Deep Neural-Menu Auctions - An AI-Driven Mechanism of Blockchain Fee Markets

Abstract

Blockchain transaction fee markets have long been plagued by volatile fees, rampant overpayment, and under-utilized block capacity. Legacy first-price auctions force users into a painful guessing game, while EIP-1559’s base-fee mechanism, though an improvement, introduces algorithmic oscillations and is vulnerable to miner exploits. This article proposes a novel solution grounded in AI-driven mechanism design: a deep neural-menu auction that reframes gas allocation as a direct, data-driven, and provably incentive-compatible mechanism.

We begin by establishing the formal economic foundations, defining user types, utilities, and the core principles of incentive compatibility and individual rationality. We then detail the architecture of our proposed system, which consists of two core components:

A Mechanism Network that ingests real-time blockchain state features (e.g., mempool congestion, fee histograms) and outputs a compact, optimal menu of $(gas, price)$ options.
A differentiable Buyer Network that simulates profit-maximizing user choices against this menu, enabling end-to-end training.

We elaborate on our training methodology, which optimizes a composite loss function balancing expected revenue and fee variance, guided by economic priors encoded as regularizers. To handle sudden demand shocks, we introduce a reinforcement learning layer that dynamically adapts the menu-generation policy. We provide theoretical guarantees of ε-dominant-strategy incentive compatibility and near-optimal revenue, demonstrating that our data-driven approach does not sacrifice economic rigor. Finally, we outline a reproducible empirical-study blueprint, detailing dataset choice, benchmark mechanisms, and statistical tests, so that future work can quantify fee-variance reduction and block-utilization gains.

1. Introduction: The Unsolved Problem of Blockchain Gas Fees

Every block produced on a smart contract platform like Ethereum represents a scarce, perishable marketplace for computational resources, or “gas.” With a fixed gas capacity $G$ per block, users who wish to have their transactions included must bid for this limited space. The design of this bidding process, the fee market mechanism, has profound implications for the network’s usability, efficiency, and fairness. Yet, existing solutions have proven deeply flawed.

1.1 The Failures of First-Price Auctions and EIP-1559

The legacy model for most blockchains was a simple first-price auction. In this system, users submit a gas price bid, and block producers (miners or validators) simply include the highest-bidding transactions until the block is full. While simple to implement, this mechanism forces users into a painful and inefficient guessing game:

Bid too low, and your transaction languishes in the mempool for an unpredictable duration, potentially failing if its conditions expire.
Bid too high, and you dramatically overpay, handing a large surplus to the block producer. This overpayment is not a minor issue; it is a systemic flaw that creates a poor user experience and extracts unnecessary costs.

Ethereum’s EIP-1559 was a landmark attempt to remedy these shortcomings. It introduced a protocol-defined base fee that algorithmically adjusts based on block utilization, aiming to keep blocks approximately 50% full. Users pay this base fee (which is burned) and can add an optional priority fee (or “tip”) to incentivize producers for inclusion. While EIP-1559 successfully smoothed some of the most extreme fee spikes and improved the user experience by making fees more predictable, it introduced its own set of pathologies:

Oscillatory Dynamics: During periods of sustained high demand (e.g., a popular NFT mint), the base fee can oscillate wildly as the mechanism over- and under-corrects in its attempt to target 50% utilization.
Producer Exploits: Sophisticated block producers can engage in strategies to manipulate the base fee for future gain. For example, a producer controlling consecutive blocks can produce an empty block to artificially depress the base fee, allowing them to include their own (or their partners’) transactions cheaply in the subsequent block.

These persistent issues demonstrate that a truly efficient and user-friendly fee market remains an open problem.

To remedy these flaws, we turn to the principles of AI-driven mechanism design. Instead of asking users for a single, speculative bid, our proposed mechanism periodically publishes a concise menu of options. Each option is a $(gas, price)$ pair, denoted $(g_k, p_k)$, offering a specific allotment of gas $g_k$ for a fixed, take-it-or-leave-it price $p_k$. Users simply select the single option from the menu that maximizes their own utility.

