Unlocking Monad’s Potential: The Critical Role of Block Production Economics
by Edward Shi and the aPriori team
Introduction
In this research post, we delve deeper into the principles of block production economics and how blockspace auctions are inevitable under a monopolistic block producer. We will explore the block production economy from an incentive engineering perspective, highlighting gas and MEV as critical design components that any core protocol team must address to maximize welfare and efficiency. We will then systematically discuss how aPriori’s blockspace auction minimizes MEV-induced spamming, fostering a more intuitive and safe user experience through orderly and predictable execution of users’ intended actions.
Finally, we will demonstrate how blockspace auctions like aPriori can enhance Monad’s block production economy by:
Reducing spam.
Maximizing welfare by ensuring block producers align with the network’s objectives, thereby achieving “user-block-producer incentive compatibility”.
To provide a comprehensive and unbiased analysis, we will explore these benefits using two game-theoretical models: one developed by our research team and another by Roughgarden et al. (2024).
Executive Summary
Main Take-Aways & TLDR:
Need for a Robust Block Production Economy: Monad’s system must be complemented by a healthy, fair, and transparent block production design. Strong incentive alignment will enhance the user’s experience and further strengthen Monad’s robustness.
Block Space Auction: A block space auction is necessary due to the finite nature of block space and the monopolistic power of the block producer over sequencing. From an incentive design perspective, gas acts as a crucial decision-making lever for the core protocol team to align incentives and maximize global welfare.
Spam Minimization: While Monad’s Carriage Cost design inherently deters spam, aPriori’s auction aims to minimize MEV-induced spamming. It does so by fundamentally altering searchers’ dominant strategies, linking strategy inclusion probabilities with bids rather than encouraging spam.
Incentive Compatibility: In a post-MEV world, no standalone gas mechanism design can fully optimize the user’s experience. An aPriori-style auction is essential for achieving incentive compatibility. Such auctions ensure that MEV-related block space is priced based on economic value rather than the block producer’s private valuations.
Engineering Incentives for Optimal Block Space Auctions
One Block Producer per Slot ⇒ Block Space Auction
We assume that for any given slot, there is one block producer with monopolistic power over sequencing the block. This block producer uniquely determines both the inclusion and ordering of transactions. We will explore auctions in a multiple concurrent leaders setting (Solana, 2024) in future blog posts. Given the finite block space per time slot, the block producer must allocate this scarce resource, effectively conducting a blockspace auction each time they sequence a block.
Game Setup: Auction Participants
We will use the game theory model developed by (Roughgarden et al. 2024) to better formulate the blockspace auction problem. First, we define a block as a finite inclusion of a list of transactions (Txs) proposed by the block producer. A block is considered feasible if it respects the protocol’s constraints (e.g., maximum block size).
Next, we define a user as an individual or entity who submits a set of Txs to the blockchain. For each Tx t , the user has a non-negative valuation v_{t, gross} towards its inclusion in the proposed block. This valuation is further adjusted by the transaction payment rule function p. Notably, this cost is typically lower when a transaction is included but subsequently reverted. The user’s valuation function for the Tx t is:
Then, we define the block producer as the stakeholder determining the finality of sequencing the block (dba, 2024). For any given slot, the block producer selects a block B from a non-empty set B of feasible blocks, known as the blockset. We assume the block producer has the largest feasible blockset B, which may include:
Txs from the public mempool (if any), wallets, trading bots, order flow channels, etc.
The block producer’s own private transactions, including MEV strategy Txs or bundles created from other user’s Txs.
We also assign the block producer a private utility function, modeling the block producer’s surplus as
This valuation can take various forms, such as additive or quasi-linear. For instance, an additive valuation like
summing over all transactions t in B, might reflect the block producer’s attempt to build atomic arbitrages from transactions across different DEXes.
Global Welfare
The principle of welfare maximization dictates that a scarce resource like block space should be allocated to maximize the total utility of all participants in the game, which for simplicity, we assume here to include:
The users (including searchers, users from wallets, dapps, etc.).
The block producer.
The token or the currency holders.
