Crypto AMA with Gauntlet & Dragonfly (11.2.19)

Guests:

  • Tarun Chitra

  • Haseeb Qureshi

Moderator:


Moderator:

Everyone, please give a warm welcome to Tarun Chitra of Gauntlet and Haseeb Qureshi of Dragonfly! 

As a reminder for everyone participating—please keep the discussion respectful at all times.

@tarun, @haseeb: could you guys start off by providing brief bios on yourselves and overviews about your respective firms? Then, a short overview of today's topic and your work? We’ll then be off to the races with questions.

Haseeb:

Sounds good, thanks for having us!

Quick bio on myself: I'm a partner at Dragonfly Capital, a crypto venture fund. I was previously at Metastable Capital, and before that was an entrepreneur, software engineer, and in my previous career was a professional poker player.

Dragonfly Capital is a $100M global venture fund with offices in Beijing and San Francisco. We're pretty unique among crypto firms in that we bring a global perspective, having offices in both SF and Beijing, and can help teams with a global go-to-market strategy. We're also backed by most of the major exchanges and mining companies, so we have strong relationships with crypto infrastructure providers around the world.

We invest in everything across the spectrum, including native tokens and equity. We are big DeFi bulls—we're backers of Maker and Compound—and we also are long ETH. (Useful background for understanding our incentives!)

Haseeb:

Short overview of the topic:

@tarun recently published a paper that analyzes the effect of on-chain lending (think Compound) on PoS security.

The argument roughly goes like this:

PoS is secure when lots of coins are staking for the network. Rational stakers will stake when the yields for staking are higher than the yield they could get elsewhere. On-chain lending provides a non-PoS-securing source of yield, and if that risk-adjusted return becomes high enough, it can end up siphoning security away from the underlying network.

There are various attacks you can imagine for this by an attacker subsidizing the lending APR. But the most interesting insight is that this can happen emergently, without any coordinated attack! It can just be various lending protocols subsidizing themselves through VC funding, or organic interest in borrowing increasing so dramatically for orthogonal reasons that the majority of assets end up lent rather than staked.

Tarun:

Sure thing, thanks for having us. 

I'm the CEO of Gauntlet, a company dedicated to making incentive assessments of cryptocurrencies and smart contracts as rigorous as those in algorithmic trading and other actuarial sciences. Our platform lets you simulate how different types of users, far past the 'honest' and 'Byzantine' types of users of formal cryptography, interact with PoS systems and smart contracts. This allows developers, traders, and investors to gain confidence in these systems and enables automation in decentralized systems that is closer to that of algorithmic trading.

Prior to starting Gauntlet, I spent 8 years working on simulation-driven research, first at D. E. Shaw Research where we build ASICs for doing drug discovery research and then in high-frequency trading. When PoS first came out, I spent some time thinking about the financial threat models that exist, especially as most of the rigorous literature implicitly assumed that the cost of security was tied to simple universal composability (UC) models from cryptography as opposed to more financial aspects (e.g. staking derivatives). In my free time in 2016, I had initially built a simulation engine for stress testing PoS consensus protocols and eventually that turned into consulting and finally a company. I love finding weird ways of applying probability theory to fields that are afraid of it :)

Haseeb:

There are basically two ways you can avoid this problem:

1) Don't use deflationary monetary policy in PoS. A deflationary policy will, to a first approximation, always end up in the overwhelming majority of assets being lent rather than staked (given some reasonable assumptions).

2) Monetary policy in PoS *must* be adaptive. You should treat your issuance rate as a dynamic thing that responds to market incentives, the same way that central banks do. Otherwise a fixed monetary policy has the potential of undergoing a rapid phase transition from mostly staked -> mostly lent, which will jeopardize the security of the network.

Haseeb:

And that's the argument in a nutshell.