This approach, grounded in the economic theory of direct mechanisms, offers some great advantages:

Incentive Compatibility: By presenting a menu, the mechanism becomes dominant-strategy incentive compatible (DSIC). The best strategy for a user is to simply and truthfully choose their most preferred option. There is no need for complex counter-speculation or guessing what others will bid. Overpayment is structurally eliminated.
Individual Rationality: The menu always includes a zero-cost “exit” option $(0, 0)$. This guarantees ex-post individual rationality (IR), meaning no user can ever be forced into a transaction that results in a negative payoff.
Dynamic Optimality: The core of our proposal is to use deep learning AI to generate these menus. A Mechanism Network, trained on real-time blockchain data (mempool state, fee history, etc.), learns to output menus that are optimized for key objectives like maximizing revenue (or burned fees), minimizing fee variance, and maximizing block utilization. A differentiable Buyer Network simulates user responses, allowing for end-to-end optimization. Finally, a reinforcement learning layer allows the system to adapt its menu-generation strategy in response to sudden, unpredictable shocks in demand.

By unifying the economic rigor of mechanism design with the adaptive power of deep learning, our neural-menu auction charts a path toward a more efficient, stable, and user-friendly fee market for the next generation of blockchains. While this article stops short of reporting numeric results, Section 7 provides a step-by-step protocol for running a rigorous evaluation on historical Ethereum data.

2. Formal Preliminaries: The Language of Mechanism Design

Before detailing our architecture, we must first establish the formal economic language used to describe and analyze such systems. This foundation ensures that our AI-driven approach is built upon solid theoretical ground.

2.1 Type Space and Utilities

In the context of a blockchain fee market, we model each user $i$ as an agent with private information. This private information is captured by their type, which in this setting is their valuation per unit of gas, denoted by $v_i$. This value represents the maximum price the user is willing to pay per unit of gas for their transaction to be processed. We assume each $v_i$ is drawn independently from an unknown distribution $F$ supported on $\mathbb{R}_+$.

We adopt the standard assumption of quasi-linear utilities. When a user $i$ with valuation $v_i$ is allocated an amount of gas $g$ and charged a total fee $p$, their utility $u_i$ is the difference between their total value for the allocation and the price they paid: $u_i = v_i \cdot g - p$ A rational user will always act to maximize this utility.

2.2 The Mechanism: From Bids to Menus

A mechanism defines the rules of the game. A general direct mechanism is a tuple $\mathcal{M} = (A, g, h)$ where:

$A$ is the set of actions available to the agents. In a direct mechanism, the action space is the type space itself, $A_i = T_i = \mathbb{R}_+$, meaning agents “report” their type.
$g: A \to [0, G]$ is the allocation rule, which determines the amount of gas each agent receives based on the reported types.
$h: A \to \mathbb{R}_+$ is the payment rule, which determines the fee each agent is charged.

Our proposal specializes this to a menu mechanism. Instead of asking for a continuous valuation report, the mechanism offers a discrete set of $K$ options, ${(g_k, p_k)}_{k=1}^K$, plus an “exit” option $(g_0, p_0) = (0, 0)$. A user’s action is simply to choose one option from this menu.

2.3 The Golden Rules: Incentive Constraints

For a mechanism to be robust and user-friendly, it must satisfy two fundamental economic constraints:

Dominant-Strategy Incentive Compatibility (DSIC): A mechanism is DSIC if, for every user, the best strategy is to act truthfully, regardless of what any other user does. In our menu context, this means a user with true valuation $v_i$ maximizes their utility by selecting the menu entry $k$ that truly maximizes $v_i \cdot g_k - p_k$. This property eliminates the need for strategic second-guessing and makes the system transparent and simple to use.
Ex-Post Individual Rationality (IR): A mechanism is ex-post IR if no user can ever be forced to accept an outcome with negative utility. The inclusion of the $(0, 0)$ “exit” option directly hardcodes this property into our design. A user can always choose to not transact and incur no cost, guaranteeing a minimum utility of zero.

