Staking, Lending, and MEV One Model to Rule Them All - Kshitij Kulkarni

foreign [Applause] [Music] great so uh yeah so today I wanted to talk about um sort of this idea of Mev redistribution uh and what it means for the economic incentives of validators I wanted to present sort of a very simple model that might help us think about uh where this Mev Revenue should go and and and and how it should be redistributed to validators so roughly the uh you know the the model is that we have sort of these validator pools or you know sets of validators that are facing uh different sources of return you know from where from uh where they can earn money uh for example they can uh they can earn rewards from staking they can uh they can participate in lending of course there's Med which is sort of the topic of this uh of this conference uh they can engage in uh sticking derivatives there's this whole variety of of places that they can collect returns from and the frame that I want to sort of uh have for this talk is that they're going to view uh how much they participate in each of these different sources as a portfolio so they're going to hold a portfolio over these different sources of uh of return and in effect what this means is that there's competition between these different sources uh and so this is not a new idea this is sort of going back to uh sort of work on a security approve of State protocols maybe all the way back to 2018 or 2019 but there's this idea that uh these different sources of returns are competing uh with each other uh based on the portfolios that uh that these validators are constructing but sort of the the really important thing to note here is that one of these sources returns is not like the others uh because staking uh serves sort of a dual purpose that in that it's uh it's it's a source of return for the validators but it's also uh securing the chain uh it's a you know the uh staking sort of acts as a privileged source of return because it controls the economic security underline chain and at the same time as competing with other sources of returns for the validators so I always want to have this frame in mind that uh we have this portfolio but sort of one part of this portfolio is important in the way that the other parts are not because it's it's uh it's security change and uh yeah so there's this question was this can we use uh Mev as an incentive to in in some sense improve uh the security of the chain or you know other other you know does it does it a router that we might have uh and can Lev act as some kind of an economic lever to induce security uh and can it be used as a way to get validators to avoid some kind of some bad economic equilibrium that might arise so we want to answer this question uh and uh so we should just set some uh terminologies we're going to have sort of this very standard model of of a proofs take protocol which which is going to hold some some token Supply denoted by sft uh it's going to have some uh reward inflation schedule given by rft and then it's going to hold some kind of uh Frozen liquidity you might think of this as liquidity that's either protocol owned if uh this Epsilon is positive or it's burned if Epsilon is negative uh and then you have a very simple sort of uh update for how the supply uh changes over time which is just you take this applied last time step you add uh however much will work out inflated uh and then you uh add or subtract the protocol and the perspective we're going to have from the validator the validator side is that again they're viewing this as a portfolio optimization problem they're thinking about I can collect returns from all of these different sources what should I do uh this is again a sort of a well-side problem they're going to do some kind of a mean variance trade-off right they're going to look at the sources of return that they can get so suppose those sources of return are I can earn from staking or I can earn from lending uh they're going to compute a mean return for each of those you know each of those sorts of course this could include other things like derivatives if they're if they're engaging those um and then they're going to trade it off against trade off the return against the variance of these with these assets uh and then here of course you have a risk parameter that tells you how you want to trade these two but the point is that this is a uh this is an optimization problem that you can solve uh if you have good estimates of the mean returns and of the variances so the important thing here is how does this how does this choice of portfolio actually update the returns that that uh that you're accruing from staking lending MVD except uh so here's a simple sort of model uh that's been uh uh that we've been looking at recently which is uh that every validator is going to have some staking yield that's going to come from two sources so one source is just a natural uh inflation of the rewards and another source which I think is of interest uh you know for uh for this event is is what we're calling sort of this Mev bonus it looks any additional value that comes from the application layer uh that is then redistributed back to the validators and this is going to be redistributed back in sort of a pro rata fashion relative to the portfolios that they're holding so I look at uh all of the rewards that come from uh uh just from the inflation of the token I look at all of the entity then I'm trying to redistribute and I send it back to the validators proportional to uh their portfolios and then you have a uh analogous sort of lending yield so you have yield that just comes from uh from your you know favorite lending protocol which takes on sort of this uh form that depends on the utilization so you look at how much uh borrowed demand there is and then you uh scale It Up by sure some risk-free rate and you update the uh the The Lending yield at type T serve according and so these are some sort of uh staking Landing dynamics that you can try to analyze of course uh here I'm just modeling sort of the deterministic part of these Dynamics I'm not actually modeling uh the randomness uh but you can sort of add that in and what we're trying to understand is how do the portfolio decisions of these validators uh namely by solving that that optimization problem the last slide uh and the fact that you have some control over this parameter how much Med you want to redistribute back into the system how does that affect the incentives here uh and in particular does it help us avoid some bad uh outcomes that we might otherwise you know have if we didn't do this we didn't redistribute this I meet me back so let me just sort of do the first the first part which is it's it's been known since sort of around 2019 and 2020 that staking which is this privileged sort of source of return that is securing the chain is competing with other sources of returns like lending endurance so in particular uh this this paper in 2019 uh by tarun showed that if you want to avoid uh sort of uh staking uh percentages going very low or below some threshold you really need uh these inflationary block reward schedules in order to achieve this if you just have sort of constant block rewards uh and certainly if you have a deflationary reward schedules uh then you're going to end up in situations where uh all of this uh all of the validators are roughly you know moving to uh to lending and you no one's taking so the the security of the networks breaks down uh and this implies that for proof of stick protocols need to actually incentivize validators to keep staking and avoid looking for other source of returns uh they might look for them of course they might