Participant:

nice tl;dr

Haseeb:

The full paper is worth reading:  https://docsend.com/view/697feid, goes into much more detail about the assumptions that were baked into the simulations @tarun ran

Tarun:

Note: Hopefully it will be on arXiv soon, I've had some trouble getting the mods to accept it because they don't feel like it fits into an existing arXiv category

Moderator:

+1. @tarun and @haseeb: anything else you'd like to add before we jump into questions?

Haseeb:

A lot of further work to do here. But one of the biggest takeaways for me is that there's a lot about PoS security we don't fully understand yet. 

TL;DR: Everything affects everything and blockchains are really complicated.

Haseeb:

Another thing I want to add, to be clear: I don't think there's a lot of reason for ETH 2.0 to be worried about this!

Haseeb:

ETH has already demonstrated a pretty flexible approach to monetary policy and a willingness to respond to these kinds of issues in real time

Haseeb:

But if ETH 2.0 goes down the road of pure deflation + txn fees (which I guess is now on the roadmap?), that sounds more problematic to me.

Haseeb:

A lot of how worrying this is also depends on how you forecast borrowing demand in the future.

Haseeb:

Anyway, let's take questions :)

Moderator:

Awesome, have @ it folks.

Haseeb:

@tarun if I say anything you disagree with, feel free to chime in or correct me

Participant:

When you say deflationary do you mean disinflationary?

Participant:

Agreed PoS likely needs active management of monetary policy but do you have any thoughts on the risks that come with such management?

Haseeb:

Oh, I have so many thoughts, too many to fit into the margin of this message.

Participant:

It seems to me that demurrage and inflation are equivalent, which lets you have "deflationary" policies. To be sure, when you say such policies are not feasible, are you only referring to those which don't have a security budget?

Tarun:

Sounds good so far! The only thing that I want to mention is that the reason that the paper uses a simplified model of PoS is so that we could prove a formal theorem about how rational portfolio holders would behave if they view their tokens as yield maximizing investments. As in most of traditional algorithmic finance, formal proof exists to define the problem space, but simulation is the only way to connect these ideas to reality (which is what we try to illustrate with this paper).

Participant:

Lol, any writings then?

Haseeb:

Active monetary policy ultimately rests on good decentralized governance, and we have no idea how to do that in general IMO. I tend to not be a fan of on-chain governance approaches because I think we have so little knowledge about what works and why it works that crystallizing/institutionalizing a framework is just a bad idea. (I see on-chain governance as basically a community committing to a set of bylaws, but without much confidence that it's the *correct* set of bylaws.) 

Here's an old blog post I wrote about this that I think I mostly still agree with: https://medium.com/hackernoon/blockchains-should-not-be-democracies-14379e0e23ad

Participant:

The paper is fairly complex, but is the takeaway deeper than "look, if people can make more money lending than staking, they'll do that and that may actually encourage people to short, pushing the rates up"

Haseeb:

That's not a bad distillation. IMO the bigger takeaways are around how to combat it, rather than just pointing at what might be a problem.

Haseeb:

We actually argued about terminology here. IIRC @tarun defines deflationary as that the rate of issuance is decreasing over time. (Correct me if I'm wrong)

Participant:

Thanks @tarun and @haseeb for your time.

Blockchains are certainly very complicated. Staking derived interest rates have a different risk profile than lending derived interest rates. Do you think DeFi protocols might take advantage of the newly available staking risk/reward profile and allocate some of their pools of assets to staking vs lending in certain cases? If that happens, then there will be an impact on blockchain security.

Tarun:

I'm going to try to address this point by formally defining our notion of disinflation. Formally, we define disinflationary policies via the block reward at height h, R[h]. The reward, for our purposes is an integer-valued function that is bounded by a continuous, differentiable function R(t) such that:

a. R'(t) > 0 for all t (marginal increase in security budget)

b. R''(t) < 0 for all t (concave)

c. R(t) is a.s. bounded by a constant as t goes to infinity 

This represents a decaying security budget and looks like Bitcoin (albeit with arbitrarily slow convergence to a fee-only market — R[h] = k/h^2 is valid, it doesn't need to be geometrically decaying like Bitcoin)

Haseeb:

You're absolutely right that staking and lending have different risk profiles and different liquidity profiles. These are nontrivial to model (and also hypothetical at the moment since ETH 2.0 staking is not yet live).

