A Machine Learning Augmented Cooperative-Game Framework for Blockchain and Non-Fungible Token-Based Artwork Trading with Zero-Knowledge Proofs

Summary

This study enhances NFT-based digital asset trading in smart city environments by integrating ML into a CoGTT framework. Implemented using smart contracts on a public blockchain and supported by zero-knowledge proofs, the framework improves fairness, adaptability, and transparency, achieving an 84% trade completion rate while accounting for execution costs inherent to decentralized systems.

Abstract

In the context of smart cities, Non-Fungible Tokens (NFTs) are transforming digital art markets by enabling secure, decentralized transactions. As NFT trading grows, incorporating intelligence and adaptability becomes crucial—making Machine Learning (ML) integration essential. However, existing models, particularly Cooperative Game Theoretic Trading (CoGTT) frameworks, underutilize ML across all trading phases. Key gaps include limited real-time adaptability, suboptimal negotiation strategies, and inadequate buyer–seller matchmaking. This research addresses these gaps by integrating ML into a three-phase CoGTT framework—ML-augmented Naive Trading, Min–Max Price Negotiation, and Equilibrium-Based Trading—to enhance decision-making and pricing. The methodology applies ML algorithms such as decision trees, clustering, and reinforcement learning (Q-learning) within a public blockchain–based simulation environment using smart contracts. The simulation uses a customized dataset reflecting both market dynamics and artist credibility. The dataset is synthetically generated to emulate an NFT marketplace while maintaining controlled experimental conditions, which may limit direct applicability to volatile real-world markets. Zero-knowledge proofs (ZKPs) are employed to preserve privacy. ZKPs are employed to preserve privacy. A comparative analysis of ML models for NFT price estimation and strategic bidding demonstrates the effectiveness of combining predictive algorithms with reinforcement learning. Linear Regression and Random Forest models both accurately estimate NFT prices, with Random Forest achieving higher real-time prediction accuracy (R² = 0.9920). K-Means clustering effectively segments market participants to support targeted negotiation, achieving a silhouette score of 0.8178. Integrating Q-learning with Random Forest enables dynamic bidding strategies that minimize the gap between recommended and actual prices. The discrete action set (decrease, stay, increase) supports interpretable, real-time bid adjustments. These findings highlight the potential for ML-driven NFT trading systems to support scalable, privacy-compliant digital marketplaces in smart cities, aligning trading behavior with market demands through automated, data-driven processes.

Introduction

The convergence of blockchain technology and Non-Fungible Tokens (NFTs) has introduced a transformative digital asset ownership and trading model, particularly within smart cities. In this environment, a Digital Artwork Trading Framework enables artists to monetize their creations and offers collectors verifiable ownership through decentralized infrastructure. This aligns well with smart city objectives such as transparency, traceability, and automation. Several factors, such as high transaction fees, limited interoperability, and inadequate copyright enforcement, hinder the adoption and scalability of these systems.

A growing body of foundational research explores these issues from multiple angles. Vujicic et al.¹ and Kumar et al.² provide technical overviews of decentralized finance and innovative contract mechanisms that underpin NFT trading. Ante et al.³ and Guan et al.⁴ examine the economic behaviors and user experiences of NFT marketplaces, highlighting volatility and strategic behavior among stakeholders. Applications beyond digital art—such as waste management⁵, secure AI trading⁶, and legal compliance⁷—demonstrate the versatility and expanding utility of NFT platforms in decentralized ecosystems.

Interdisciplinary approaches have also emerged to enhance these platforms. Game theory has been employed to address incentive structures, ownership disputes, and regulatory compliance, as seen in works by Sun et al.⁸, Gao et al.⁹, and Shao et al.¹⁰. These studies design equilibrium-based and penalty-driven models to encourage fair behavior and efficient resource allocation. Simultaneously, machine learning (ML) techniques are being introduced to improve fraud detection, price prediction, and content valuation in NFT ecosystems^11,12, offering data-driven strategies to optimize trading efficiency^9,10. Recent studies have begun to explore NFT price prediction using deep learning and visual features. Seyhan and Sefer¹³ proposed a deep learning model for predicting both primary and secondary NFT sale prices, demonstrating improved accuracy over baseline models. Similarly, Pala and Sefer¹⁴ employed transfer learning on image-based NFT attributes to forecast sales characteristics, highlighting the importance of visual features in price determination. These works complement our approach by emphasizing alternative data modalities, whereas our framework integrates machine learning with game-theoretic negotiation for dynamic and adaptive trading.

