Perpetuities as block rewards

Research and Development
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Let us define a “perpetuity tokens” as a special token with the property that it pays its owner 1 tez immediately, then γ tez after a period Δ_t, then γ^2 tez at time 2 Δ_t, and, in general, γ^n tez at time n Δ_t. The constant 0 < γ < 1 represents how fast the payout decays. In principle, γ = 1 should be a perfectly fine choice, but people might get weirdsies out of it, so let’s stick with γ < 1. Over time, this perpetuity token would mint and pay out about 1 / (1 - γ) tez.

Note that if a perpetuity token is issued at time 0, by time Δ_t it is equivalent to γ perpetuity tokens issued at time Δ_t and thus the two are fungible.

The reason I’m referring to those as “tokens” is to insist on the fact that they can be owned and transferred like a regular token. In order to periodically introduce these perpetuity tokens into the ecosystem, they could be created as rewards for the bakers, instead of tez.

Now, on to the why.

To get this out of the way immediately, this is not a way to create “passive income” or anything of the sort. There is no underlying economic activity represented by the tez minted by a perpetuity, it’s pure inflation. If you thought this is the point, it’s ok, it’s a common fallacy. You’re not alone, but you need to study more economics.

The main benefit of creating these long-duration instruments is that we could observe their tez denominated price directly on the blockchain. This is a purely endogenous signal and a potentially very interesting one at that! This signal can be used to be measure confidence in the future of the chain. The lower the confidence that the chain will be functioning in the future, the lower the willingness to hold these perpetuities. This signal could be used as a target for prediction markets and a futarchy based governance system.

For concreteness, the order of magnitude I have in mind is a half-life of one year.

Potential issues:

  • Ideally Δ_t should depend on time, not blocks. It would be simpler to align it with cycles, but that would mean making sure to change the payout of perpetuities if the cycle length or block time is amended. Perhaps it should be indexed on blocks, but with a very clear indication that it is intended as a proxy for time?

  • Inflation from baking rewards would affect the tez denominated price of perpetuities since it discounts the future. This is fine, but one has to remember that changes in the inflation rate will affect the perpetuity price in a way that has nothing to do with confidence. Perhaps it would be better to index the perpetuity payouts on the total supply?

  • There’s a potential risk that participants irrationally see this as implicitly “better” than tez and start giving it a monetary premium, letting this thing take on a life of its own. Perhaps, letting anyone mint those for 1 / (1 - γ) tez can at least put a cap on that phenomenon.

  • Introduces complexity that needs to be explained.

  • For every person who thinks this is a magical free lunch, there will be one equally mistaken person who thinks this dooms the platform becomes it attempts to conjure up a free lunch. Diffusing the ensuing argument and explaining to both parties that there is no lunch may suck up considerable time and energy.

Nota Bene :

  • I thought about perpetuities a lot circa 2014 as a way to solve long range nothing at stakes issues before concluding that the problem was overrated.
  • A friend mentioned to be last year that someone was thinking of using perpetuities as block rewards in Cosmos, but I don’t know who that was.
  • Yield as an endogenous target for futarchy is a neat idea I heard about at Web3 last year.
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This is nice, but it involves a modification to the protocol the way I read it. Why not the following?

Create a token contract that is effectively a xtz delegation reward future. I would deploy a contract with some amount of xtz and delegate the balance to a highly-respected baker. Once the current cycle completes I’m guaranteed a share of the baking rewards and the amount is known up-front. The contract would now allow interested parties to buy my future returns at some discount and automatically distribute them once they are received from the baker. This has similar characteristics as the proposal above.

An argument could be made for example to offer a 0 or even negative discount if you think the network would be particularly busy at a later date and the baker would collect significant fees on top of the preordained baking/endorsement rewards.

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Is the payout decay intended to observe implied discount rates as a prediction for some form of present value discounted price?

How would perpetuity tokens impact the value of each other, if at all?