What will exchanges do, given this? Probably depends on a huge number of factors: how stable are yields, how risky lending is perceived, how good is their infrastructure at different things, how much is borrow interest growing at any given time

Participant:

But the geometric decay gets the people going

Haseeb:

For practical purposes though, in the short to medium term, it's likely that staking will have pretty juicy yields, and is just less complex from a risk perspective. Smart contract risk, business risk, bank run risk, migrating to new versions of contracts, all that stuff gets eliminated if you just stake instead of lend. So my guess is exchanges will prefer staking, but that's really just a guess.

Participant:

Isn't this about targeting a baseline security spend / staking rate required to sufficiently secure the network? Vitalik has always suggested a target stake rate (token staked / circulating supply) for ETH2 of 10% as the required security threshold. The reason ETH can target a relatively low stake rate is because it has a high market cap, and thus 10% of the market cap represents a high cost of attack in absolute value terms.

Participant:

Couldn't an active monetary policy that addresses the paper's concerns simply rely on a curve that increases yield as the total number of staked tokens decreases, keeping humans out of the loop?

Tarun:

The main implication is that the risk profiles of the users in a PoS system will determine whether there are correlated 'bank runs', where everyone tries to unbond simultaneously and use their tokens in a strictly more optimal manner. We look at a situation in which risk profiles don't change over time but are drawn independently from a random ensemble. The fact that you get correlated bank runs with independent risk profiles is quite surprising — if there was a correlated set of risks, you expect everyone to leave at the same time. But here, we can *still* get that behavior, even though the agents assess risk independently.

Participant:

And by the way, isn't that what Polkadot does? Last I checked (but that was make a year ago) they were planning to target x% staked and have a Dutch auction to set the reward so that at least that much gets staked

Haseeb:

I think this is a good mental framework. You want security spend to be pretty stable and continuous. What's unfortunate about this paper is that it implies that there are likely to be sharp phase transitions when stakers are chasing higher yields in DeFi, unless that's mitigated by active monetary policy. The point of the paper is that it's actually pretty subtle how to accomplish this.

Tarun:

What stops a competing network from writing a Compound-like smart contract, seeding it with liquidity, making yields high temporarily, and then shorting (via borrowing from the contract) the pair Attacked Token / Attacker's Token?

Tarun:

There are more dynamic attacks here, especially if you are running another network and you want to decay security on a competing network

Participant:

Forgive me for maybe having missed this in the paper, but can you guys walk us through the mechanics of an actual attack? Maybe a few different types? Let's say once the malicious borrower has corned the supply.

Haseeb:

+1. These are not operating in closed ecosystems. That's part of the reason why we advocate smart people / DAOs / whatever in the cockpit to be able to respond to active attacks

Tarun:

This is akin to what happened in the early day of electronic US equities markets, where BATS (then an upstart) would buy up liquidity on Arca/Island and then post it locally

Participant:

Do you think there's any historical parallels to draw for governance? To me off chain governance looks like splits between countries/kingdoms, with more extreme examples being something like the formation of the Holy Roman Empire (tons of tiny little kingdoms) or the Balkans after the Ottoman Empire collapsed. In one case it formed a very distributed whole, and in the other many distinct entities.

Haseeb:

Ha! That's a good question, I don't know that I have a great answer to that. But to me, the distinction between formalized / on-chain governance vs informal / off-chain governance is more about having a formalized process and governance through some kind of voting system. I don't think they really lie on a balkanized vs centralized axis.