Recent literature underscores the growing impact of blockchain and NFT technologies in securing digital ecosystems and restructuring market dynamics. Blockchain integration enhances asset security, fraud resistance, and decentralized ownership in digital platforms, particularly in gaming and virtual economies¹⁵. Simultaneously, NFT-driven crypto-aesthetics and decentralized art markets reveal complex sociotechnical interactions that reshape artistic value, ownership, and cultural production¹⁶, while empirical studies indicate that NFT pricing is predominantly governed by scarcity, creator reputation, and market dynamics¹⁸. Quantitative and network-based analyses further demonstrate that strategic optimization and structured interaction networks significantly influence economic outcomes, stability, and success patterns in decentralized marketplaces and related systems^19,20.

Despite these advancements, current NFT trading frameworks—particularly those based on Cooperative Game Theoretic Trading (CoGTT) —remain limited in adaptability and decision-making capabilities. Figure 1 shows the architectural diagram of the proposed ML augmented cooperative game theoretic trading (CoGTT) framework. Existing models are predominantly static, often relying on heuristic or rule-based strategies that fail to account for complex, dynamic market conditions and user behavior. This results in inefficient trades, poor pricing strategies, and limited transaction fairness.

This research proposes a Machine Learning–Augmented CoGTT Framework for decentralized digital asset trading platforms to address these limitations. Structured into three progressive phases—ML-augmented Naive Trading, Min-Max Price Negotiation, and Equilibrium-Based Trading—the framework leverages supervised, unsupervised, and reinforcement learning techniques to improve market analysis, strategic negotiation, and equilibrium discovery. Specifically, classification models (e.g., Decision Trees), clustering algorithms (e.g., K-Means), and dynamic learning methods (e.g., Q-learning) are used to optimize trade matching, price setting, and negotiation strategy.

This ML-augmented architecture is deployed over the smart contract–enabled blockchain platform (here, the Ethereum blockchain), ensuring decentralized, transparent, and autonomous execution of trades. To protect user data and maintain confidentiality, ZKPs are integrated, enabling cryptographically secure validation of transactions without revealing sensitive information. ML-driven insights directly influence smart contract logic, embedding predicted prices and adaptive thresholds that respond to real-time market dynamics.

In summary, this study introduces a scalable, privacy-preserving, and intelligent trading framework deployed on a public blockchain with a gas fee and deployment cost calculation table in Table 1 that significantly enhances the efficiency (as reflected in Table 2 and Table 3), trustworthiness, and adaptability of NFT trading systems. By tightly integrating machine learning with game-theoretic logic and blockchain infrastructure, the proposed solution aligns with the goals of smart cities—delivering a secure, fair, and user-inclusive platform for digital asset exchange.

This study proposes a hybrid framework that integrates machine learning with cooperative game-theoretic trading (CoGTT) to support pricing, negotiation, and decision-making in NFT-based digital art markets. Predictive models are coupled with smart contracts to enhance process automation, fairness, and security in trading environments. To address privacy and compliance requirements, ZKPs are employed for price matching, ownership validation, and authenticity verification. The framework adopts a three-phase structure consisting of machine learning-assisted naive trading, min-max price negotiation, and equilibrium-based trading, providing a coordinated approach for scalable NFT marketplace operations.

The comparative analysis in Table 4^{8,9,10,13,14,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38} highlights the integration of blockchain, NFTs, machine learning, and game-theoretic models across decentralized domains such as digital markets, IoT security, and energy systems. Prior studies demonstrate that combining advanced learning models and blockchain mechanisms enhances pricing accuracy, security, transparency, and equilibrium optimization. Empirical and analytical evidence indicates improvements in efficiency, fraud mitigation, cost reduction, and fair incentive allocation through hybrid ML–blockchain frameworks.

Protocol

The framework for blockchain-based NFT artwork trading is structured as a multi-layered protocol that integrates smart contracts, privacy-preserving mechanisms, game-theoretic modeling, machine learning algorithms, reinforcement learning, and gas-cost evaluation within a unified architecture.

