Bitcoin, Ethereum and Pigou: the economics of transaction fees

The economics of transaction fees in cryptocurrencies are poorly understood. In a previous post I raised some questions about how using tx fees to compensate for hashing costs (as Bitcoin’s declining coinbase award increasingly does over time) can be incentive-compatible with transaction demand for cryptocurrency. There, I was concerned about the distribution of seigniorage between existing coin holders and hashing costs, and what this implies for tx fees.

A new post on the Ethereum blog focuses on another aspect of transaction fee economics: a tragedy of the transaction verification commons.

The essence of the problem is this. In Bitcoin, tx fees are effectively set by what tx miners choose to include in their blocks. The creator of a tx can pay any fee he chooses, but miners are free to ignore a tx, so a payer who pays a relatively large fee is more likely to have a faster-than-average confirmation time. On the surface, this looks like a market mechanism. But it isn’t. The miner gets the tx fees of every tx included in a block that the miner solves. But every node on the network pays the costs of verifying a transaction; tx must be verified before relaying and building on top of a solved block. Therefore, a miner will include any tx with a fee in excess of his computational costs of verifying it (and reassembling the Merkel tree of his block), not the network’s computational costs of verifying it.

A single, very large block containing many transactions with many inputs/outputs can bog down the network. To deal with this, the Bitcoin protocol imposes a 1MB upper limit on the size of a block. This isn’t a great solution. Not only does it put an upper limit on the number of tx Bitcoin can process per unit of time, it does nothing to rationalise tx fees to tx verification costs.

It’s like an airline that puts a 1000 suitcase (irrespective of size/weight) limit on luggage per flight, and deals with the problem of >1000 suitcases by prioritising those passengers that volunteered to pay a fee. Those who pay the lowest/no fees have their bags kicked off the flight, and placed in a que to for inclusion in subsequent flights (that employ the same 1000 suitecase limit). What will eventually happen is that those with big, heavy bags will pay the highest fees and have their bags included in the flight, as those fees will still be lower than the actual cost of shipping the luggage. Those with small/light bags will get kicked off, unless the passenger is willing to pay more than the marginal cost of shipping his bag. If airlines are a competitive market, those guys will eventually just chose to travel on a different airline that doesn’t ask them to subsidise pack rats.

From Ethereum’s post:

The question is, is this kind of market the right model for Bitcoin transactions? To answer this question, let us try to put all of the players into roles. The resource is the service of transaction processing, and the people benefiting from the resource, the transaction senders, are also the buyers paying transaction fees. So far, so good. The sellers are obvious the miners. But who is incurring
the costs? Here, things get tricky. For each individual transaction that a miner includes, the costs are borne not just by that miner, but by every single node in the entire network. The cost per transaction is tiny; a miner can process a transaction and include it in a block for less than $0.00001 worth of electricity and data storage. The reason why transaction fees need to be high is because that $0.00001 is being paid by thousands of nodes all around the world.

It gets worse. Suppose that the net cost to the network of processing a transaction is close to $0.05. In theory, even if the costs are not borne by exactly the same people who set the prices, as long as the transaction fee is close to $0.05 the system would still be in balance. But what is the equilibrium transaction fee going to be? Right now, fees are around $0.09 simply because miners are too lazy to switch. But then, in the future, what happens once fees become a larger share of a miner’s revenue and miners have a large incentive to
try to maximise their take? The obvious answer is, for a solo miner the equilibrium transaction fee is $0.00001. If a transaction with a fee of $0.00002 comes in, and the miner adds it, the miner will have earned a profit of $0.00001, and the remaining $0.04999 worth of costs will be paid by the rest of the network together – a cryptographic tragedy of the commons.

The Ethereum guys have defined the problem clearly. And I’m not encouraged by what (I think?) is the current thinking of the Bitcoin developers in dealing with this problem. From the Bitcoin Foundation’s blog:

I’ve been working on teaching the wallet code to estimate how low a fee (or priority) a transaction needs, at the moment it is sent, to be accepted by miners and included in the next block or three. The estimates are based on watching transactions as they are broadcast on the network and keeping track of which of those transactions are accepted into blocks.

The danger with estimating transaction fees is miners have an incentive to try to game the estimate to make transaction fees higher. For example, if the estimate was based on the average transaction fee for all transactions in the last N blocks, miners could add very-high-fee pay-to-self transactions to the blocks that
they mine to drive up the average. However, by only considering fees for transactions that have been broadcast on the network that threat is eliminated– miners could broadcast very-high-fee pay-to-self transactions, but would end up paying those high transaction fees to other miners. The transaction estimation code also uses median transaction fees, not averages, to make it much harder for a minority of transactions to influence transaction fees.

But this won’t work in the end, for even a perfect estimate that is not contaminated by strategic actions by miners will still be an estimate of the marginal cost of tx verification faced by a single miner, not the network as a whole.

It’s not surprising that the Ethereum developers have cut to the core of this problem. In Bitcoin, you can at least be sure that the execution of scriptSig and scriptPubKey will halt after time proportional to tx size. Not so with Ethereum’s Turing-complete scripting language. For Ethereum, the problem of rationing network resources over tx verification and contract computation is acute. The project simply will not work without an economically equilibrating solution to this problem.

Their current thinking is that tx fees should be destroyed (no recipient) and calculated along the lines of a Pigovian tax via a some mechanism of miner or ether holder consensus. I’m not convinced that this will work, but this post gives me confidence that the guys behind Ethereum are taking the economics of crypto seriously. Let’s all pitch in and help them solve this problem.

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2 thoughts on “Bitcoin, Ethereum and Pigou: the economics of transaction fees

  1. In the departure from the original “everyone generates blocks” model to “miners rule Bitcoin” the fee’s purpose has been lost.
    In a peer to peer network, nobody pays because everybody has provided part of the infrastructure and would be incurring the costs, if not all the benefits.
    Fees do provide a selection criteria and reward for miners, but mostly (along with others related to bitcoin days destroyed) fees are to dissuade spamming the network.
    The cost to the rest of the network that you describe is paid by the rest of the network as part of the price of participation. What of the SPV parasites then you might ask?
    Participation in Bitcoin includes the benefit of ego-gratifyingly altruistic support of SPV clients. In many cases full client node operators will have SPV client devices and directly benefit from full clients too.

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