Introduction
The Helium community has made a mistake. Implementing "net emissions" eventually removes any incentive for anyone to hold HNT. This is a serious problem for those of us who believe in the future of Helium and, more generally, DePIN, so let us consider it.
In the deflationary burn-and-mint model, tokens are destroyed and created, with the rate of burn dominating the rate of mint. The mathematical model describing this is given by
\[
\begin{align}
-\dot V &= -\rho V - \frac{w}{M}V + y \newline
\dot M &= - u + w \newline
u &= \frac{M}{V} y
\end{align} \]
where $V$ is the fiat value of the network, $M$ is the amount of tokens in circulation, $w$ is the mint, $u$ is the burn, $y$ is the fiat revenue, and \(\rho > 0\) is the market discount rate. The model above is aggregate and derived based on a much more complex model of individual behavior and competitive strategy. It describes burn-and-mint tokenomics generally and, in particular, does not assume deflationary tokenomics, i.e., that $u > w$.
As considered elsewhere on this blog, the problem with deflationary burn-and-mint is that, if $w$ tends to zero, reward issuance $u$ eventually follows, meaning that miners might one day not receive adequate rewards. The concept of net emissions, introduced in HIP-20 at the same time as the invention of deflationary burn-and-mint, seeks to remedy this by emitting a minimum amount of tokens $w$ that is the lesser of $u$ and some constant $K$. We will analyze this in detail, but let us note that the problem becomes immediately apparent at equilibrium \(u = w\). In this case, $$ -\dot V = -\rho V - \frac{u}{M}V + y \newline = -\rho V $$ where we used the fact that \(u = \frac{M}{V} y\) to cancel out the $y$ term.
The implication is that any network implementing net emissions is worthless at equilibrium because the solution to the value equation is \(V = 0\). While it may not currently pose a problem, the concept of net emissions is fast becoming entrenched in the Helium tokenomics with the introduction of HRP-2025-03.
Before anyone runs a victory lap, please take some time to read this post, where I show that the dominant strategy of each HNT token holder in the presence of net emissions will eventually be to convert all their HNT to fiat as fast as possible.
Notation
List of important symbols:
\(V_k\) - value (NPV) function
\(M_k\) - circulating token supply
\(y_k\) - fiat network revenue
\(u_k\) - token outflow (burn)
\(w_k\) - token inflow (mint)
\(\gamma\) - time discount factor
\(\gamma_d\) - token deflation factor
Analysis
The derivation of the canonical equations is rigorously presented in this conference paper. A more accessible and less rigorous derivation is available on this blog.
Having given some thought as to why the concept of net emissions is so attractive, it seems to me that the proponents of net emissions may not recognize that something can have a price but still hold no long-term value. The well-known Twitter thread by JM Fayal, co-author of HIP-20, conflates the existence of a token price with the existence of a discounted present value and exhibits this misconception.
The problem becomes evident in the discrete-time case, where it is easier to see the dilution of token holders by those who obtain newly-minted tokens, e.g., miners: In discrete time, every participant must choose how many tokens to convert to fiat (either by buying direct credits or selling to someone in need of direct credits) and how many to hold. At equilibrium, the value to the holder must remain the same before and after the sale; it can so happen that the dilution is large enough that the holder has no incentive to hold on to their tokens and would be better off converting them all into fiat.
The result is a monetary collapse for, while the token might still have a price because fiat demand always exists, holders are in a race to dump their token as fast as possible. The only limit is the rate of mint.
This remainder of this section presents an analysis of how this collapse occurs in a model of the Helium network tokenomics.