We outline two further assumptions:
Assumption 1: For all participant groups involved, they have quasi-linear utility functions.
Assumption 2: Gas paid out by participants will be transferred between different groups of participants. For example, in EIP-1599 we can think of tip payment as a transfer from users to the block producer and base fee burn as a transfer from the block producer to token or currency holders.
We can now write the global welfare function evaluated on any particular block as:
where v_{BP}(B) is the block producer’s private valuation regarding the input block and v_t is the user’s valuation for the Tx t submitted.
Critical Auction Component 1: Gas
From an incentive design perspective, the core protocol team aims to maximize W(B), considering that the block producer has monopolistic power over sequencing the block B. Typically, core protocol teams develop the gas fee mechanism, or more formally, the transaction fee mechanism, which is hardcoded into the protocol specification as part of its opcode. This mechanism is intended to guide participants, especially the block producer, on how to build the block.
We define a transaction fee mechanism as a set of two rules:
Payment Rule: Define
\(p_t(B, \vec{b})\)as a function that specifies the payment for each transaction t in B from the creator to the block producer for including t in B, given the bids \vec{b} of all known transactions.
E.g. for both the first-price auction and the EIP-1599, the payment rule would be
\(p_t(B, \vec{b}) = b_t \ \forall t \in B\)
Burning Rule: Define
\(q(B, \vec{b})\)as a function that specifies a non-negative amount of fees to be burned for the block B, given the bids vec{b} of all known transactions.
E.g. for first-price auction
\(q(B, \vec{b}) = 0 \ \ \forall t \in B\)and for EIP-1599
\(q(B, \vec{b}) = \sum_{t \in B}r \times s_t\)where s_t is a publicly known gas limit for t and r is the basefee parameter. Together s_t and r defines the reserve price r x s_t.
Once the gas or transaction fee mechanism is determined, the block producer’s utility function is updated to incorporate both the payment rule and the burning rule. The block producer’s utility function for any given block B is defined as:
We emphasize the following observation:
💡 Given that the block producer has a private block valuation function v_{BP}(B) , the transaction fee mechanism (payment + burning rule) acts as a decision function through which core protocol teams can control to soft influence block producers in building blocks that maximize certain protocol objectives (e.g. user maximization, welfare maximization, incentive compatibility, etc.).
Attentive readers might wonder: if gas or the transaction fee mechanism serves as a lever through which block producers balance their private valuations with the protocol’s incentive structure, how effective is it? If gas alone can achieve desirable system-wide properties like incentive compatibility, why introduce additional auction structures? We will discuss the effectiveness of the “gas knob” shortly. But first, let’s examine another critical design factor: MEV and MEV-induced spam.
Critical Auction Component 2: MEV & MEV-Induced Spam
It is well recognized that empirically, MEV has turned out to be the most critical design factor influencing the block production economy. We summarize some of the key negative externalities arising from raw, unregulated MEV activities from the Chrous One research post (Franklin et al.).
Here's a table summarizing the negative externalities of ill-addressed MEV on Ethereum and Solana:
As evidenced by Jito on Solana and Flashbots on Ethereum, addressing MEV in a robust and sustainable manner has always been a major thread through which core blockchain protocols iterate (aPriori Research 2024).
aPriori’s Auction: Cutting MEV Spam
Introduction & Background
In this section, we will delve into the issue of MEV-induced spamming, beginning with a discussion on the robustness of Monad’s gas design against such spamming activities. We will then present a game-theoretical model to illustrate the fundamental incentives for searchers to spam in the absence of a structured auction mechanism. Furthermore, we will update the game-theoretical model to illustrate the effectiveness of implementing an aPriori-like auction in fundamentally altering searchers’ behaviors and reducing spamming.
Monad’s Defense against DDoS Attack Vectors
Deferred execution introduces a potential DDoS attack vector, as consensus nodes without access to the up-to-date state might include transactions from accounts that have exhausted their gas.
