Solana Issuance From First Principles

Solana has issuance for two reasons. The first is to incentivize validators to stake the native token, increasing security. The second is to incentivize staked validators to participate honestly in the protocol. These may seem similar but it is possible to have one without the other. For example a network might unconditionally issue tokens to validators regardless of whether they participate in the protocol and achieve security through slashing but have no incentives for validators to vote in a timely manner. Theoretically it is possible to incentivize honest behavior in the protocol using a stick approach rather than a carrot approach e.g. slashing; however, psychologically slashing carries very negative connotations so it is best to incentivize good behavior with carrots rather than sticks. 

So higher issuance gets us more security and better incentives to participate honestly in the protocol  but comes at the cost of a net heat loss due to the inefficiency of transfers within the system. We can write this in terms of the utility for the network as a function of issuance:

U(i) = V(S(i)) + W(H(i)) - λi

Where V(S(i)) represents the security term which has decreasing marginal utility in stake amount S(i) which is a function of issuance, and W(H(i)) represents the honesty term which is the utility gained from honest participation in the protocol H(i).

Issuance as a Leaky Bucket

The final term is λi which I call the leaky bucket cost. This represents the fraction of transfers lost due to taxes or middlemen with market power. 

Critically, λ < 1. I think there is a common misconception that every drop of issuance is a cost to the network but mathematically if these transfers were perfectly efficient, meaning they did not result in any increased tax burden or fees from staking providers with lots of user lock in (e.g. Binance, Coinbase), then issuance would not be costly to the network at all. Unfortunately we live in the real world where taxes and market power do exist so λ > 0.

To compute the optimal issuance policy then, assuming V, S, W, and H are all increasing in their inputs, we can take the first order condition and solve for i:

λ = S'(i)V'(S(i)) + H'(i)W'(H(i))

So we have an equation that should be true if we are at optimal issuance, it seems natural to ask whether that equation is satisfied today. Before we can do this we need to estimate λ. Looking at the current validator commission % it seems the going rate for commission is somewhere between 4-8%. Many validators without their own pool of users to draw upon have 0% commission. On the tax side tax treatment differs widely depending on jurisdiction and whether the entity filing is an individual or corporation. For US individuals in the highest income tax bracket, validator rewards are treated as ordinary income and taxed at a 17% (37% vs 20%) higher rate than long term capital gains. For US companies, the tax rate on ordinary income and capital gains is the same but capital gains taxes can be offset by losses.

Offsetting is important even if the market cap of Solana is flat and that is the only holding in the portfolio of the entity because inflation induced capital losses cannot be used to offset validator rewards which are treated as ordinary income.

Based on stake commission data above and tax treatment (which is most acute for US citizens filing individuals who don’t make up the whole population of stakers) we can place somewhere in the range of 5-10%. At current inflation rates of .0435 and FDV of 120B that's

λi ≈ .1 * 120B * .0435 = 522M

This number is on the same order of magnitude as annual Solana fees.

Is Today's Issuance Optimal?

Now that we have an estimate for λ, we can compare it to the other terms in the equation. The S'(i)V'(S(i)) term is relatively small because V'(S(i)) is not large. Ask yourself this question: if Solana doubled its security budget today would that cause any marginal increase in usage of the network? In my opinion the answer is probably not. The other term H'(i)W'(H(i)) is small for a different reason. Recently, due to the introduction of timely vote credits, we have seen validator performance on the network greatly improve. Validators are now missing very few slots per epoch, voting in a timely manner almost every slot and fork rate is very low as a result. Based on this we know that H'(i) must be very small because there isn’t really much more utility we could get from stronger incentives to run a performant validator given that we have so few missed slots and forks on the network today.

A Market Based Alternative

Given this analysis it seems clear that issuance today is higher than it should be under the optimal policy. But what does the optimal policy look like? In SIMD 228, we proposed a new market based issuance policy that lowers issuance when stake rate is higher. Under the proposal the new inflation rate and corresponding validator rewards would be

r(1 - √s)

v(s) = i(s)/s = r/s * (1 - sqrt(s))

Why This Curve?

Why pick this curve as opposed to a variety of other curves we could’ve chosen?. There are two vectors on which we should evaluate the curve. The first is generosity: does the curve still give enough rewards that we can expect to have sufficient stake to secure the network, even if MEV rewards change substantially from here?

For this curve, ignoring MEV rewards we would see the same validator rewards as we have today at 65% of the supply staked with 30% of the supply staked.

Under today's reward curve issuance rewards are around 6.25%. Solving for the staking rate at which rewards would be the same under the new curve we get:

0.0625 = *(1 - √s) 0435/s
(1 - √s)/s = .0625/.0435

s ≈ .3

This means that we know with certainty that the staking rate after the change to be between 30-65% and very likely in the 45-55% range. So we know the curve is generous enough.

The other vector on which to evaluate the curve is responsiveness. If the curve is too responsive to changes in the staking rate, then it could result in discouragement attacks where large stakers prevent others from staking either by censoring stake transactions or by bribing them not to stake. The more responsive the curve is, the more incentive there is to participate in these activities. The 1 - √x curve strikes a happy medium in that issuance rate is still responsive to stake rate but not so responsive that discouragement attacks would be worth the effort to engage in.