In most cases, direct democracy (or direct plutocracy) has not fared well historically. Referenda, especially in California, tend to have pretty dire track records. And for the most part, all of these blockchains are still highly experimental technologies, and as such are still in the stage where IMO they should be governed by smart, thoughtful, and capable technical leaders who can make quick decisions and weigh evidence well. Most on-chain governance systems today actually look kind of like this, mostly because the "thought leaders" of these systems *are* the founding technocrats and voter turnout is quite low.

Haseeb:

But I expect these things to change over time and likely in a more chaotic and populist direction once these systems mature.

To be clear, I think on-chain and formalized governance is a good long-term goal. But I think it's really dumb to start there and assume we'll be in good hands. It's like committing to a constitution and system of governance before we actually have any historical precedents to learn from. It's noble, but you'll also probably be someone else's history lesson.

Tarun:

For sure. The main idea is that rational validators who have token wealth W view their assets as (tokens_staked, tokens_lent) (with tokens_staked + tokens_lent = W). This portfolio needs to rebalance, as yields change. In the case of Compound, yields change as a deterministic function (also called a bonding curve) of two things:

1. Supply of tokens lent

2. Borrowing demand for tokens

When this yield changes, a rational agent, when they reach an unbonding period, decides (based on their risk profile) whether to move some of their tokens from staking (at the end of an epoch / unbonding time) or to staking (if the lending yield is lower). At a high-level, the 'risk profile' of a user can be thought of as the following:

a. If they are 'risky', they move ALL assets from staking to lending is the lending yield is better than the staking yield.

b. If they are 'not risky' they move a TINY fraction of their their tokens (they'd prefer intertia).

In the system, we model different risk profiles, sampled from a distribution that depends on the 'time risk' of staking vs. lending (e.g. staking might be 'safer' but I have low convexity, since I am locked up for a long time, whereas lending is 'less safe' but I can perform capital calls efficiently).

In these systems, as a function of the parameters (slashing_rate, epoch_length, minimum_time_of_loan), you get qualitatively different behaviors. In physics and probability theory, this is called a 'phase transition' —- you move through a continuous phase space and hit a point where macroeconomic observations hit a discontinuity

Haseeb:

Anyway, this is getting a bit too philosophical! Back to the paper :P

Participant:

I agree, I was more talking about potential outcomes of governance rather than how we get there.

Participant:

Lol of course

Participant:

Nothing stops this, but the curve would cause yields to go up dramatically if enough people move from staking to lending markets, incentivizing people to return to staking, which would keep the network secure. Not only that, but it would be more or less instant, whereas adjusting monetary policy with humans in the loop would likely have significant time lag. Does the increased attack vector of humans in the loop justify the increased flexibility?

Tarun:

This type of rebalancing of token portfolios, by the way, is EXACTLY what happens in the ETF markets. An the type of issue we find here resembles the very famous 2018 'Volmageddon' incident in the volatility futures market https://www.bloomberg.com/news/articles/2019-02-06/the-day-the-vix-doubled-tales-of-volmageddon

Participant:

The paper focused on PoS systems, but how does this compare to say derivative markets and Bitcoin security? Seems like a similar problem.

Participant:

This isn't an actual attack though. Just a lowering of the security.

Haseeb:

To be clear, this was modeled in the paper. ETH 2.0 intends to have returns to stakers be 1/sqrt(total_staked),, which is exactly a function like what you're describing.

Tarun:

If you're secure by up to 1/3 of capital and your capital goes down by 99%, then 1/3 of 1% is 'very low security' and easy to attack

Haseeb:

The sharp phase transitions still occur in spite of this increasing rate of return.

Participant:

Got it, thanks!

Participant:

Also, paper assumes that staking is purely an economic decision. There are other intangible reasons to hold a token + stake. How do you factor that into the analysis? ie: I could get better risk adjusted returns lending on lending club than staking in a PoS network.