The process begins with the development of smart contracts defining core functions such as participant registration, asset listing, order submission, and transaction execution. These contracts enable user onboarding, asset registration, and secure order handling. To assess correctness and efficiency, contract logic was tested, and execution costs were recorded under different transaction speed settings.

ZKPs are incorporated to validate artwork authenticity without disclosing sensitive details. Each transaction undergoes dual verification through on-chain checks and ZKP validation, ensuring confidentiality and data integrity. The modular ZKP design functions independently of the main smart contracts, allowing integration and supporting deployment at scale. Proof generation and verification latency were evaluated to assess feasibility.

A web-based interface was implemented using a general-purpose framework. The interface includes modules such as a landing page, artist dashboard, and trading platform. Wallet-based authentication enables transaction signing, while upload and minting functionalities allow artists to tokenize digital works.

At the market design level, the Cooperative Game-Theoretic Trading (CoGTT) model employs a structured three-phase negotiation mechanism. The first phase applies direct price matching based on submitted bids and asks. Unmatched participants proceed to the second phase, which uses negotiated min–max pricing strategies, including midpoint valuation methods. If no agreement is reached, trades advance to the third phase, where Nash equilibrium principles are applied, and iterative negotiations continue until equilibrium-convergent prices are reached. These phases are implemented as modular algorithms: naive matching (Algorithm 1), midpoint brokering (Algorithm 2), Nash equilibrium trading (Algorithm 3), and an integrated workflow (Algorithm 4).

Machine learning models are integrated into the trading process for decision support. Market features such as bids, asks, trading volume, historical price data, and reputation scores are used for predictive modeling. Linear Regression (Algorithm 5) estimates fair prices, with performance evaluated using mean squared error (MSE). K-Means clustering (Algorithm 6), supported by feature normalization and PCA-based dimensionality reduction, segments users into clusters, assessed by the silhouette score. Random Forest (Algorithm 7) provides additional price forecasts, validated through both MSE and R². An integrative algorithm (Algorithm 8) combines regression, clustering, and Random Forest outputs into a dynamic decision flow for adaptive trading.

Reinforcement learning through Q-learning is applied to optimize bidding strategies. The state space is defined by current price levels and bid values, while actions include increment, decrement, or retain. A Q-agent is trained using feedback from Random Forest predictions, learning policies that reduce pricing error and increase participant utility. Simulations are conducted until convergence to equilibrium-aligned policies, and outputs are validated in simulated trading environments.

Gas consumption for each contract function is systematically recorded, with transaction costs calculated under varying speed settings. For example, the registerArtist() function consumed 90,123 gas units, with corresponding costs benchmarked against market ETH prices. These evaluations identify trade-offs between cost and execution efficiency.

The framework’s performance was assessed using multiple metrics. Linear regression achieved an MSE of 4.54 × 10⁻²⁸, while K-Means clustering produced a silhouette score of 0.8178. Random Forest yielded an MSE of 0.1311 with an R² of 0.9920. Q-learning outputs were evaluated for convergence and equilibrium alignment under different pricing conditions. These results indicate the feasibility of the proposed approach for supporting NFT artwork trading under blockchain-based market conditions.

Proposed cooperative game theoretic trading (CoGTT) framework for digital art trading

The innovative hybrid approach cooperative game theoretic trading (CoGTT) framework combines a game-theoretic NFT trading approach with additional pricing mechanisms and Nash equilibrium to improve the efficiency and coordination of NFT markets. The proposed approach is built on a smart contract-enabled blockchain platform. The approach leverages advanced cryptographic techniques and ZKPs to ensure secure and private transaction verification. ZKPs allow for the validation of ownership and transaction details without disclosing sensitive information about buyers or sellers.

This proposed approach introduces strategic interactions between creators, buyers, and intermediate brokers within a decentralized marketplace. This model aims to optimize trading outcomes, balancing incentives for all participants while considering competition and cooperation dynamics. While the proposed framework primarily focuses on naive bid–ask matching, midpoint-based negotiation, and Nash equilibrium-based settlement, other methods such as second-price auctions exist and remain relevant in NFT markets. In digital artwork trading, the auctioneer determines the transaction price using approaches:

Consumer bidding price: The price is set directly based on the buyer’s highest bid. This method reflects the maximum value the buyer will pay for the artwork, fostering competitive bidding.