The Revelation Principle, a cornerstone of mechanism design theory, assures us that by restricting our focus to mechanisms that satisfy these properties (truthful, direct mechanisms), we lose no generality in the set of outcomes we can achieve. This is why we can confidently build our system around a menu-based approach without worrying that a more complex, indirect bidding language could achieve superior results.

At the heart of our proposed system lies a two-part deep neural network architecture designed to learn and deploy optimal fee-market menus. This architecture directly translates the economic principles of mechanism design into a practical, data-driven framework. It consists of a Mechanism Network that acts as the intelligent auctioneer, generating the menus, and a Buyer Network that serves as a differentiable model of a rational user, enabling the entire system to be trained end-to-end.

3.1 The Mechanism Network ($M_\theta$): The Intelligent Auctioneer

The Mechanism Network, parameterized by weights $\theta$, is responsible for dynamically creating the menu of $(gas, price)$ options for each block. It functions as the core intelligence of the fee market, adapting its offerings based on real-time network conditions.

Input: Sensing the State of the Network

To make informed decisions, the network ingests a high-dimensional feature vector $z \in \mathbb{R}^d$ that summarizes the current state of the blockchain’s transaction market. This vector includes critical indicators of demand and congestion, such as:

Mempool Gas Percentiles: Statistics on the total gas demanded by pending transactions at various fee levels.
Fee Histogram Moments: The mean, variance, skewness, and kurtosis of the fee rates in the current mempool.
Average Transaction Wait Time: The average time transactions at different fee levels have been waiting for inclusion.
Other time-series data, such as the base fee from recent blocks or the utilization rates.

This feature vector $z$ provides a rich, real-time snapshot of network demand, allowing the mechanism to be proactive rather than purely reactive.

Architecture and Output Generation

The network itself is a standard feed-forward architecture (e.g., two fully-connected hidden layers with ReLU activations). Its key innovation lies in its two specialized output heads, which generate the menu’s gas allocations and fees through carefully chosen activation functions that embed economic constraints.

For a menu of $K$ options, the network outputs two sets of raw logits:

Gas Logits $\tilde{g} \in \mathbb{R}^K$: These are unconstrained real values representing the proportional allocation of gas for each menu item.
Fee Logits $\tilde{p} \in \mathbb{R}^K$: These are unconstrained real values that will determine the price of each menu item.

These logits are then transformed into a valid, economically sound menu:

Gas Allocation Normalization: To ensure the total gas offered in the menu is feasible with respect to the block gas limit $G$, the gas logits are passed through a softmax function and scaled by $G$. The gas quantity for menu option $k$, denoted $g_k$, is calculated as: $g_k = G \cdot \frac{\exp(\tilde{g}_k)}{\sum_{j=1}^K \exp(\tilde{g}_j)}$ This elegant formulation ensures that the total gas allocated across all menu items sums exactly to the block capacity, $\sum_k g_k = G$.
Fee Positivity: To ensure fees are always non-negative, the fee logits are passed through a softplus activation function: $p_k = \log(1 + e^{\tilde{p}_k})$
Embedding Individual Rationality (IR): The final menu option, $(g_K, p_K)$, is hardcoded to be the (0, 0) “exit” option. This is a critical design choice that directly embeds the ex-post Individual Rationality property into the mechanism. Any user can select this option to guarantee themselves zero utility, ensuring they are never forced into a loss-making transaction.

3.2 The Buyer Network: A Differentiable Model of User Choice

To train the Mechanism Network, we need a way to evaluate the quality of the menus it produces. This requires predicting how users will react to them. A perfectly rational user would simply choose the menu option $k$ that maximizes their utility $u_k = v \cdot g_k - p_k$. However, the argmax function is non-differentiable, which means we cannot use gradient-based optimization to train the system.

The Buyer Network solves this problem by providing a differentiable approximation of a user’s best-response choice.