Valuation of the Helium network
The discrete-time canonical equations are given by
\[
\begin{align}
V_k &= \frac{M_k-u_k}{M_k - u_k + w_k}\gamma V_{k+1} +y_k \newline
M_{k+1} &= M_k - u_k + w_k \newline
u_k &= \min\left\{\frac{y_k}{\gamma V_{k+1}+y_k}(M_k + w_k),M_k\right\}
\end{align}
\]
The Helium network is semi-deflationary, with \(w_k\) halving every other year and any burn \(u_{k-1}\) less than or equal to $K$ being re-emitted. To simulate this, we introduce the relationship
\[
\begin{align}
w_{k+1} &= \tilde w_{k+1} + \min\left\{K,u_k\right\} \newline
\tilde w_{k+1} &= \gamma_d \tilde w_k
\end{align}
\]
where \(\gamma_d\) has been introduced as a deflationary factor in place of a schedule.
As we have already shown in the Introduction, the above leads to monetary collapse. One way, and perhaps the only way to avoid this is to use a fiat-fixed rewards scheme as introduced here. If one wishes to couple high deflation in the early years with stability in the later years, this can be done as well. We therefore consider the following scheme
\[
\begin{align}
w_{k+1} &= \max\left\{\tilde w_{k+1}, 0.5\frac{M_k}{V_k}y_k\right\} \newline
\tilde w_{k+1} &= \gamma_d \tilde w_k
\end{align} \]
where at least half of network revenue is re-emitted to miners in order to sustainably reward them.
Results
Steady-state simulation
In the first simulation, we assume a constant revenue $y$ of $1 billion per year. We simulate the net emissions case with a limit $K$ of 50,000 HNT per month. We choose the initial circulating token supply \(M_0\) to be 6 million HNT and the yearly discount factor \(\gamma\) to be 0.9.
The results clearly show a collapse at about year 18 with an impact on the tokenomics throughout the simulation. In the first subplot, the value of the blockchain is consistenly lower than in the fixed-fiat case, with monetary collapse leading to \(V = y\). The fact that the value does not become zero is a discretization artifact; the faster the update time, the faster tokens may move and the faster value tends to zero, as in the continuous-time case considered in the Introduction.
The second subplot shows that the token supply collapses to \(M = w\) as expected; the only tokens held are those that have just been minted and are then immediately ready to be sold between ticks. The third subplot shows that price exists in both cases but, due to the lack of liquidity in the case of net emissions, mean that price is not a measure of value. The final subplot shows the value transferred to miners. In the case of net emissions, the entire value is transferred after collapse and this is why there is no incentive to hold the token.
Growth simulation
We now consider revenue growth where the revenue $y$ evolves according to the logistic equation $$y_{k+1} = y_k + ry_k\left(1-\frac{y_k}{y_s}\right)$$ where the initial revenue \(y_0\) is $2.4 million per year, the rate $r$ is chosen so that revenue doubles in the first year, and the steady-state revenue \(y_s\) is $1 billion per year.
The results confirm monetary collapse, this time by year 37. Curiously, in the case of net emissions, more value is accrued to holders at the beginning. This is because miner rewards, measured in fiat, are much lower in the case of net emissions until the day of collapse, when the switchover happens rapidly. In any case, a higher initial token value should not play a determining factor here as one could always lower the amount of reward going to miners in the fixed-fiat case.
Another curiousity is the rapid, exponential convergence to steady state experienced in the fixed-fiat case. This is typically good to see in any response as it implies predictability and suggests the presence of robustness.
Conclusion
This post considered the concept of net emissions in the tokenomics of the Helium network and demonstrated that its implementation eventually results in monetary collapse as holders are aggressively diluted by newly-minted tokens.
What should be done
Even though the simulations suggest that the problem may be years away from appearing, it is unclear how chaotic market forces might impact poor tokenomics choices. The Helium community should probably fix this in favor of provably stable and, preferably, robust tokenomics.
In particular consider that, if the price of the token does not reflect the value of the network, then it becomes difficult for service providers to make economic decisions. Even well before collapse, because the market capitalization of the token does not equal the discounted cash flow of revenue, the use of net emissions makes it impossible to measure the impact of economic decisions on the overall health of the network.