Average price method: The price is calculated as the midpoint between the buyer’s offered and the seller’s asking price, creating an equilibrium. This equilibrium price computation:

Equilibrium (EPrice) = DArt_APrice + DArt_BPrice

This approach aims to balance the interests of both the buyer and seller, leading to a fair and mutually agreeable transaction. These methods provide flexibility in pricing strategies, catering to diverse preferences and market dynamics in the digital artwork trading ecosystem.

3-phase game-theoretic-based cooperative trading model

This section introduces an innovative 3-phase game-theoretic-based cooperative trading approach, specifically designed for digital artwork. The approach dynamically adjusts both bidding and asking prices to optimize trading efficiency and fairness, as shown in Table 2 and Table 3, facilitated by a broker. It aims to improve fairness, efficiency, and profitability in decentralized NFT markets, striking a balance between the interests of creators and artwork buyers. Figure 2 illustrates the proposed 3-phase trading system model for digital artwork, with the detailed algorithm provided in Algorithm 4. The proposed CoGTT framework efficiently completes the digital artwork trading process in three phases: a) Naive Trading based on asking and bidding prices, b) Trading based on the Negotiated Min-Max Price, and c) Trading using the Nash Equilibrium method. In the first phase, naive trading is initiated based on the initial information from creators and buyers. The second phase involves trading based on the negotiated min-max prices between sellers and buyers for the remaining untraded requests. Finally, the third phase utilizes the Nash Equilibrium method to finalize the trading process.

First phase - Naive trading on asking and bidding price:

In the first phase, digital artwork creators (providers) are organized in ascending order based on their asking prices, along with their minimum selling prices. Similarly, buyers (consumers) are arranged in ascending order according to their submitted bidding prices, along with their maximum bidding prices. The minimum asking price of creators and the maximum bidding price of buyers are kept confidential. A cooperative approach is then employed to match buyers and creators, facilitating the allocation of artwork where the buyers’ bidding prices align with the creators’ asking prices. This allocation may involve a single creator or multiple creators, as long as the combined asking prices fall within the buyer’s bid. Buyers who are unable to secure artwork in this phase due to pricing constraints will proceed to the second phase. The details of the trading approach are outlined in Algorithm 1.

Second phase - Trading on negotiated min-max price

In the second phase, the requests of unmatched buyers are addressed to complete the trading process, utilizing the minimum asking prices from digital art creators and the maximum bidding prices from buyers. The trading approach employs various methods, including Middle Value, Intraday Mid Point Value, and Market Equilibrium, to determine a midpoint value that enhances trading efficiency. The specifics of these midpoint approaches are discussed in the following subsections. The details of the trading approach are provided in Algorithm 2.

Middle value: A brokering approach incorporated to find the mid value between the creators and buyers with a simple mid value approach. For example, if the bidding price for a digital art is 50 and the asking price is 52, then the middle value can be found by averaging the bid and ask prices.

Intraday mid point value: Incorporated brokering approach marks the minimum trading price of the same type of arts, also marks the maximum price of the same type of arts, and uses the following formula to calculate the mid value: (Current High of Day + Current Low of Day)/2. This mid value is set as the trading transaction price if the mid value is more than the art creator’s minimum asking price and less than the buyer’s maximum bidding price.

Market equilibrium: The mid price, is an important indicator of market equilibrium. It reflects the price at which the art creator (asking price) and buyer (bidding price) for an asset align. This value is calculated by averaging the highest bidding price and the lowest asking price, providing traders with a fair representation of the current market value, unaffected by extreme bid or ask prices. The formula is presented in the following 3 equations.

 

Third phase - Trading on the Nash equilibrium method

In the third step, the remaining untraded requests’ extended information, like the minimum asking price from creator and maximum bidding price from buyer revealed to both sides so that they would settle on an equilibrium point where the buyer’s bid price is as high as they are willing to go and the creator’s ask price is as low as they are willing to accept. The details of the trading approach are presented in Algorithm 3.

In the first and second phases of the framework, confidentiality and incentive alignment are employed to discourage strategic misreporting of prices. Buyers’ maximum willingness-to-pay and creators’ minimum acceptable prices are maintained as confidential values during allocation, limiting opportunities for manipulation through underreporting or overstatement. Because matching decisions rely on ranges (minimum ask and maximum bid) rather than explicit disclosures, attempts to misreport prices increase the likelihood of exclusion from Phase 1 or Phase 2 allocations, thereby reducing trading opportunities. Furthermore, the protocol advances to a third phase based on the Nash Equilibrium when earlier trades are unsuccessful. In this stage, iterative adjustments lead to convergence on outcomes that more accurately reflect participants’ true valuations. This progression discourages misreporting in the earlier phases, since failed attempts at manipulation only postpone execution and ultimately necessitate truthful revelation of valuations for successful trade completion.