The Softmax Selector with Temperature

Given a user with valuation $v$ and a menu ${(g_k, p_k)}$ generated by the Mechanism Network, the Buyer Network first computes the utility score for each potential option:

\[u_k = v \cdot g_k - p_k\]

It then uses a softmax function with a temperature parameter $\alpha$ to convert these utility scores into a probability distribution over the menu choices. The probability of a user choosing option $k$, denoted $\pi_k(v; z)$, is:

\[\pi_k(v;z) = \frac{\exp(\alpha \cdot u_k)}{\sum_{j=1}^K \exp(\alpha \cdot u_j)}\]

The temperature $\alpha$ is a crucial hyperparameter that controls the “sharpness” of the user’s decision-making:

As $\alpha \to 0$, the choice probabilities approach a uniform distribution, modeling a user who chooses almost randomly.
As $\alpha \to \infty$, the output of the softmax function converges to a one-hot vector, placing all probability mass on the single option with the highest utility. This perfectly mimics the behavior of a purely rational $argmax$ utility maximizer.

During training, we can use a technique called temperature annealing, starting with a low $\alpha$ and gradually increasing it. This allows the model to explore the solution space broadly at first and then fine-tune its strategy as training progresses.

Ensuring Incentive Compatibility

Because the softmax function is an approximation of a perfect best response, the resulting mechanism is not perfectly DSIC. Instead, it satisfies a slightly relaxed but practically powerful property known as ε-dominant-strategy incentive compatibility (ε-DSIC). The potential utility gain a user could achieve by making a suboptimal choice is bounded by a small value ε, which is a function of the temperature $\alpha$ and the minimum utility gap between options ($\Delta_{\min}$). The bound is approximately $\varepsilon \lesssim (K-1)e^{-\alpha\Delta_{\min}}$. By using a high temperature $\alpha$ in the deployed model, we can make ε vanishingly small, ensuring the mechanism is strategy-proof for all practical purposes.

4. End-to-End Training Methodology

With the architecture defined, the next step is to train the Mechanism Network to generate optimal menus. This is achieved through an end-to-end training process that minimizes a composite loss function over a large dataset of historical blockchain states. The methodology is designed to balance competing economic objectives while ensuring the resulting menus are well-behaved.

4.1 Data Pipeline

The training process begins with a robust data pipeline. We collect a large set of $N$ historical mempool snapshots, ${z^{(i)}}$. For each snapshot, we need a representative sample of user valuations to simulate their responses. Since true valuations are private, we construct a proxy distribution $\hat{F}$ by fitting a smoothed kernel-density estimate to the gas prices of successfully included transactions from the recent past. For each snapshot $z^{(i)}$, we then draw a batch of $M$ user valuations ${v_j^{(i)}} \sim \hat{F}$ to use in the training step.

4.2 Composite Loss Function

A single objective is insufficient to capture the goals of a sophisticated fee market. Maximizing revenue alone could lead to extreme fee volatility, while minimizing variance alone might sacrifice revenue. Therefore, we optimize a composite loss function that intelligently balances three key objectives, controlled by weighting hyperparameters.

4.2.1 Expected Revenue (to be Maximized)

The primary objective is to maximize the expected revenue (or burned fees) generated by the mechanism. This is formulated as the negative expected payment, averaged over all sampled snapshots and user valuations. The expected payment is calculated by weighting the price of each menu option, $p_k$, by the probability that a user will choose it, $\pi_k$.

\[L_{\mathrm{rev}} = -\frac{1}{NM} \sum_{i=1}^N \sum_{j=1}^M \sum_{k=1}^K \pi_k(v_j^{(i)}; z^{(i)}) \cdot p_k(z^{(i)})\]

4.2.2 Fee-Variance Penalty (to be Minimized)

To combat fee volatility and create a more stable, predictable market, we introduce a penalty on the variance of the fees paid by users with different valuations. For each state $z^{(i)}$, we calculate the expected fee $\overline{p}(z^{(i)})$ and penalize the squared deviation from this mean. This encourages the network to generate menus where the prices chosen by different users are clustered more closely together, smoothing the overall fee distribution.

\[L_{\mathrm{var}} = \frac{1}{NM} \sum_{i,j} \left[ \sum_k \pi_k \cdot p_k - \overline{p}(z^{(i)}) \right]^2, \quad \text{where} \quad \overline{p}(z) = \sum_k \pi_k \cdot p_k\]

Finally, we add two regularizers based on economic priors to ensure the learned menus are simple and intuitive:

Sparsity ($L_1$ Penalty): An $L_1$ penalty on the gas allocations ${g_k}$ encourages the network to set some allocations to zero. This results in simpler menus with fewer effective options, reducing cognitive load for users and simplifying analysis.
Monotonicity Penalty: We enforce a natural property that a user should not pay less for more gas. A hinge-loss penalty is applied to any menu where a larger gas allocation $g_k$ is offered at a lower price $p_k$ than a smaller allocation $g_{k+1}$.

