Ethereum POS economics question about gravitating all ether supply to stake

Question

Please, dispel my doubts about POS, miners rewards and too strong incentives to participate in it that could lead to almost total supply of ether locked in stake.

So, we have:

E_t - total Ether supply at time t.

S_t - total Ether at stake at time t.

R_t - reward that goes to stakers at the end of time t (which could be defined as some sort of function F: R_t = F(S_t), it doesn’t matter now).

IR - inflation rate of Ether due to increasing supply.

IR = E_t+1 / E_t - 1 and E_t+1 = E_t + R_t. (big simplification here because of a lag with which the miners would spent their reward on market which should lead to inflation afterwards, but it doesn’t matter here).

IR = E_t+1 / E_t - 1 = (E_t + R_t) / E_t - 1 = R_t / E_t.

Simultaneously miners interest rate for the same period is:

MR = R_t / S_t.

Therefore, MR > IR while S < E.

I mean that miners would get constantly higher than inflation rate while ether at stake is less than total supply.

Then, if it is relatively friction-less to stake ether, and if it is really safe to do this, this looks like a perfect bond: everybody could participate and get rate higher than inflation with no risk.

If there were something like this in financial markets, then, no doubts, soon all the money supply would be in such bonds.

If there is not enough risk of losing S, this builds a strong incentive to rise S till it reaches E: S → E. All ether would be at stake which freezes the economics. I mean something like negative deflation effects which leads to major crisis. Nobody wants to spend any wei, because what you lose is not just this wei, but a guaranteed inflation-free income on top of it. You have no motive to make any business and take risks if you could simply put all money at a deposit which is by definition yields you more than inflation.

I have tried to find any answer and excuse me in advance if I missed something. For now I have found only something in this paper: “Incentives in Casper the Friendly Finality Gadget”. From the paper there would several risk types:

• Loosing private keys, but this don’t count, this is general risk of using cryptocurrencies, stake it or not.

• losses due to network latency and timeouts which could be mitigated by mining in pools.

• Presence of malicious miners which leads to NPCP/NCCP (see paper) penalties. But what if there would be no malicious miners? And anyway, in the long run there would be two types of situations for honest miners: either NPCP/NCCP penalties would be such that you constantly lose money and you opt out, either you still get higher than inflation income on average.

So the question is that I see a strong market incentive to put all ether at stake and no force to prevent the situation when S→E and complete disappointment after.

As I see now there could be only two types of such forces: different issuance model or some difficult-to-calculate-in-advance risks to put money at stake.

Of course this is relevant to the time of complete mass adoption of Ethereum. But still.

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Update

I have found this paper: https://docs.google.com/document/d/1Xf_iHGI51Lp6nVHPZo0SdUw60-NA6YJUvk2s-eYaxLE

citation 1:

maxDeposit - the maximum deposit allowed to become a proof of stake validator. If you want to deposit more, you must purchase multiple slots. Set to 50000

citation 2:

Alongside this, another question is how to target the minimum entry size and a possible entry fee. One approach is to auction entries, thereby resolving many preference revelation issues and allowing targeting a fixed PoS participation rate, but at the cost of introducing or exacerbating selfish-mining attacks.

If I understand them correctly, there is talk about entry fee to become a validator/validator candidate (thus participate in issuance) which could be defined by market. Looks like this is the thing that will balance the incentives to be full in.

Answer 1

Technical limitations

There are a few things that act together to prevent all ethers from being tied up in staking, or at least make it economically unattractive. The source for the info comes from here and here. However, I am adding my own interpretation and drawing additional inferences.

• There is a minimum amount of ether required to stake (1250 ether), which increases with number of validators. This provides the first hurdle: people with relatively few ethers are unable to stake unless they pool their resources. Some users may not wish to do this, since it involves trusting another party.
• Ether is locked up during staking. This means that, even if everyone were to trust "pool staking", at least in the proposed hybrid-staking period, newly mined ethers would be unable to be used for staking. (I'm assuming the lock prevents adding ethers as well as removing them, but I'm not sure; this does not affect the other points in this answer, though).
• There is a maximum of 250 validators. Thus, for people with lesser amounts of ether, they cannot "go solo" with staking. If we assume all validators are acting rationally, then it is in their own interests to prevent others from also performing validation by pooling with them. Why? As I'm sure you've figured out, if there is monetary inflation of, say, 5% and everyone's balance is growing by 5%, they're no better off than they were before, thus defeating staking as an economic incentive to secure the blockchain. However, this does not prevent the actual securing of the blockchain.
• There is a penalty for remaining a validator for a prolonged period of time. Sure, you can move your ethers around to a new account to become a "new" validator, but the 250 validator limit may prevent you from joining the set of validators until there is more churn.

Economic notes

As pointed out by @Distic, there are two kinds of inflation: monetary inflation (more money being printed) and price inflation (the nominal price of things going up). One can have one without the other, but hoarding can be an issue even with monetary inflation. If the usage of Ethereum as a value store keeps increasing, the price per ether (denominated in a "stable" fiat) will increase to enable the flow. This can lead to price deflation, denominated in ether. Conversely, if the use of Ethereum as a value store drops, even if no new ethers were being produced (no monetary inflation), one would expect to see price inflation, denominated in ether.

The hoarding issue can happen whenever people expect to see price deflation (i.e., whenever they expect the amount of goods/services the unit of account can purchase increases). We even see this with products: just before a new iPhone is expected to be released, I'm guessing Apple sees a drop in sales (unrelated to other companies' sales eating into Apple's). They hold onto their dollars because they think that the same amount of money will soon buy something of higher value.

Answer 2

I think there are some mistakes.

The first is when you call "inflation rate" the increase rate of monetary mass, but it is a mistake you share with a lot of people among the cryptocurrency community. Inflation rate is an increase in prices. The difference is that while bitcoin and ether have a positive and high increase rate of monetary mass, they have had a negative inflation rate on the long run. Roughly, you can measure the inflation rate through e.g. the "bitcoin t-shirt" index : inflation rate = (t-shirt price at year n+1 / t-shirt price at year n) - 1.

Probably you will say that, in the long run, the monetary mass increase rate should equal inflation rate, but I don't know about any experimental verification about that, even for so-called "fiat" currencies. For example, look at the increase rate of monetary mass, look at the 9% increase of M1 (currencies and liquidities) and remind that the ECB fails to reach its inflation goal of 2%.

There can be several explanations for this :

• the need for a currency increases with the size of the population using it : a 200-people economy needs approximately twice more coins of the same value than a 100-people one. That's basically what we have seen in cryptocurrencies: there are more and more people wanting it, so the increase of the monetary mass has been overcompensated by the increase of the population.

• some prices cannot change fast enough to adapt.

• ...

Your second mistake is that you seem to forget about the fact that you cannot use your monney when it is staked. So the observed inflation rate should more be something like (E_{t+1} - S_{t+1})/(E_t - S_t) as only the available currencies are dealt with products. This also puts a deflationary pressure on the currency, but in the same time you cannot use your money to invest, or pay your bills and taxes. If the cryptocurrency is broken during your stake, you will not be able to exchange it. This has a cost.

Your third mistake is that there is hidden costs in staking. For example you need to have your node synchronized at any time, which means your computer is always on, and you have to spare some RAM, CPU, etc. for it to work. There are also transaction cost for you to stake.