A Primer on Game-Theoretic Analysis of DePIN Protocols

As DePIN’s market share grows to $30 billion in an estimated $2.2 trillion addressable market, the formal study of the sector remains sparse. While DePIN projects focus on rapid iteration and implementation, formal research plays a crucial role in solidifying the proven elements of protocol design—pouring concrete into the foundations, in a sense —and occasionally proposing new designs. If founders build for too long on the wrong foundation, their structures will eventually fail. 

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DePIN teams may reach for well-established research in other sectors to inform their protocol design. DeFi and L1 design is well explored in the literature - just about everyone in crypto knows what FlashBots and LVR are. Founders and protocol designers in DePin assume that they can glean insights from these papers, repurpose or reinterpret the results, and apply them to their own projects. 

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The problem, however, is that DePIN is structurally different enough to warrant its own study. By applying results from DeFi research to DePIN protocol designs, founders are unknowingly importing assumptions and frameworks that may not be applicable to their own protocols, even if the end results or theorems seem perfectly sound at face value.

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Our research will focus on an interesting and growing vertical in the DePIN space: energy. As we will discuss in detail, energy protocols require novel designs that have not been formally modeled. Our initial scope will be modeling the structure of Glow, a quickly growing solar energy platform, and analyzing the primary drivers of energy DePIN token value. In the long-term, these shorter articles will culminate into a full-length paper on the topic.

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Preliminaries

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Defining DePIN

Defining DePIN robustly can be difficult – Decentralized Physical Infrastructure Network sounds intuitively correct when thinking about Helium or Hivemapper, but it becomes clear that you can classify most crypto protocols as physical infrastructure with enough squinting. Solana is technically a network of decentralized physical nodes (computers) that act as infrastructure, as is Ethereum or most L2 sidechains. To avoid this, our first task is to clearly and unambiguously define DePIN:

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1. A distributed blockchain protocol with the primary goal of coordinating and rewarding a network of specialized hardware nodes.
   • Specialized hardware is physical infrastructure to produce or generate a service beyond consensus.
2. Nodes must be producing a non-consensus service for sale first and foremost, and tokens are minted as a result of their service provided. This differentiates DePIN from protocols in which minting tokens is the goal output of the nodes.
3. The protocol must facilitate the market for the service provided.

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Why Energy? 

When selecting a DePIN sector to analyze, we look to sectors that present sets of actors with minimal overlap, well-defined limits on what can and cannot be part of the protocol, and structures that can be accurately modeled without exceeding complexity. This is not to avoid complexity as a whole, as our analysis will inevitably become more sophisticated, but to develop and verify a simpler initial model. Additionally, energy protocols fall cleanly into our definition, as energy producing hardware is clearly specialized and nodes operate with the primary goal of generating energy reliably.

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Within the set of energy protocols, we specifically look at those that directly incentivize the generation of energy. There are several energy DePIN protocols that coordinate actual energy generation to energy derivatives trading. One of these protocols that we look to analyze is Glow, a protocol aimed at implementing its own carbon credit standard for solar farms. Glow has gained traction with significant investment and attention, onboarding 68 solar farms with a combined 50,000 panels contributing to the network. Its unique incentives and protocol design make it a strong candidate for analysis.

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Our Approach

Developing a model of a cryptoeconomy is an open problem space, and the tools we choose are motivated by specific desired outcomes. In general, we are looking for actionable insights, meaning that we want to be able to easily recommend optimal design choices based on our model. Instead, our research aims to model each design choice and suggest new structures altogether when the currently implemented choices are all insufficient. 

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Towards this end, our model can incorporate a few modeling techniques: 

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• Agent-Based Analysis – models the individual agents and their actions as they participate in the economy. This approach is powerful for finding second and third-order effects of agent behavior. By modeling agents with some stochasticity, we can simulate and uncover results of our protocol design not implied by theory. 
• Dynamical System Analysis – a popular approach for cryptoeconomic modeling, adapted from use in ecological and evolutionary modeling. We model the economy as a series of states evolving over time, describing structures like token supply and agent behavior by how they evolve from timestep to timestep. 
• Game-Theoretic Analysis – model the agents as players in a game, where we quantify their incentives as functions of one another. This model also does not explicitly define the protocol or exogenous structures, but incorporates them into each agent’s incentives. 

