Questioning the game theory behind Tezos' liquid proof of stake mechanic (LPoS)

Delegating in Tezos does not give you any rewards. Rewards only go to stakers who do have a slashable deposit. Some if not most stakers choose to reward delegators, which ensures that, on the net, the amount paid to stakers is the minimum required to provide economic security for the protocol. I encourage you to read the white paper.


Yes, I am fully aware of that. In fact, it was implied when I said that each baker decides its own take rate, which is a very important aspect in the argument I’m making: even if the protocol doesn’t reward the delegators directly, bakers are rewarded proportionally to the voting power they’ve been delegated which creates the situation I described.
Now, set this aside, I invite you to read the post again since you appear keen to address my points.

I think there are multiple game-theoretically sound staking schemes. You mentioned Eth2 (no delegation) and Tezos (liquid PoS with delegate slashing but no delegator slashing), and there’s also Cosmos- or Polkadot-style systems in between (delegated PoS with lockups and delegate+delegator slashing).

I think you could spend a lot of time arguing about distinctions between the approaches, but my impression is 1) they all work, and 2) if they ever seemed vulnerable the protocols could change.

One cool thing about the delegated- and liquid-PoS approaches is that in economic equilibrium the protocol pays exactly the correct cost to bakers for running the network. This isn’t a feature of Eth2’s model IIUC. OTOH, I wonder if this feature might be a reason Tezos doesn’t have more bakers as it would tend to make baking unprofitable.

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There is nothing wrong about rewarding delegators for doing nothing else than delegating. This is equivalent to not rewarding delegators and punishing the stakeholders who don’t participate (by either delegating or baking).

Indeed but delegators still take some risks: delegates can vote against their interest and keep a larger part of the rewards than agreed upon.

You make good observations, and what you said at the end is my main point. I think we have evidence that there isn’t enough incentive to set up enough bakeries, and that is a problem because 1) less nodes, less decentralization in general, and 2) not a lot of tez is actually locked in the network and one could argue that this is a security problem. The reason why this happens is that the most profitable bakers can undercut everyone else with the consequence that other players are priced out of the baking game, and even solo baking isn’t worth it when you can just delegate instead and get a very similar rate.
I’d also add the following observation: one of the main advantages of LPoS implemented at the protocol level is that you don’t have to deal with a different token for your staked tez (e.g. STETH with Lido), but it turns out that you end up creating a very similar structure regardless (ctez) because things don’t quite work out when the tez isn’t in directly in your wallet but instead in a smart contract. I see it as a telltale sign that this model is fundamentally not the right one to pursue.

It is wrong if it creates the situation where simply delegating gives very similar rewards to baking directly which leads to less bakers in general. This is a reality that everyone has noticed, and I believe this is the culprit.

I agree with the overall, maybe in theory the Liquid staking system works to keep the system safe, however, it is not really incentivising to get more bakers.

Most of our economy works on exactly the same principle. Sure there are market failures but i do not think calling it unsound is justified.

Staking rolls do not get slashed directly but their staking rewards would be in jeopardy if they delegated to a shady baker. Nevermind the hit on the value of their assets which would be much more than the gain due to promised higher staking rewards. But ppl do stupid myopic things, so valid point.

I also dont think that the number of bakers is particularly informative. The important thing is the distributíon of staked rolls per baker.

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I propose a system of POS, where all delegation is put into a pool and this pool evenly spreads out rewards across all nodes depending on the node operators collateral as a % of the entire collateral of all the nodes.
What this does essentially is, make Node operators fight to lock in the most collateral, whilst at the same time, create a level playing field to get voters to bake with you.

I get what you mean about ctez - when engineering a system, it’s often a warning sign when there are two things that appear to serve the same role. But I’m not sure your stETH example works, because it seems to add a counterparty risk that LPoS doesn’t have. IIUC, Eth2 doesn’t have delegation built in at the protocol level. So, doesn’t that mean that under the hood, Lido is entrusting actual ether to the custody of various stakers? If so, isn’t that a vulnerability? And if it is a vulnerability, isn’t it useful for the base protocol to offer trustless delegation, yielding something like LPoS? Please correct me if I’m wrong - I’m not familiar with Lido.

Regarding the number of bakers: 1) There have been some recent high-profile departures, which is sad, but 2) It seems to me the roll distribution is still quite healthy (392 bakers with the biggest having 4.8% of the total). Do you disagree?

If you think about this from the standpoint of sound money, Tezos’ liquid PoS framework makes sense because it removes the tension between the usability and soundness of the currency.

Namely, if you lock up your ETH in a staking contract, you give up the right to use it. If you don’t, then your holding is being inflated away.

On Tezos, the LPoS mechanism effectively makes inflation (from block rewards) non-dilutive, making for a sounder asset. I wrote an article here if you want to read more about it.

P.S. I know that Lido stETH solves this problem on ETH. But it does create an extra layer of complexity, governance and risk.