Haseeb:

Maybe, but attackers will be very happy to see it.. :)

Participant:

Hi guys, coming in late here - thx for doing this AMA! Hope this wasn't asked yet: how do you think would tokenized stake/stake derivatives influence the attack described? E.g. if there's a yield to be earned on tokenized stake, the attacker needs to outperform that extra yield, correct? Do you forsee other factors that impact the equilibrium provided tokenized stake exists in some form?

Participant:

Wow. Is it possible that other algorithmically-determined staking returns could avoid the phase transition? Or is some sort of governance unavoidable?

Tarun:

Basically, if the hash power derivatives market were particularly liquid, then you could maybe see something similar happen. Selling Bitcoin futures, however, is different than this form of security because there is extra risk and tx fees involved versus lending. Technically, if, say, Bitcoin futures are in contango and don't converge by expiry, then you as the underwriter of a future or option (e.g. selling one) is incurring second-order gamma risk, which is impossible to hedge in any market other than oil and ES

Haseeb:

Completely fair. This wasn't modeled in the analysis, it assumed that stakers are trying to maximize their risk-adjusted returns given their individual risk preferences. If there's a large set of stakers who are ideologically committed to staking regardless of counterfactual yields, that can ameliorate some of the security concerns. But I don't know that this is good to bet on.

Haseeb:

People used to make this argument about Bitcoin mining, and I think today it's pretty hard to say with a straight face. (Though to be fair, staking has pretty different dynamics from mining and is likely to result in a very different distribution of coins.)

Participant:

Betting that people make irrational decisions might be something worth betting on 😂😂

Haseeb:

Sure, but betting they'll make irrational decisions in your favor is always a little risky...

Tarun:

For sure. We actually have one assumption that is a 'measure of altruism'. Assumption 11 assumes that S_t - \ell_t > \delta S_t, which says that the total staked quantity is AT LEAST \delta \in (0,1) times the total money supply. If this parameter is large, we say that there is \delta% of the money supply staked. This parameter controls the rate of convergence of all of the constants in Claims 1-4 (which is in the appendix)

Participant:

This is great, thank you!

Haseeb:

Oh I forgot about this. There is actually a parameter for altruism in the simulation, haha.

Participant:

Fair :)

Participant:

Just following up on this as well. What do you believe to be the difference between lending v. PoS and derivatives v. PoW?

Participant:

Not sure if I've seen anyone model out the risk of derivs on BTC security, but would be worthwhile

Participant:

(and apologies if you already answered this somewhere else but I missed it)

Haseeb:

A simple way to think about this is: if the lending rate spikes and the staking rate is constant, then a large group of people will rebalance over to staking all at once. I can certainly imagine a few algorithmic policies that would deter this kind of mass migration out of staking, but they'd probably need to target an ideal rate of staked assets

Moderator:

Are there any other promising ways to defend this attack in addition to using a flexible monetary policy? (e.g. longer unbonding periods, etc.)

Participant:

Apologies in advance for the lengthy message

Appreciate the color. I know you mentioned that you don't think ETH 2.0 has to be worried about this because of their currently malleable monetary policy, but the currently proposed issuance model for ETH 2.0 would be "permanent" post launch and deflationary/disinflationary (issuance is a fixed nominal amount based on the quantity not % staked). I actually think the low yield creates a bigger risk, particularly in the short term, for this type of pseudo-discouragement attack because the yield threshold that lending rates need to exceed is much lower. I was hoping to get your thoughts on that dynamic.