The outputs of the machine learning (ML) algorithms are not treated as isolated predictions but are actively embedded into the three-phase cooperative game-theoretic trading (CoGTT) framework to guide pricing, negotiation, and equilibrium discovery. The connections are now described as follows:

Phase 1-Naive trading with linear regression: The linear regression model generates a fair price benchmark by averaging the bid and ask features against historical trends. This predicted fair price is then compared to both the buyer’s submitted bid and the creator’s asking price. If either party reports a value that deviates significantly from the predicted fair price, the allocation is deprioritized, reducing the incentive for misreporting. Thus, the regression output acts as a filtering mechanism that determines which trades are considered viable for direct allocation.

Phase 2- Min-max negotiation with random forest: The random forest model refines dynamic price estimation by incorporating bid-ask spreads, trading volume, and reputation scores. These predictions are directly used to calibrate midpoint-based negotiation methods (Middle Value, Intraday Mid-Point, Market Equilibrium). For example, when a midpoint price is computed, the random forest prediction is applied as a corrective factor to ensure that the negotiated value is consistent with market behavior. This integration ensures that brokering outcomes are anchored to learned market patterns rather than arbitrary arithmetic midpoints.

Phase 3- Equilibrium-based trading with K-means clustering: At this stage, buyer and seller participants are first segmented into clusters based on behavioral features (bid/ask aggressiveness, reputation, historical activity). This segmentation ensures that negotiations toward equilibrium occur among comparable participants, which reduces volatility and improves fairness. The cluster assignments thereby serve as group-level constraints on whose prices can be considered in equilibrium discovery.

Reinforcement learning (Q-learning) integration: Q-learning builds upon the random forest predictions to optimize dynamic bidding strategies. Each time the agent adjusts a bid (decrease, hold, or increase), the reward signal is calculated relative to the Random Forest–predicted fair price. Over multiple episodes, the Q-agent learns policies that minimize pricing error and maximize utility, and these policies are directly enacted in Phase 3 equilibrium trading. In practice, this means that buyers’ bid adjustments during equilibrium discovery are informed by strategies that have been optimized and validated during training simulations.

Together, these mechanisms demonstrate that the ML outputs serve as decision-support engines tightly coupled with the CoGTT phases. Linear regression enforces realistic initial allocations, Random Forest grounds negotiations in empirical market behavior, clustering structures the equilibrium process, and Reinforcement Learning drives adaptive strategy refinement. By explicitly linking algorithmic predictions to operational decision points, the framework ensures that trading is not only automated but also informed by market-adaptive intelligence.

Datasets, features, and reproducibility framework

Dataset definition and motivation

NFT and digital asset trading environments are characterized by multiple market and participant attributes, including buyer bid price, seller ask price, historical transaction price, transaction volume, and participant reputation. As no publicly available NFT dataset simultaneously provides all of these attributes, this study employs synthetically generated datasets to enable controlled protocol validation while preserving realistic market behavior. Dataset sizes range from 100 to 1000 transactions, depending on the experimental scenario and model requirements.

Each dataset record consists of the following fields: Bid, Ask, Historical Price, Volume, Reputation, and Fair Price, where the fair price is defined as the arithmetic mean of the bid and ask values.

Synthetic data generation process:

Buyer bids are sampled from bounded uniform distributions, using ranges such as [90, 110] for small-scale experiments and [100, 1000] for large-scale simulations. Seller ask prices are generated by adding a positive stochastic offset to the corresponding bids, modeling realistic bid–ask spreads. Historical prices are drawn from normal distributions centered on bid values with additive noise to simulate market volatility. Transaction volumes are generated as integer values within predefined ranges (e.g., [1, 10] or [100, 1000]), while participant reputation scores are sampled from uniform distributions either in [0, 1] (normalized trust scores) or [0, 5] (star-rating representation). All experiments use fixed random seeds (numpy.random.seed(42)) to ensure deterministic and repeatable dataset reconstruction.