The Combined Objective

These components are combined into a single loss function, with hyperparameters $\beta_{\mathrm{var}}$, $\beta_1$, and $\beta_{\mathrm{mono}}$ controlling the trade-offs:

\[L(\theta) = L_{\mathrm{rev}} + \beta_{\mathrm{var}}L_{\mathrm{var}} + \beta_1 \sum_k |g_k| + \beta_{\mathrm{mono}} \sum_{k=1}^{K-1} \max\{0, (g_k - g_{k+1})(p_k - p_{k+1})\}\]

This composite loss is minimized using the Adam optimizer over mini-batches (e.g., 32 snapshots × 64 valuations). During training, we simultaneously anneal the temperature $\alpha$ in the Buyer Network, gradually increasing it from a low value (e.g., 1) to a high value (e.g., 50). This allows the model to explore broadly at the start of training and then converge to a sharp, near-deterministic policy.

5. Theoretical Guarantees

A primary advantage of grounding our AI-driven framework in mechanism design theory is the ability to provide formal guarantees on its economic properties. While the network is trained on empirical data to optimize practical objectives, its architecture and the principles behind its training ensure that it remains robust, strategy-proof, and economically sound.

5.1 ε-Dominant-Strategy Incentive Compatibility (ε-DSIC)

Because the Buyer Network uses a softmax function with temperature $\alpha$ instead of a pure $argmax$ operator, it models a “close-to-rational” rather than a perfectly rational agent. Consequently, the mechanism is not perfectly DSIC. However, we can prove that it is ε-DSIC, meaning the potential utility gain from behaving dishonestly (i.e., selecting a suboptimal menu option) is capped by a small value, ε.

For any menu option $k$ that is not the utility-maximizing choice, its selection probability $\pi_k$ is bounded by $\pi_k \le e^{-\alpha\Delta_{\min}}$, where $\Delta_{\min}$ is the minimum difference in utility between the best option and any other option. This means no user can gain more than ε by misreporting, where ε is bounded by:

\[\varepsilon \le (K-1) \Delta_{\max} e^{-\alpha\Delta_{\min}}\]

Here, $\Delta_{\max}$ is the maximum possible utility difference on the menu. By annealing the temperature $\alpha$ to a sufficiently high value during training and deployment, we can make this bound arbitrarily small, ensuring the mechanism is strategy-proof for all practical purposes.

5.2 Exact Ex-Post Individual Rationality (IR)

The mechanism satisfies the strongest form of individual rationality—ex-post IR—by construction. The hardcoded inclusion of the (0, 0) “exit” option in every menu guarantees that every user, regardless of their valuation, always has access to an action that yields a non-negative (specifically, zero) utility. This completely eliminates the risk of participation for users, a critical feature for fostering trust and adoption in a decentralized environment.

5.3 Revenue Approximation Guarantee

While our primary loss function targets empirical revenue on a given data distribution, we can also provide a theoretical link to the performance of a fully optimal mechanism. Myerson’s seminal work on optimal auctions provides a characterization for continuous bidding environments. By viewing our menu mechanism as a discretized approximation of the optimal continuous pricing rule, we can leverage established results from the “simple versus optimal” literature.

Under mild regularity conditions on the user valuation distribution $F$, it can be shown that by discretizing the optimal virtual-value pricing curve into $K$ well-chosen menu options, the mechanism’s expected revenue achieves at least $(1-\varepsilon) \times \text{OPT}$, where OPT is the revenue of the fully optimal (continuous) auction and $\varepsilon$ is a term that decreases as the number of menu items $K$ increases (specifically, $K = O(1/\varepsilon)$). This result extends the powerful guarantees from auction theory to our practical, discrete-menu setting, ensuring that our mechanism is not just empirically effective but also theoretically near-optimal.