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Our full study will contain a mixture of all three of these tools, but for the scope of this article, we will illustrate applications of light game-theoretic analysis to parts of Glow’s economy. 

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An Introductory Model of Glow

Glow takes a different approach from other DePIN protocols in coordinating distributed energy. While building a decentralized protocol to actually serve electricity on the grid is not feasible, DePIN can create net impacts by incentivizing users to electrify or sell energy back to the grid. Glow's mission is to redefine the carbon credit standard by implementing their own design and network. An important implication of this is that Glow’s network carbon credits are not officially recognized as part of the Verified Carbon Credit Standard. Instead, their goal is to grow the legitimacy of this standard as a new protocol for more efficiently allocating carbon credits.  We’ll illustrate an analysis of Glow using game-theoretic methods.

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Network Overview

Glow’s protocol is designed to onboard solar farms, incentivize them to maximally produce carbon credits, and sell those credits on the market. This is accomplished with two tokens, GLW and GCC. GLW is the protocol token and the foundation of the protocol – value should be accrued to this token as much as possible, as farms, auditors, and councils are all incentivized with GLW. Glow Carbon Credits (GCC), are tokenized carbon credits produced by farms. GCC is auctioned off to buyers, who must purchase using GLW, creating buy pressure and linking value between the tokens. Additionally, GLW used to purchase GCC is burned, adding deflationary pressure.

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Solar Farm Incentives

Glow onboards solar farms by requiring them to commit 100% of their revenues from electricity generation to the protocol for 10 years. The protocol requires farms to pay a ‘Protocol Fee’ in USDC, which roughly equals the total revenue of the farm over 10 years, along with other variables like the expected growth of energy prices. The Protocol Fee is not added to a rewards pool for 16 weeks, after which it is vested each week in equal installments for 4 years. After paying this fee, farms are rewarded in two ways:

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• GLW Rewards – for 4 years after paying the protocol fee, farms are eligible to receive GLW rewards. GLW is inflated at a fixed rate weekly, and farms receive a portion equal to the ratio of their weekly Protocol Fee installment and the total rewards pool for that week. If a farm's weekly vest is $1000 USDC and the rest of the farms vest $9000 USDC that week, the farm gets a tenth of the GLW inflation.  
• USDC Rewards – Farms are rewarded based on the portion of the total GCCs produced in a given week. If a farm produces 10 of 100 total GCCs produced by Glow in a week, they receive 10% of the USDC reward pool for that week. 

 If we model solar farms as agents, their utility functions would look like this:

This simple utility function helps us understand how solar farms quantify a choice: should I join Glow? If we assume farms to be rational, any value greater than zero means that they should join the network. To expand on these terms, we account for the fact that farms must discount future revenues based on their time preference 0<i<1, or how much they value receiving revenue now as opposed to i weeks in the future. As the number of weeks in which they are vested may be changed in future protocol updates, we denote N to be the number of weeks they are locked into Glow.

What does this imply? Farms have to believe that the 10 year discounted rewards from Glow offset their revenues and the cost of procuring their upfront capital for the Protocol Fee. This implies that GLW tokens must appreciate over time, as farms must have confidence that the rewards pool will equal or exceed their revenues if they had not joined Glow. Note that this assumption varies depending on how competitive a farm is, but we are collapsing those incentives into one function for simplicity. For example, a highly competitive farm comprising a larger portion of the rewards pool will earn their revenues back, and any non-zero value of GLW rewards will result in a profit. Less competitive farms will not earn enough USDC to make their revenues back, and are more reliant on GLW value.

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An additional risk is the continued validity of Glow’s Carbon Credit standard, which is a proprietary standard not recognized widely. The value of GLW is tied to the value of GCC, as buyers on the market must purchase GCC with GLW. If the value of the carbon credits is not sustained, there is reduced value accrual to GLW. In a worst case scenario where GCC demand reduces and the flywheel of joining farms dries out, protocols will earn very little rewards after 4 years of their 10 year buy-in. 

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In reality, Glow rewards have produced massive returns on investment for early adopters, as is standard for bootstrapping protocols. Some farms have seen 2-3x returns in the first week of reward eligibility. Rewards will and should reduce dramatically for late adopters, but must still be attractive enough for farms to continue joining the protocol.