To address this issue, Monad introduces the concepts of carriage cost and reserve balance. These mechanisms effectively provide an account budget for “in-flight” orders. The carriage cost is charged against the reserve balance during consensus when the transaction is included in the block and is then deducted from the execution balance at execution time. Finally, the transaction cost is refunded back to the reserve balance after a delay period. This design ensures that nodes can check up-to-date expenditures, even without full state access when consensus is reached.
While Carriage Cost and Reserve Balance primarily focus on de-risking the potential of gas over-usage by users (for validators), we will demonstrate how aPriori-like auctions will structurally modify searchers’ dominant bidding strategies, thereby making Monad even more robust against MEV-induced spamming.
For the rest of this section, we will explore two scenarios and corresponding game theory models: one without an aPriori-like auction and one with it. These models highlight the positive impact of an aPriori-like mechanism on spam reduction by modifying Searchers’ dominant strategy settings.
Without Block Space Auctions
Modeling Assumptions
First, let’s explore why Searchers spam or send repeated strategy transactions (Txs) to the leading node. Searchers aim to get their strategy bundle or Tx included in the block, ideally with priority. If they notice a positive relationship between the inclusion probability and the number of transactions they send, they are incentivized to spam. This creates a negative feedback loop as searchers head towards a tragedy of the commons, where they’ll be increasingly forced to spam as others spam. This positive correlation often stems from the underlying node design.
In Solana's client architecture prior to version 1.18, the lack of global scheduling in its multi-threaded execution model led to indeterministic ordering, which inadvertently incentivized spamming as a strategy to statistically increase transaction inclusion (aPriori, 2024). Such randomness links inclusion and ordering to spamming behavior.
We can now formalize our empirical observations into a set of practical yet general modeling assumptions:
Inclusion Probability: The likelihood of a searcher’s transaction being included increases with the number of transactions they send, adjusted by a correlation parameter κ.
Cost: The cost for a successful transaction includes actual gas usage and prices, while failed transactions incur a reversion price.
Carriage Cost: As the Carriage Cost acts as a refundable deposit, we assume searchers always have sufficient operational capital, so it does not affect their PnL.
Model Setup
We define the following notations:
n_i is the number of repeating strategy Tx or bundle sent by searcher S_i
N is the total number of Txs or bundles sent by all searchers, where
\(N = \sum_{j = 1}^{n}{n_j}\)R is the reward for having the strategy Tx or bundle included and executed
p_i is the probability of at least one Tx from S_i is included, which is positively correlated with n_i and adjusted by the correlation parameter κ
g_i is the actual gas usage for the strategy Tx forwarded by S_i
ϕ_i is the actual gas price per gas unit for the strategy Tx forwarded by S_i
δ_i is the reversion price (per gas unit) modeled as the cost incurred by failed strategy Txs
Then we can write that the probability p_i that at least one strategy Tx from S_i is included, adjusted by the correlation parameter κ, can be modeled as:
Searcher’s Utility Function
We can model the Searcher’s utility function as the expected PnL for spamming the leading node, breaking it into two scenarios:
At least one strategy Tx gets included:
This event happens with probability. p_i.
The realized PnL is
\(R - \phi_i g_i - (n_i-1) g_i \delta_i\)which is the strategy reward minus the cost of one successful strategy Tx and the reversion costs for the n_i-1 failed transactions.
All submitted strategy Txs get reverted:
This event happens with probability 1 - p_i
The realized PnL is -n_i g_i δ_i since all submitted strategy Txs are reverted.
Searcher’s Dominant Strategy
Combining these, we derive the expected PnL as:
Substituting p_i = κ ⋅ n_i/N into the equation, we get:
To find the Searcher’s dominant strategy, we maximize {E}[π_i] via the first-order condition:
Assuming a symmetric Nash equilibrium where all searchers send the same number of transactions
we have N = n^2. Substituting into the first-order condition, we get:
Solving this quadratic equation, we find:
The equilibrium quantity of spam transactions sent in the absence of block space auctions has the closed form solution:
Here we plot n as a function of g_i, ϕ_i and reverting ratio δ_i / ϕ_i = γ in (0,1].