Definitely agree with your take that forcing lending markets to have a rate cap would reduce the viability of this type of attack (even though it likely wouldn't happen for the reasons you discussed). I was wondering what your thoughts are on the effectiveness of making the collateral match the asset that you're borrowing? Using asset X as collateral to massively borrow asset X and attack asset X's network being much lower EV vs using a stablecoin or a different asset as collateral

Tarun:

Very good question! As in normal finance, one would actually want to view your VaR (or possibly beta-adjusted VaR) as a portfolio of:

(staked_tokens, lent_tokens, discounted_tokens_committed_to_staking)

The notion of discounted_tokens_committed_to_staked is a form of implied volatility. If we assume that the current implied volatility of staking derivative tokens is s then we basically can say that a long staking future of quantity q at time dt before expiry should have value proportional to e^{s * dt} q.  [0]

From here, we can again do something like what we do in the paper (Markowitz mean-variance optimization) and try to search for a similar phase transition. In reality, if validators ever approach the financial sophistry of normal markets (which they'll have to do if they want to EVER optimize PNL), then they'll have to be rebalancing these portfolios all of the time. Some of the biggest quantitative trading firms (namely HRT and Jane Street) make almost all of their earnings on creating and redeeming baskets of stocks, options, and derivatives that are quite similar in payout strucutres to a portfolios of tokens, derivatives, and lending.

[0] If you know any stochastic calculus, then you know this is a simplification as I'm asssuming that the implied volatility is stationary over time. But I'll leave this for a longer form medium :)

Haseeb:

sqrt(staked_assets) isn't aggressive enough given realistic volatility in borrow rates

Haseeb:

Longer unbonding periods can definitely help. @tarun can offer more color on this.

Tarun:

@haseeb loves thinking about this! I think he honestly will give a better answer and I think he is going to write something up (it does come up in his excellent earlier work)

Moderator:

Also, @tarun can you walk us thru the major notable assumptions of your analysis? What related future work are you interested in seeing?

Haseeb:

BTW, for anyone who's interested in this kind of work, or applying it to other networks or optimization problems, definitely reach out to @tarun. Gauntlet does this kind of simulation-based analysis for tons of major projects including Compound, Kadena, Uniswap, etc.

Haseeb:

I have to run now but hopefully Tarun can finish off the remaining questions 🙏🙏🙏

Moderator:

Thanks for joining us @haseeb!

Haseeb:

Thanks everybody for all your questions!

Participant:

Thanks Haseeb!

Participant:

Thank you Haseeb 🙏

Participant:

Yes! Saw he mentioned as a point of further exploration in his previous paper @hasu would love to work on this with you

Tarun:

Indeed, I think that if I were crazy enough to try to start a protocol (alas, too risk averse 😣) I would try to have an emission schedule of the following form:

1. R'(t) > 1 for 0 < t < T — have a fast growing supply until some time T to onboard all presale people onto staking

2. R'(t) ~ mu + sigma * N(0, 1) for T < t < 10T. Add in a random lottery to ensure that validators feel 'oh shoot, I shouldn't lend, what if I get a 2-sigma yield'

3. R'(t) = Theta(constant) for t > 10T level off

Tarun:

Adding in some type of beacon / lottery returns (which I would only trust after millions of simulations of expected payouts, of course) can mitigate large collective rebalances. We've spent some time working with our customers on designing things akin to this that use some of the existing on-chain entropy

Tarun:

Yep! I tried to spend a lot of time directly illustrating this in the assumptions section 

1. Minimum Staking Supply ('level of altruism')

2. Martingale selects block producer(s) [e.g. no DDoS susceptibility, cannot have something like the Stellar network halt of May]

3. No external markets (we don't consider *external* lending from someone like Genesis — this could be competive, if they're responsive and have inventory, but we would need to model this based on historical crypto lending data, which I don't have and probably only Genesis/Matrixport/Tagomi have)

4. No random money supply (can't do my little thing to thwart rebalances above)

5. No shards

6. No transaction fees

Tarun:

Future work:

1. Adding in staking derivatives as per the design suggested by Sunny (Cosmos) [which would give quantitative fortitude to the question asked by @Felix] 

2. Add in transaction fees (at Gauntlet, we've spent a lot of time building models for transaction fees + spikes in demand, so this is a natural next step that we would work on with a protocol)

3. Historical trading data / synthetic shock data (see the response that occurs when validators are allowed to trade)

Moderator:

Gotcha, thanks a ton for the thoughtful response.