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Glow’s Incentives

On the other side of this game, Glow’s problem of onboarding farms is complex. For early adopters, the size of their farm is less relevant, as the pool of rewards is sparse and the initial speculation around GLW will incentivize all types of farms to join. Early adopters have a higher chance of comprising a large portion of the reward pool and receiving more GLW. As this pool of rewards dilutes, however, only farms with large enough protocol fees to gain a substantial share of the pie are incentivized to join. To combat this, Glow’s main solution is to ensure GLW appreciation. As the reward pool dilutes, the value of GLW must increase proportionally.

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Additionally, there is an edge case in which farms can join Glow early, earn massive returns on their investment, and stop producing Carbon Credits or electricity altogether and invest their returns elsewhere. This is an extreme scenario that requires the rewards pool to dry out, as running a farm has little overhead and they can continue earning USDC for producing Carbon Credits. An interesting theoretical result of this, however, is that malicious farms that stop producing Carbon Credits actually reduce the competition for honest farms – if a farm stops taking a pie of the USDC rewards by not producing GCC, other farms can take a larger cut, and new farms are incentivized to join and take their spot. While this is an edge case, it can cause a misaligned incentive for farms to churn after capturing value and creating space for more farms to do the same.

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To try and simplify this web of incentives, we can model Glow’s utility as a tradeoff between onboarding farms and GLW devaluation. Note that we are heavily abusing mathematical notation for the sake of simplicity. 

The first term represents the flow of joining farms. What are the inputs to each of our terms? For joining farms, their incentives are simply GLW value and the size of the reward pool, which is a function of the number of farms already onboarded and their sizes. GLW devaluation, on the other hand, is a catch-all term that encompasses the inflation of GLW, the continued demand for GCC (and the resulting GLW burn), and other non-quantifiable metrics like hype and interest. 

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The most controllable of these inputs is GLW inflation and burn. Currently, the inflation rate of 230k GLW weekly is fixed. The deflationary pressure is from the GCC market, in which the GLW used to purchase GCC is burned. In an ideal scenario, this deflation will outpace inflation and prop up the value of GLW. 

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Interpretation and Building a Complete Model

Within this set of utilities, protocol designers have a model for how the moving parts of their design affect each other. When making decisions and tweaking parameters, these kinds of models help provide a birds-eye view of the second-order effects. The natural next question for protocol designers is what the theoretical ‘equilibria’ of our model look like. To accomplish this, we will build out the technical details of each agent’s utility, relate them as a dynamical system, and solve the optimization problem for the variables we’re interested in. For example, a more rigorous utility function for the protocol looks like this:

R(t) is the revenue without Glow and GLW(t) and USDC(t) represent GLW and USDC rewards for week t. CCFarm(t) represents the cost of producing Carbon Credits in week t, and R(t) is a farm's projected revenues without joining Glow. We’ve expanded the terms to be more specific in the amount of GLW and USDC farms earn while also accounting for the cost of producing Carbon Credits. The function still is not fully detailing terms like Cost of Capital and GLWFarm(t), but we will expand on these terms in our next piece. With this groundwork, we can define rigorous utilities for farms and the protocol (including the agents that make up the protocol), and try to solve an optimal value for GLW emissions and farm onboarding. 

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The result of this work can help us answer some more specific questions. For example, Glow’s reliance on GCC demand can be reduced by introducing new ways to reduce the circulating supply of GLW. Token buybacks, dynamic emissions, and staking are all potential solutions, but require further study to prove out. What are the optimal inflation scenarios in different demand conditions? How does adding token buybacks change the incentives of farms compared to dynamic emissions?

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Conclusion

Our simple model in this piece is a good starting point to think about the dynamics present in a DePIN protocol. With an understanding of the general flow of tokens and value, we can dive deeper on individual utility functions and expand them to make them more rigorous. As we develop theoretically, our tools of dynamical systems and simulation can help us suggest concrete improvements and issues with the protocol. Glow’s protocol design can be modified experimentally to find more optimal inflation schemes and to add guardrails on GLW value which we will explore further and compare to entirely different protocol designs. 

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Additionally, Glow’s design has novel features that may be generalizable to all DePIN protocols. For example, GCC is essentially a token mapped 1:1 with units of service, and other protocols may benefit from using this dual-token model to more directly tie their rewards token to the actual output of the protocol. Our goal is to formally build this model out and study the implications in other DePIN sectors, beginning with other energy protocols like Daylight. 

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Thank you to the Glow team for helpful discussions and review of our work.