WLOG, we assume the correlation parameter κ=0.5 and MEV transaction return R=0.1 eth. Moreover, we choose two empirical reverting ratios, 0.9 and 0.3 to represent the cost of a reverted transaction against the reserved gas cost.
The results demonstrate that under equilibrium conditions, the spamming activities, as measured by the number of spamming transactions, exhibit a super-linear scaling relationship with both gas price and gas usage. Notably, this super-linear relationship is more pronounced for gas price compared to gas usage.
Implications
Under the assumption that a Searcher’s inclusion probability is positively correlated with spamming due to randomness in the validator’s client design, the Searcher’s dominant strategy is to spam the leader node with n repeated copies of the same strategy Tx. The number of repeated transactions n grows as the square root of the MEV strategy PnL (R - g_i ϕ_i - g_i δ_i) , normalized by (g_i δ_i) and scaled by the correlation parameter κ. This indicates that as the MEV strategy revenue R grows big relative to gas costs, Searchers are strongly incentivized to spam with a relatively large n. One other dynamic here that the simplified utility function does not account for is that due to the nature of nodes, it is possible that spamming also reduces the chances of competitor transactions being included. This would mean that n_searcher actually constitutes a negative term in the other searcher’s probability (Pi) function. This dynamic means searchers’ incentive to spam may be even more sensitive to R than the simplifying assumptions here predict.
With Block Space Auctions
Modeling Assumptions
Recall that Searchers will do everything they can to increase their inclusion probability p_i. Under the no block space auction case, if they see a positive correlation between p_i and the repeating number of Txs they send, they’re incentivized to spam.
Under a PBS-like auction mechanism, the searcher’s behavior and utility function change significantly. The inclusion probability is now determined by the auction bids rather than spamming the leader node. For practicality, we will analyze a PBS-style first-price sealed bid auction here, in which searchers typically bid slightly less than their value to maximize their surplus. This is due to the nature of the first-price auction, where the highest bidder wins but pays their bid price. We first outline the assumptions:
Bid Shading: In a first-price sealed bid auction, bidders often bid less than their true value (a practice known as bid shading) to ensure a positive payoff if they win.
True Value Incentive: Unlike second-price auctions, where bidders are incentivized to bid their true value, first-price auctions require strategic bidding to balance winning and maximizing surplus.
Searchers’ Strategy: Searchers must determine an optimal bid that balances the probability of inclusion and the cost of bidding, adjusting their bids slightly below their true value to account for competition.
Model Setup
We define the following notations:
b_i: Bid amount placed by Searcher S_i for strategy transaction inclusion.
β: Bid shading factor where Searchers apply to their true bid optimized for the first price sealed bid auction setting, where 0 < β < 1.
R: Reward for having the strategy Tx or bundle included and executed.
p_i: Probability that the bid b_i results in at least one Tx from S_i being included.
g_i: Actual gas usage for the strategy Tx forwarded by S_i.
ϕ_i: Actual gas price per gas unit for the strategy Tx forwarded by S_i.
Searcher’s Utility and Dominant Strategy
We can model the Searcher’s expected PnL in the first-price sealed-bid auction setting with the following two scenarios:
At least one strategy Tx gets included:
For simplicity, let’s model the inclusion probability as p_i = b_i/B, where B represents the total bid amount required to ensure inclusion. This normalization factor ensures that the inclusion probability sums up correctly across all searchers.
The realized PnL for this case is R - b_i - ϕ_i g_i
No strategy Tx gets included
In this case, the probability is 1 - p_i
The realized PnL here is 0
By combining these two scenarios above, we can then write the expected PnL as:
To find the optimal b_i, we also apply the first-order condition with respect to b_i and set it to zero:
Considering the bid shading factor with 0 < β < 1, we thereby have that:
here we conclude that in a first-price sealed bid auction, Searcher’s dominant strategy changes by bidding slightly less than their true value represented by
This strategic bidding reduces spamming incentives by aligning bids with the transaction’s economic values.