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No, the decay is intended to avoid people freaking out over an infinite sum. Normally, I would suggest gamma = 1, but gamma < 1 saves a lot of educating.

??

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Right there, that’s enough to ensure that won’t work. The numbers will be muddied by whoever happens to be selected.

You’re never guaranteed anything, the reward belongs to the baker, your off chain agreement cannot be enforced on chain.

It’s missing key characteristics like being riskless, having a very long duration, and being fungible.

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Thanks for the write up! I see your proposal as a main step and building block towards Futarchy. I remember one of the best ‘benchmarks’ to see if a proposal holds or not was the price of Tezos. What do you see as main benefits of this “endogenous signal” (perp token price) versus the actual Tezos price?

No need for an oracle? More long term focussed than a spot price?

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The fact that it’s endogenous is a big advantage, you don’t need to rely on an oracle (decentralized or not) to adjudicate such a market.

There’s also a certain purity to it. If you’re looking at a “price” you’re benchmarking yourself against something else, it can be a bit self-defeating. When people say, 1 btc = 1 btc, 1 doge = 1 doge, that’s what they refer to.

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Regarding Cosmos, I believe here are some directions being explored for staking derivatives, but was not able to find a specific mention of the perpetuities idea in their forum

Edit: updated for clarity

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That’s a different discussion. This is not a staking derivatives. In general, financializing staking seems like a bad idea, but that’s a longer and separate discussion.

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Hello All,

Thanks to Arthur for letting me know this discussion was happening. I’m the “someone” he mentioned who was thinking about using perpetuitites as block rewards in Cosmos. (I wasn’t actually thinking it would be used for the hub, but rather in another zone)

The original goal was to use perpetuities to derive a market estimate for the risk free interest rate, and then use that as part of a stable coin / decentralized monetary policy. This was with gamma equal to 1, so that by a combination of the NPV formula and Geometric Series, we expect the market price of the perpetuity would be equal to 1/r where r is the discount rate, or the nominal risk free rate of interest. (minor note: this is with the first payment being at one time step after acquisition, if the first payment is at time 0, then the price would be 1 + 1/r which makes things more complicated)

Different people could have different discount rates / expectations of future inflation, but the market would converge to some particular implied rate which could be used in a trustless way to set things like staking rewards.

I agree that gamma=1 might be harder for people to accept, since it directly contradicts the monetary ceiling ideas that Bitcoin and others have introduced to the space. (I’m not a huge fan of those) I think it’s worth noting though that the aggregate effect of any fixed quantity of perpetuity in the system goes away over time. (ex: if there was 5% monetary growth due to perpetuities creating money, but no new perpetuity were being created, the monetary growth rate would decline over time and eventually go to 0% asymptotically.) If perpetuity were being continuously created, then the monetary growth rate due to them would converge to their own growth rate, and thus still be bounded. (ex: quantity of perpetuity grows at 5% per year, monetary growth rate due to them would trend towards 5%)

In my original design this was the core of how monetary policy would be informed, adjusting the creation rate of perpetuity so as to indirectly change the creation rate of money, in such a way that the inflation was stable / low. This can’t really be done automatically though, since the nominal rate includes both expected inflation and the real interest rate, and it’s only inflation that we would want to limit.

I would also note, that this complicates the usage of this price as a signal of confidence in the chain / network, as failing token prices (or the expectation of falling token prices) would imply increased inflation and thus higher nominal interest rates and lower perpetuity prices. While expectations of more productive economic activity would raise the real interest rate, and thus also lower the price of perpetuities (ie people would sell them to buy other investments which are now having higher real yields, until the price/implied yield converge to the new nominal risk free rate).

This is a pretty big text dump, and I could go on, but I’ll leave it at that for now. This is part of a larger DiFi project that I’m currently working on building a proof of concept for, and would be happy to describe/discuss in more detail if people are interested.

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