Data scheme, storage, and access

All datasets are stored in CSV format with a fixed six-column schema: (bid, ask, historical_price, volume, reputation, fair_price). Each CSV file typically contains approximately 1,000 records, unless otherwise specified. For decentralized reproducibility, dataset files are uploaded to IPFS, and the corresponding content identifiers (CIDs) are logged alongside smart contract addresses in configuration files. This design allows independent retrieval of identical datasets without reliance on centralized storage.

Dataset preparation and splitting

Datasets are split into training and testing subsets using an 80/20 train–test split implemented via train_test_split with random_state=42. Five-fold cross-validation is applied during Random Forest hyperparameter tuning, while feature scaling using StandardScaler() is applied where required, particularly for clustering and PCA-based workflows.

Machine learning models and parameterization

All machine learning models are implemented using established libraries with fixed configurations to ensure reproducibility. A complete summary of parameters and values is provided in the accompanying table. Linear Regression (LR) employs a least-squares estimator with bid, ask, historical price, volume, and reputation as inputs and fair price as the target variable. Performance is evaluated using Mean Squared Error (MSE). K-Means Clustering is applied to scaled feature subsets, optionally reduced using Principal Component Analysis (PCA) with two components capturing over 90% variance. The number of clusters is selected in the range 2–3 using elbow and silhouette criteria. Random Forest Regression (RF) is used for non-linear price estimation with 100–200 trees, depth and split parameters tuned via five-fold cross-validation. Model performance is evaluated using MSE and R². Q-Learning is implemented as a tabular reinforcement learning approach with 31 discretized price states, three bid-adjustment actions, and fixed learning parameters (α = 0.1, γ = 0.9, ε = 0.1). Convergence is assessed through stabilization of episodic rewards. Computationally, Linear Regression and K-Means complete in seconds for datasets up to 10³ samples, Random Forest training requires seconds to minutes depending on scale, and Q-learning converges efficiently due to its low-dimensional state space.

Blockchain execution, privacy, and cost logging

Smart contract deployment and execution

Smart contracts encoding the trading logic are written in Solidity (pragma ^0.8.20) with compiler optimization enabled (200 runs) and deployed on the Sepolia test network using standardized development frameworks. Wallet-based transaction signing is performed through a browser-based wallet connected via an RPC endpoint. Gas usage for contract deployment and transactional functions is logged automatically, and execution costs are computed using contemporaneous ETH/USD conversion rates.

Zero-knowledge proof integration

Privacy-preserving verification is implemented through a ZK-SNARK pipeline, including circuit compilation, trusted setup, proof generation, and on-chain verification. Proofs are generated off-chain and verified on-chain using a dedicated verifier contract deployed alongside the main trading contract, enabling validation of ownership and transaction correctness without revealing sensitive participant data.

Software environment and execution workflow

All experiments are conducted on a 64-bit Linux system with a fixed hardware configuration. Machine learning workflows are executed in a Python environment, while blockchain development and front-end interaction rely on a JavaScript-based stack with fixed framework versions. Front-end applications are built and served using a package manager, smart contracts are compiled and deployed using standardized development frameworks, and ZKP verification is integrated into the transaction execution flow.

Exact software versions, compiler flags, wallet configurations, IPFS pinning policies, execution commands, and example CIDs are documented in the reproducibility file to facilitate independent replication.

Operational outcomes and completion rates

The robustness of the deployed protocol is reflected in its execution statistics. Core smart contract functions achieve high completion rates, with an overall success rate of 84% across all transactional operations. Detailed function-level execution counts and completion rates are reported in the corresponding results table.

Algorithms

This section introduces a three-phase cooperative game theoretic digital artwork trading framework, where a broker is utilized to gather available artwork units and their asking prices from creators and the required units and bidding prices from users. Based on the proposed approach, the broker then facilitates transactions between creators and users. The trading process unfolds in three distinct phases: In the first phase, a naive trading algorithm is applied to the asking and bidding prices, as outlined in Algorithm 1. The second phase introduces a min-max price negotiation-based trading algorithm, presented in Algorithm 2. Finally, the third phase utilizes a Nash Equilibrium-based trading algorithm, detailed in Algorithm 3, and Algorithm 4 integrates all three algorithms into the comprehensive three-phase cooperative game theoretic digital artwork trading approach. Algorithm 5 shows the Linear Regression for Fair Price Prediction. Algorithm 6 shows the K-Means Clustering for Buyer/Seller Grouping. Algorithm 7 shows Random Forest for Price Prediction in Real-Time Negotiation. Algorithm 8 shows Machine Learning-Based NFT Trading Algorithm Flow. The algorithms 5–8 are a part of algorithm 8.