6. Dynamic Adaptation via Reinforcement Learning

A statically trained Mechanism Network, even one that takes the current state $z$ as input, operates with a fixed set of weights $\theta$. This is effective under relatively stable market conditions, where demand patterns fluctuate within a known distribution. However, blockchain environments are subject to sudden and dramatic regime shifts, events like high-profile NFT mints, popular airdrops, or flash-loan-driven arbitrage cascades, that can fundamentally alter the valuation distribution of users. A static model may be slow to adapt to these “black swan” events.

To ensure our mechanism remains robust and optimal in real time, we introduce a second layer of learning: a dynamic adaptation policy trained with reinforcement learning (RL). This meta-learner’s job is not to generate menus directly, but to tune the parameters $\theta$ of the Mechanism Network itself in response to major demand shocks.

6.1 The Problem as a Markov Decision Process (MDP)

We frame this meta-learning task as a Markov Decision Process (MDP), building on the concepts of AI-Driven Mechanism Design.

State ($z_t$): The current state is the same feature vector $z_t$ used by the Mechanism Network, capturing the real-time conditions of the mempool.
Action ($a_t$): The action is the selection of a new set of parameters $\theta_t$ for the Mechanism Network, $M_\theta$. This represents a high-level strategic shift in how menus are generated.
Policy ($\pi_\phi$): The policy is a separate, lightweight neural network parameterized by weights $\phi$. It takes the state $z_t$ as input and outputs the updated weights for the Mechanism Network: $\theta_t = \pi_\phi(z_t)$.
Reward ($r_t$): After the Mechanism Network operates for a block (or a small window of blocks) with parameters $\theta_t$, the meta-learner receives a reward that mirrors our core objectives. The reward for block $t$ is the expected revenue minus a weighted penalty for fee variance: $r_t = \mathbb{E}_v[p_{\kappa(v)}] - \lambda \cdot \text{Var}_v[p_{\kappa(v)}]$ where $\kappa(v)$ is the index of the menu item chosen by a user with valuation $v$, and $\lambda$ is the trade-off parameter.

6.2 Training with Proximal Policy Optimization (PPO)

The goal is to train the policy network $\pi_\phi$ to maximize the cumulative discounted reward over time. Given the high-dimensional and continuous action space (the weights $\theta$), we employ Proximal Policy Optimization (PPO), a state-of-the-art policy gradient algorithm renowned for its stability and data efficiency.

PPO works by making incremental updates to the policy network $\pi_\phi$. In each training step, it uses a clipped objective function that discourages large, drastic changes to the policy. This prevents the meta-learner from making excessively aggressive updates that could destabilize the fee market. Instead, it learns to make smooth, controlled adjustments to the underlying menu-generation logic.

This two-tiered system provides the best of both worlds:

Short-Term Reactivity: The Mechanism Network $M_\theta$ reacts block-by-block to routine fluctuations in the mempool state $z$.
Long-Term Adaptability: The PPO-trained policy network $\pi_\phi$ adapts the entire strategy of the Mechanism Network over longer timescales (e.g., minutes to hours) in response to major, persistent shifts in market dynamics. This allows the fee market to remain near-optimal even during periods of extreme congestion or unforeseen events.

7. Empirical-Study Methodology Blueprint

Although we do not publish results in this blog, the community needs a clear recipe for validating neural-menu auctions. Researchers who wish to implement or replicate our claims should follow the instructions below.

7.1 Data Collection

Block range: pick at least 3 million consecutive Ethereum main-net blocks to cover multiple demand regimes (e.g., blocks 12,000,000–15,000,000, spanning London and Dencun).
Snapshot timing: capture the mempool state 10 s before each block timestamp to avoid peeking at transactions already included.
Feature extraction: store percentile gas-prices, higher-order moments, mean wait times, and the rolling base-fee vector $b_{t-16:t}$.