look for them off chain but we're not modeling that right now we're just modeling how much they can get from activities that you can you can actually monitor and this is also turns out to be true for uh staking versus uh sort of uh derivatives so it turns out that there's certain kinds of face transitions where the validators are uh the the derivatives are in fact parasitic on the on the on the proof stake system and so this sort of sets the stage for well if we want to solve this of course one one way to solve this is just to inflate the rewards and then just you know keep uh uh keep you know validators taking that way but we have sort of another lever available to us now uh which is uh Mev uh and the question is can this any be bonus in fact act as a way of bypassing this problem of uh having inflationary reward schedules or having to inflate your token too much in order to secure uh in order to secure the network and so the question is how does this you know sort of mathematical question is how do these Dynamics sort of depend on this parameter Alpha and on this uh schedule uh on this med extraction schedule queue so one assumption that you can try to make is that this Q this this med extraction schedule is in some sense dependent on the lending on the yields that you're getting from lending and why do what is the reason to believe this might be the case well because lending yields are roughly correlated with the rates at which liquidations are happening uh and you might want to say something like nav in the future is is going to be correlated with the number of liquidations that are happening so you could sort of try to put these modeling assumptions and it's actually this this did turn out to be the case during say the Terra collapse in 2022 but we want to understand how these Dynamics behave as a function of this Alpha and one can do sort of similar kinds of experiments and sort of theory uh but the upshot here is that you can show that if this Alpha is sufficiently larger if you're actually doing this redistribution back to validators you can avoid having to do this inflationary sort of pilot inflationary reward schedule and in fact you can get away with things like constant uh inflation and even in some cases deflationary rewards something like a Bitcoin uh reward schedule uh which uh the staking sort of uh and lending papers sort of 2019 said would not work so if basically validators are allowed to be incentivized to state from sort of this application layer value that's collected by the protocol then you can sort of massively reduce the requirements for necessary didn't sound device validators to state and this is sort of uh very interesting because uh otherwise you would have to you know you would have to find some way of keeping them uh keep keep keeping them engaged and trying to maintain security so what I want to say now is that Med redistribution sort can act as an incentive mechanism to prevent people from uh from for pulling stake away from uh from from the network and in some senses acting uh as a mechanism more generally uh uh to incentivize can be used as a as an a mechanism to incentivize good behavior in proof stick protocols so usually we think of meds sort of this parasitic uh sort of thing but it it has these use cases as trying to incentivize uh sticking words but of course this is not the end of the story right because uh all I've said is that if you if you redistribute this thing back it might sort of help you know help secure the network uh but the way that you do the redistribution and sort of the mechanics of this redistribution actually matter matter a ton uh so uh you know it's it was noted that if you have these validator pools that are uh that are uh doing this smoothing or redistribution where they're uh paying out MBD rewards uh and some proportion to the amount that everyone has staked this can actually reduce the variance of the returns that validators are collecting uh and uh so basically the smoothing is is allowing validators to have some kind of predictable recurring revenues uh and this also because if your costs are the way we set up this portfolio optimization problem they're trading off a risk reward uh it might sort of have uh it might cause validators to have less propensity to shift their portfolio allocations radical they they might have more stable allocations over time and this might be desired for various reasons uh not including you know just you know you you want you don't want them to move around their stake temperature so there's this predictability problem which is you know how do you how do you how do you do uh redistribution to reduce variance but uh I now just at the end just want to end on some future directions that uh redistribution sort of uh needs to think about or redistration research these thing about which is the first one that immediately comes to mind is what are well what are the centralizing Tendencies of this redistribution if I'm if I'm taking this this Revenue that's uh uh that's been collected by the protocol I'm just passing it back to the validators does it set up some kind of uh bad feedback loops that uh sort of uh end up centralizing stake uh or end of centralizing you know a certain validator so I think this is a very important problem that uh I think should be studied a lot more and then the next kind of class of questions uh that I uh I was thinking about future future directions is how can we use sort of these existing transaction fee mechanisms uh that that are already present uh in perfect Networks they could be that so they could be modified to implement redistribution and practice and why does this matter well you need if you're doing this redistribution you need actually some way to ensure things like off-chade Agreements are not happening uh offshade agreements between uh validators themselves and or validators and uh and you know and and other parties uh and sort of this is roughly the question like what is the Cooperative game theory of validator tools do they have an incentive to actually stay in the pool and collect these rewards do they have an incentive defect uh and collect rewards in some other way and not do the redistribution so I think uh uh the game theory is sort of the Cooperative game theory of these validator pluses uh is sort of relatively understudied and it'll be very interesting to see how this redistribution actually affects people's propensity to participate in the in these ports and then broadly uh can we prove things like uh sort of the closed loop incentive compatibility of this mechanism that I'm going to do this redistribution after already collecting Mev revenue from uh from users uh what is sort of the closed loop and sentence structure of this of this process uh I think that would also be very exciting to study uh so yeah so roughly what I wanted to end on is and maybe redistribution can act as a way of incentivizing good behavior at least from a security from an economic security perspective uh Improvement stake protocols uh and can sort of allow you to avoid these really bad inflationary sort of exponential inflationary reward schedules and make them sort of better uh and perhaps even constant or deflationary in certain environments um however this comes at a pretty you know potentially comes at a big cost which is you might end up you know centralizing uh uh the validators and also there might be other kinds of game theoretic phenomena that are happening like off-chain agreements between validator pools or between members of the validator pool to defect from the redistribution that they're uh so with that I will uh just end here and if there's any questions we have time for questions