The proposed framework implements a three-phase Cooperative Game Theoretic Trading (CoGTT) mechanism to systematically handle NFT-based digital artwork transactions. In the first phase, naive trading is performed using direct bid-ask matching, as formalized in Algorithm 1. Buyers are ordered by descending bidding prices and sellers by ascending asking prices, enabling sequential allocation of artworks within buyer budget constraints. Buyers unable to complete a trade in this stage are forwarded to the second phase, where negotiated min-max pricing is applied using Algorithm 2. This stage computes a midpoint price between the seller’s minimum asking price and the buyer’s maximum bidding price, which is further adjusted using market demand and real-time trading indicators. A trade is executed only if the negotiated price remains within the permissible bid-ask range. For transactions that still remain unresolved, the framework advances to the third phase, where Nash equilibrium–based trading is applied using Algorithm 3. Here, iterative price adjustments based on participant utilities converge to a stable equilibrium price, ensuring rational settlement. These three stages are orchestrated within a unified decision workflow defined in Algorithm 4, which integrates direct matching, brokering, and equilibrium resolution into a single trading pipeline.

To enhance pricing accuracy, adaptability, and strategic decision-making, the CoGTT framework is augmented with multiple machine learning models. Algorithm 5 applies Linear Regression to estimate a baseline fair price using observable market features, serving as an interpretable filtering mechanism during initial trade evaluation. For real-time negotiation, Algorithm 7 employs a Random Forest regressor to capture non-linear pricing patterns influenced by bid–ask spreads, historical prices, volume, and participant reputation. Participant behavior is further structured using Algorithm 6, which applies K-Means clustering with PCA-based dimensionality reduction to group buyers and sellers into behaviorally similar clusters, improving stability during equilibrium negotiations. These models are integrated into a unified ML-driven trading workflow described in Algorithm 8, where Linear Regression supports Phase 1 filtering, Random Forest refines Phase 2 negotiation prices, clustering informs Phase 3 participant grouping, and reinforcement learning optimizes bid adjustments toward the Nash equilibrium. Together, these algorithms ensure that the proposed framework is not only theoretically grounded but also adaptive, data-driven, and suitable for dynamic NFT marketplace environments. All the algorithms are listed in Supplementary File 1.

Results

The proposed blockchain-based approach for digital artwork trading leverages ZKPs. Each trading method is encapsulated in a smart contract, with essential functionalities—such as artwork creator registration, user registration, and trading mechanisms—defined as dedicated contract functions. The blockchain platform’s environment parameters used in the simulations are outlined in Table 1.

To maintain consistency, all trading methods adhere to standardized public blockchain param...

Discussion

This research proposes a machine learning-augmented cooperative game theoretic trading (CoGTT) framework for NFT-based digital art markets, aimed at improving pricing accuracy, strategic negotiation, and decision-making efficiency. The approach integrates supervised, unsupervised, and reinforcement learning models—such as Decision Trees, K-Means, and Q-learning—on a smart contract–enabled blockchain platform to enable decentralized, transparent, and adaptive trading. A three-phase structure is introduce...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Hardhat (Blockchain Development Framework)	Hardhat	v2.19.1	https://hardhat.org
MetaMask (Wallet Extension)	MetaMask	v11.10.0	https://metamask.io
Next.js	Next.js	v14.1.0	https://nextjs.org
Node.js	Node.js	v20.11.1	https://nodejs.org
NVIDIA RTX 3060	NVIDIA	https://www.nvidia.com/	Intel Core i7-12700H
Pinata	Pinata.cloud	v2.1.0	https://www.pinata.cloud
Pinning policy	Pinata.cloud	—	https://docs.pinata.cloud
React	React	v18.2.0	https://react.dev
Remix	Remix	v0.31.0	https://remix.ethereum.org
Solidity (Compiler Language)	Solidity	v0.8.20	https://soliditylang.org
Ubuntu	Ubuntu	22.04 LTS	https://ubuntu.com