Moderator:

Folks, Tarun has ~15 more minutes of time. Get your questions in please!

Tarun:

longer unbonding, lots of lotteries for reward sizes (but be very careful when designing these!!!!! 😈)

Participant:

This lottery seems pretty cool - but seems like sth like this would encourage pooling stake with the big guys even more. Unless you're a really lucky small pool :]

Tarun:

To your second question, I think that differences in liquidation rates for different forms of collateral could cause validator risk aversion. If we take a larger view on this and view the big validation pools (Coinbase, Binance, BT, Blockdaemon, etc.) as holding portfolios of many staked coins, we might find situations under which validators have high entropy marginal distributions for risk tolerance for certain coins (and we get results similar to those in the paper), whereas for coins that have historically had a lot of liquidations (e.g. if some staking coin were in MCD on it and the deflationary spiral of liquidations -> selling -> more liquidations -> ... led to dampened covariance estimates) might end up being dominantly staked

Tarun:

indeed, this is why the coupling to a Gaussian process I described above is probably far from ideal. You can find other ways to generate randomized rewards (for a certain period), which basically corresponds to the network itself trading off variance in estimated security spend to mitigate withdrawals. Also, as Vitalik pointed out on Twitter, ETH2 has a pretty conservative withdrawal window, which bounds how much risk cartels of validators can take in a single unbonding event

Tarun:

There's no perfect solution, but you can use careful modeling and numerical methods to optimize your way to something that is reasonable

Participant:

What do you hope will change as a result of your paper @tarun ? Has anyone in the Eth2 community of devs/researchers provided feedback? Thank you!

Tarun:

I mainly hope to bring awareness to the fact that not all of finance is 'bad' (which I sometimes note more acutely in crypto), especially when thinking of staking, which has a lot of direct financial analogues. Plus, using simple techniques from quantitative finance is very useful to do when performing portfolio construction in this space (especially if you're a fund that has a hybrid VC / trading structure and you have to carefully quantify your cost of illiquidity) .

At the protocol level, I'm really hoping to cause a change in the types of quantitative measures that are used and presented to investors / users. Right now, most emission schedules are almost random and bereft of statistical rationale. I think that this framework should at least force larger investors (who do have a fiduciary duty to their LPs!) to step back and reevaluate the token economics of the networks that they are helping grow.

With some luck, we can create quantitative standards that resemble those in mature fields.

Participant:

Sorry if this has been asked already. Wouldn't interest payments likely balloon exponentially? And, at a certain point, probably no one would even lend due to the counterparty risk. Additionally maybe there isn't even enough on-chain collateral to post in order to borrow the necessary amount of Eth? Apologies if these are addressed in the paper, haven't had a chance to read it yet!

Tarun:

This is a good question! The phase transition in the paper (which, if you're familiar with phase transitions in discrete probability is directly analogous to the Galton-Watson transition for phylogenetic trees) shows that if the emission rate is too low, the eventually rational agents will always lend to traders who want to go short. It is true that we assume a 'mean-field' model for borrowing demand (e.g. if there are a bunch of cascading liquidations, then the probability distribution that we sample borrowing demand from doesn't change), but provided that there is a) time where borrowing demand for shorting is high and b) the time interval is greater than a few epoch lengths then you can still have this type of drainage.

But this is a great identification of another point of future analysis: Do too many cascading liquidations in on-chain lending (MKR / Compound) eventually lead to a 'levelling-off' of this phenomena? This relies on us modeling external trading (as cited above!) and is hard to prove a theorem for (which was part of the goal of this — simplest non-trivial model with a formal result)

Tarun:

I should also note one other thing, we analyzed the Compound bonding curve because it was the most robust and easiest to study mathematically. Simulation results were similar for dYdX's bonding curve, but it was signficantly more difficult to get a formal result.

Moderator:

Awesome, and thanks everyone for tuning in and asking excellent questions!

Participant:

Thanks so much @tarun