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  1. ctez is not a liquid staking solution, its objective is to avoid a conflict between decentralised governance and DeFi.
  2. It would be great to see more bakers set up on the network, but I don’t think the liquidity or illiquidity of PoS have anything to do with it. An ETH2.0 staking pool would also remit rewards to its participants.
    A network shouldn’t overpay for its security. The Tezos model lets the free market decide.

If people who delegate are purely profit maximizing (evidence shows they aren’t) then the system is equivalent to one where an auction is held to set the block reward so that 10% are staked. Adding a bit of discretion on the part of delegators is probably a good thing, the main issue is not something that you cite: tax efficiency.

Arthur, regarding tax efficiency, is this something ctez solves? I.e. it appears to me that ctez turns income into capital gains, because instead of getting more tez you hold ctez and the price of it goes up. I understand you’re not a tax lawyer, etc., but I appreciate your thoughts.

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This is exactly the kind of mentality that I identify as the problem. Inflation is supposed to be dilutive for some participants, otherwise who is really contributing to the security to the protocol isn’t benefiting. If getting full (or almost) inflationary rewards takes just the tiny effort of naming a baker without any downside, then clearly the incentives aren’t there to properly compensate who is actually contributing resources to the network.

My point is that this problem is automatically solved when you use staking pools on top of barebones PoS, while with LPoS, which was supposed to bring convenience, you end up recreating a very similar structure from a UX perspective for solving a problem that really you didn’t expect to have.

You are completely right about Lido, Eth2 doesn’t have delegation at the protocol level so what happens essentially is that delegation systems are abstracted and built on top of the protocol with the help of smart contracts, which then has the immediate property that you can easily get a token in exchange representing your stake in the pool. Now, various entities can setup pools. Most often you will see centralized exchanges setting up pools, but you also see more virtuous approaches such as Lido taking the lead, where the trusted parties for its service are decided by its governance.
So yes, it is arguably not perfect either. But these are just structures that naturally form starting from the simplest model of proof of stake. So I’d rather go with Occam’s razor and let the free market decide which higher structures work better while maintaining the core incentives sound.

Regarding the stake distribution, yes Tezos arguably has the best out of any other pos chain out there. But I don’t think that’s related to the staking model being used but rather it’s just a consequence of having a fairer initial distribution and a longer history than others.

It’s not 100% non-dilutive. In practice dilution is minimized down to the cost of securing the network.
If 100% XTZ is delegated, then the extent of dilution is the average baker fee percentage.

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Hey omarino, I think you make some interesting points, the two main ones I’ll summarize as:

  1. Well designed systems typically have minimal yet complete feature sets that can be built upon by 3rd parties (Unix design philosophy).
  2. Staking rewards should be targeted at those making real contributions to the network and as such should be dilutive for most casual users.

I generally agree with both, but I don’t see how either principle applies in a strong way here:

For 1), Tezos includes delegation at the protocol level while Ethereum does not. At the end of the day, both are effectively delegated proof of stake (that’s what Lido enables). But, Ethereum’s DPoS is arguably riskier because you have to send actual ether to validators and trust them to custody it for you. If I were a protocol designer, I could see myself choosing to include delegation at the protocol level to remove this risk from the system.

For 2), I think the fix would be to allow delegator slashing (not just delegate slashing) to make Tezos like Ethereum (actually, more like Cosmos or Polkadot). I like this idea and would probably vote for it given my current understanding of things. Still, things seem to be working fine as-is, and Bitcoin proves you don’t even need slashing at all to maintain consensus.

BTW, regarding 2), I think incentivized lockups could be a partial fix. I just made a post about them.

Delegator slashing is definitely an interesting concept and would work in the direction we are seeking, but when paired with liquid staking it once again creates unexpected behaviour whenever the tez isn’t directly in your wallet but rather in some contract where you still though retain control over it. It would be very weird for example to put a bid for an NFT and then you come back to it with the bid halved in value because the contract delegated to a baker that misbehaved at some point.
Regarding whether or not to include delegation at the protocol level (in the context of lock-up), truth is that even if you do then you end up with some providers that allow you to make your tokens liquid with the help of additional structure, while regular validators only allow delegations as admitted by the protocol, so this sort of “centralizing” force is still present. This is not speculation, it has already happened on Terra where liquid staking services exist and are popular even though the protocol allows (non-liquid) delegation.
Given these observations it would come very natural to think: “okay, then let’s make both delegation AND liquid staking native at the protocol level”; and you end up with the Tezos’ LPoS model, which is the other end of the spectrum. But in doing so you have skewed a lot of the initial incentives you set out to have and also have to deal with weird quirks such as smart contracts delegation.
All in all, I am quite convinced that pure PoS is the best model, but does it mean that the other models don’t work? Probably not. Just not as well, in my opinion.
Sorry for the long text, I’ve loved this discussion as it’s pushed me to really think through all the different models.