7.2 Valuation Proxy

For every historical block, assemble the set of successful transactions and record their paid gas-prices.
Fit a Gaussian-kernel density estimator to this sample to obtain a smoothed valuation distribution $\hat F_t$.
When simulating block $t$, draw user valuations $v\sim\hat F_{t-1}$ to respect causal ordering.

7.3 Benchmark Mechanisms

Label	Description
FPA	Legacy first-price auction, using historical bids unaltered.
EIP-1559	Replay historical base-fee evolution; users add a 2-gwei tip.
Static-Menu	Best menu from offline training, frozen weights.
Deep Neural-Menu	Menu generated online by $M_\theta$; PPO meta-learner disabled for ablation.
Deep Neural-Menu + RL	Full model with online PPO updates.

7.4 Evaluation Metrics

Fee variance: per-block variance of paid fees.
Block utilization: $\frac{\text{gas used}}{G}$.
High-value latency: 99th-percentile inclusion delay for valuations $v>\mu+2\sigma$.
Social welfare: mean user utility $E[u]$.

7.5 Experimental Design

Train/validation split: train on the first 60%, validate on the next 20%, test on the final 20% in chronological order.
Hyper-parameter search: random-search 50 trials over $K\in{4,8,12}$, Buyer temperature schedule $\alpha_{\text{final}}\in[20,60]$, and regulariser weights $\beta$.
Statistical testing: use a 10,000-sample block bootstrap; report 95% confidence intervals and mark differences significant at $p<0.01$.
Ablations: (i) remove variance penalty, (ii) remove monotonicity penalty, (iii) fix PPO learning-rate to 0 to isolate RL gains.

8. Deployment Pathways

Deploying a computationally intensive model like our Mechanism Network—and later validating it with the methodology of Section 7—requires a hybrid on-chain/off-chain design that preserves the core principles of decentralization and trustlessness.

Off-Chain Computation: The trained Mechanism Network $M_\theta$ would be run off-chain by block producers (validators or sequencers). At the beginning of each block proposal, the producer would feed the current network state vector $z$ into the model to generate the optimal menu for that block.
On-Chain Publication and Verification: To ensure transparency, the producer must publish the computed menu on-chain, for example, by including it or a commitment to it (e.g., a Merkle root) in the block header. To prevent a malicious producer from publishing a faulty or exploitative menu, they would also be required to publish a zero-knowledge succinct non-interactive argument of knowledge (ZK-SNARK). This ZK-proof would serve as a cryptographic guarantee, allowing anyone to verify that the published menu is the correct output of the publicly known Mechanism Network for the given public state $z$, without needing to re-run the computation themselves.
Wallet and User Interaction: User wallets would fetch the current, verified menu from a node via an RPC call. The wallet software would then locally compute the user’s optimal choice by maximizing their utility ($v \cdot g_k - p_k$) and submit a transaction that references their chosen menu item (e.g., “I claim option #3”).
Protocol Enforcement: The blockchain’s consensus rules would enforce the fees. When processing a transaction, the protocol would verify that it claims a valid menu option and would charge (and burn/distribute) the exact fee $p_k$ specified in the block’s published menu.

This pathway leverages the efficiency of off-chain computation while using on-chain cryptography to maintain the trustlessness and verifiability essential for a decentralized protocol.

9. Conclusion: Towards a More Perfect Fee Market

The persistent challenges of blockchain fee markets—volatility, overpayment, and inefficiency—are not mere engineering problems; they are fundamentally problems of mechanism design. By reimagining the gas auction as a direct, truthful neural-menu mechanism, we can structurally solve these issues. Our approach aligns user incentives with protocol objectives, eliminates the speculative guesswork of bidding, and dynamically adapts to market conditions.

The blueprint we provide for unifying three distinct fields—mechanism-design theory, deep learning, and reinforcement learning—charts a path forward; once the empirical protocol of Section 7 is executed, the community will be able to measure the concrete benefits with rigor. By continuing to bridge the gap between economic theory and cutting-edge AI, we can build the foundational infrastructure for a more perfect, decentralized economy.

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