Comparison and Implication
We now summarize the comparison of MEV-induced spamming:
Without a block space auction: Searchers are incentivized to spam the leader node with n repeated strategy transactions, driven by the positive correlation between inclusion probability and n, along with the MEV strategy PnL and gas cost.
With a block space auction: In a PBS-like first-price sealed bid auction, searchers bid strategically based on the economic value of their MEV strategy, leading to a more efficient and less spam-prone process.
These scenarios are not mutually exclusive. Even with a block space auction, if randomness persists in the block producer or leader node’s client architecture, inclusion probabilities may still depend on the auction bid and the number of repeated transactions. The key takeaway for cryptoecon designers is that searchers will maximize their inclusion probabilities by any means. Therefore, to mitigate negative externalities, block space auction providers like aPriori must collaborate with validators to ensure searcher inclusion probabilities are primarily influenced by truthful bidding, reducing reliance on spamming.
Reimagining Incentives: Overcoming the Impossibility Theorem with aPriori in a MEV-Rich World
In the previous section, we identified the gas or transaction fee mechanism as the core protocol team’s decision tool to influence block producers to balance their private valuations with the protocol’s desired incentives. Now, we delve into the Impossibility Theorem by Roughgarden et al. 2024), which states that under a game-theoretical setup, no non-trivial gas or transaction fee mechanism can optimize users’ bidding experiences if block producers always aim to maximize their private incentives.
User Utility Affected by Block Producer Valuations
First, let’s examine how the user’s utility or bidding experience is affected by the block producer’s balance between private valuations and gas. Given that a block producer has unilateral control over the block they choose to publish, with the gas or transaction fee mechanism serving as a recommended allocation at best, we can formalize the actual allocation rule adopted by block producers, which accounts for both the private valuation v_{BP}(B) and the gas mechanisms.
Define an allocation rule
as a function that specifies the block producer builds, given the bids \vec{b} of all known transactions, the block producer’s private valuation v_{BP} and the blockset B. The inclusion function is defined as:
We update the user’s individual utility functions to incorporate the block producer’s allocation:
Note that the only decision variable that is directly under the user’s control is the bid b_t submitted with the transaction.
Incentive Compatibility Notions
We can now formally define incentive compatibility notions. Our goal is to show that if a transaction fee mechanism design is incentive-compatible for block producers, then there’s no way it’s going to maximize user experience in the bidding process. Firstly let’s recall the precise definitions for gas-associated incentive compatibilities.
Block Producer Incentive Compatible Gas Design
We call a gas design incentive compatible for block producers if the payment rule p and burning rule q always instruct the block producer to form an allocation rule x that maximizes the block producer’s surplus. i.e. For every block producer valuation v_{BP}, every blockset B and every choice of transaction bids \vec{b}, the payment rule p and the burning rule q always result in an allocation rule x, such that:
User Compatible Gas Design
We now check on the other side and see how any gas design can be incentive compatible for users. More technically, we call a transaction fee mechanism dominant-strategy incentive compatible (DSIC) if there’s a bidding strategy σ such that, for every BP valuation v_{BP} and blockset B, every user i with transaction t, every valuation v_t for i, and every choice of other users’ bids b_{-t}, we have:
We can view (16) as a strong and formal definition of maximized user experience which says that there always exists a consistent bidding strategy that if users bid according to the recommended strategy they always get to maximize their utility. Furthermore, the optimal bidding strategy only depends on what the user knows individually and his or her private valuation of the transaction v_t and nothing else. Note that such bidding strategy is indeed desirable since when general users submit transactions, they just want to simply bid based on how much they privately evaluate the transaction and nothing else.
Impossibility Theorem
We now present the main Impossibility Theorem, which states that:
If a transaction fee mechanism is dominant-strategy incentive compatible with bidding strategy σ (i.e. maximizes user experience) and also block producer incentive compatible, then the payment rule p ≡ 0 for all σ.
In other words, only the trivial gas design alone can maximize the user’s bidding experience given block producer’s monopolistic power and incentive maximization setting.
