think it works that way.

Also note paxful blog which claimed they are doing 5% of the txns. This is pretty inflexible demand and very rapid growth.

 

[Erdogan]

Peter, I thought the above charts assume that orphan risk is a marginal cost. I think Gavin says he wants a response to his question with the very reasonable assumption that orphan risk and marginal cost is zero. Please could you respond assuming this.



Gavin, this is a well studied area of economics and is called a cartel. In order for a cartel to work and not break down, it is often said the following conditions are helpful:

1. One dominant producer

2. High barriers of entry and exit

3. No anonymous producers

4. A small number of producers

5 Commoditized product

In order for the threat of punishing defectors to work the industry needs certain characteristics. I would argue these characteristics are unhealthy to have in Bitcoin mining.

At the same time we have seen many cartels break down in recent decades, in areas from oil to diamonds. With improved regulation and better information sustaining cartels is becoming more difficult. I do not think Bitcoin should move in this direction, as otherwise there is always the risk that the cartel breaks down.

By the way I don't think its a good idea to model cartel pricing into mining code by default, one can never get these kinds of things right. This is why BIP100 is so clever, it provides an open framework for cartel like pricing to dynamically form in the market, without an actual cartel.

A cartel needs the coersive power of the state (often created through regulative capture) to exert value destructing pressure. If that is not present, the prices and volume can not deviate too much from the wants of the customers. It will probably not be seen as a cartel, rather a business sector standards organization.

 

[Peter R]

Peter, I thought the above charts assume that orphan risk is a marginal cost. I think Gavin says he wants a response to his question with the very reasonable assumption that orphan risk and marginal cost is zero. Please could you respond assuming this.

Zero-marginal cost is a degenerate form of the nonzero case. It's the same answer either way: the optimal strategy for the Cartel is to select the block size that maximizes the producer surplus (the area of the orange region). If the supply curve is zero, then the orange region becomes a rectangle extending to the horizontal axis. The block size, Qmax, that maximizes this area will be greater than what it was for the nonzero-cost case.

 

[jonny1000]

Peter

I appreciate this helpful diagram. I understand we will never have perfect competition, but we could have a mining industry similar to this.

My basic thought is that industry dynamics change over time, and for some periods we could be near the top left. I.e. perfect competition and zero marginal costs. It is at this point removing an economically relevant blocksize limit may not work. Please let me know your thoughts on the top left position. It seems we agree fees fall to near zero?

Please note the top left is also the most desirable position. High competition and low orphan risk costs are positive. Maybe I am naturally an optimist, but I think the top left is likely.

I agree we need a market driven dynamic blocksize limit, but it needs to work in the top left. This is why I support BIP100, as it works in all the scenarios.

 

[Peter R]

@jonny1000

Yes, I agree that in the case of zero marginal costs and perfect competition that fees fall to zero.

I think we disagree on two points:

1. You seem to think that (total orphaning risk) ~= (total fees), whereas I only agree that (marginal orphaning risk) ~= (marginal fees). I believe total orphaning risk can be significantly less than total fees and I think I've convincingly demonstrated this in sections 3 - 5 of my subchains paper.

2. You seem to worry that the marginal cost of block space in a free market might be too low (leading to higher costs to operator a node), whereas I worry that it might be too high (leading to fewer people using Bitcoin).

I disagree that we will be operating in the top-left sector of the table. I suspect that we are presently operating--and will continue to operator--in the mid-right sector (non-negligible marginal cost of block space + imperfect competition).

 

[Erdogan]

I think it is rather unnecessary to figure out the edge cases of no cost and no usefulness. It is obvious that neither of those can happen. If there is no potential to earn with mining, why bother, why take the risk? If there is no usefulness to a transaction, why plunder with bitcoin anyway? What is interesting, is where will the price land. In the OP, the poster already stipulated that the market will be divided into several quality groups of transactions, which will have different prices. Good, that is reasonable to expect.

It is easy to see the supply and demand in action with a market that has become traditional. Is is more difficult to envision a market that is in change. For example, is there a problem with the salt market? No, it is rather stable. A few hundred years ago, it was not, and it was politicized. Now, salt is so cheap that you can not find shops selling small portions. After you have aquired a hamburger and walked away, you can not find a salting service down the sidewalk. It is too cheap (the transaction cost is too large compared to the goods). You can buy salt by the kilogram, or may be packages with special types of salt by the hundreds of grams. In eating places, you can add salt for no extra cost, the seller just makes sufficient masses of salt available, incorporating the cost in the other offers. If that would not be the case, each customer could bring his own salt. The salt market functions satisfactorily. Salting your hamburger is a micro-market, extremely low cost, and extremely low marginal usefulness. And in the background, salt is moved over the oceans in bulk.

We don't necessarily need to know where the price will land. All we know is that, as long as there is demand, and as long as anybody is free to enter the market, there will be a price.

You could even incorporate the potential of too low difficulty in the market. If the difficulty at the price equilibrium is considered too low, someone will supply something that makes it more secure, maybe a low price chain will fork off and disappear.