Discussion and Implication
The Impossibility Theorem basically says that given block producers always try to build blocks that maximize their own utility, there’s no non-trivial gas design alone that the core protocol team can come up with to maximize a straightforward user’s bidding experience. As a result, Roughgarden recommended three design options following the Impossibility Theorem to overcome these issues, including:
Give up on the “good UX” or “user value-based bidding” at least as it is expressed by the DSIC property. More or less this is the status quo for chains in which BPs are sufficiently motivated to be active.
Give up on the Block Producer Incentive Compatible (BPIC) property, presumably compensating with restrictions on block producers’ behavior. (trusted hardware, cryptographic techniques).
Expand the Transaction Fee Mechanism (TFM) design space, which incorporates block space auctions or block producer competition so that a BP’s private valuation can be exposed.
Closing Remarks: How aPriori Helps?
aPriori is following the third option, to build a block space auction system so that the MEV-related activities can be diverted out of block producers’ private valuations and shared with relevant stakeholders. In particular, we summarize some of the benefits below:
1. Diversion from BP’s Private Valuation:
In a traditional setting without block space auctions, BPs have monopolistic control over the block construction process. They can privately assess the value of including certain transactions, often based on MEV opportunities, and select those that maximize their own surplus. This private valuation is opaque and can lead to inefficiencies and unfairness, as block producers may prioritize their interests over those of the network participants and overall welfare.
2. Block Space Price Discovery through Competitive Bidding:
Block space auctions introduce a competitive bidding process where searchers (entities specialized in finding MEV opportunities) bid for the inclusion of their transaction bundles. By requiring searchers to submit bids, the system reveals the true value of these transactions in a transparent manner. The highest bids reflect the market value of the MEV opportunities, which would otherwise be privately assessed by the block producers.
3. Improved UX:
The competitive nature of the auction also leads to improved UX (in bidding strategy) by creating an environment for more predictable bidding strategies. This also reduces the potential for unfair practices, such as frontrunning or selective inclusion based on private interests.
Conclusion
Our research began by examining the dynamics of MEV extraction in the absence of block space auctions. We demonstrated that without such mechanisms, searchers are incentivized to engage in spamming behaviors, leading to a tragedy of the commons scenario. Our model revealed that the equilibrium quantity of spam transactions scales super-linearly with both gas price and gas usage, particularly when the cost of reverted transactions is high relative to the reserved gas cost.
This analysis underscores the critical need for robust economic mechanisms in blockchain systems. In order to fully capitalize on Monad’s technical strengths, it is crucial to have a robust, transparent, and incentive-compatible block production economy. The concept of a block space auction is central to this strategy, where a monopolistic block producer allocates block space—a scarce resource. This setup inherently ties the distribution of block space to the block producer’s discretion, influenced by both public gas bids and private valuations.
Given that the block producer has private valuations, no non-trivial gas mechanism alone can optimize the user’s experience. This is because the block producer’s decision-making is influenced by private incentives, making it challenging to achieve a fully incentive-compatible system through gas fees alone. Here, aPriori’s block space auction becomes critical, fundamentally altering searchers’ dominant strategies. By tying searcher inclusion probabilities to auction bids rather than spamming activities, aPriori minimizes MEV-induced spam and fosters a healthier, more efficient ecosystem.
Moreover, aPriori addresses the challenge posed by the block producer’s monopolistic power and private valuations. It diverts MEV-related value from the opaque realm of block producer discretion into a transparent auction setting. This transparency ensures that transactions are priced based on true economic value, rather than being influenced by the block producer’s private interests.
In essence, while Monad’s technical innovations lay a strong foundation, the integration of aPriori’s economic mechanisms enhances the overall ecosystem. By fostering a fair and transparent block production environment, aPriori helps ensure that block producers act in alignment with the network’s best interests, ultimately benefiting all participants. This synergy between cutting-edge technology and thoughtful economic design will drive Monad towards a more resilient and scalable future.
References
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aPriori Research. “MEV Landscape in the Parallel Execution Era.” Substack, 18 May 2024, https://0xapr.substack.com/p/mev-landscape-in-the-parallel-execution-era. Accessed 23 July 2024.
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