# Maximizing NFT Incentives: References Make You Rich

Guangsheng Yu1⋆, Qin Wang1⋆, Caijun Sun2, Lam Duc Nguyen1,
H.M.N. Dilum Bandara1, Shiping Chen1 1CSIRO Data61, Australia
2Zhejiang Lab, China

###### Abstract.

In this paper, we study how to optimize existing Non-Fungible Token (NFT)
incentives. Upon exploring a large number of NFT-related standards and real-
world projects, we come across an unexpected finding. That is, the current NFT
incentive mechanisms, often organized in an isolated and one-time-use fashion,
tend to overlook their potential for scalable organizational structures.

We propose, analyze, and implement a novel reference incentive model, which is
inherently structured as a Directed Acyclic Graph (DAG)-based NFT network.
This model aims to maximize connections (or references) between NFTs, enabling
each isolated NFT to expand its network and accumulate rewards derived from
subsequent or subscribed ones. We conduct both theoretical and practical
analyses of the model, demonstrating its optimal utility.

NFT, Blockchain, Incentive, References, DAG

⋆ These authors contributed equally to the work.

##  1\. Introduction

Non-Fungibie Tokens (NFTs) made a big splash in mid-2021 (wang2021non, ) and
have since become a major player in the market. The peak week saw a whopping
$3.24b in NFT transactions (22/8/2022-29/8/2022, $\mathsf{TheBlock}$111Data
sources by $\mathsf{TheBlock}$ https://www.theblock.co/data/nft-non-fungible-
tokens/nft-overview; $\mathsf{Dune}$ https://dune.com/hanxilgf/nft-overview;
and https://dune.com/hildobby/NFTs; $\mathsf{DappRadar}$
https://dappradar.com/rankings/nft/marketplaces.). Recently, the average daily
trading volume has reached $36m, attracting over 14k active daily traders (Jan
2024, $\mathsf{Dune}$1). Originating in the Ethereum ecosystem, NFTs have
spread across mainstream platforms like Solana, BNB chain, Polygon, Avalanche,
Optimism, and Rarible ($\mathsf{DappRadar}$1). Trading is bustling on
specialized platforms such as Blur, OpenSea, OKX-NFT, Tensor, Reservoir,
LooksRare, X2Y2, and Sorare. Even the previously underestimated Bitcoin
ecosystem (binance1, ), leveraging the inscription technique (li2024bitcoin,
), has stepped into the NFT arena and introduced new NFT products like BRC20
and Ordinals, finding success in mid-2023 (wang2023understanding, ).

ERC-721 (erc721, ) has emerged as the de facto standard for NFTs, accounting
for the majority (98.8%, $\mathsf{Dune}$), and the remaining 1.2% mostly
follow the ERC-1155 (erc1155, ) standard. These standards play a pivotal role
in establishing the core functionalities of NFTs, namely, minting and
transferring. The minting process involves the creation of a new NFT, and it
is typically executed through a smart contract on the blockchain. During
minting, unique metadata (e.g., name, description, and associated media file)
are defined. Once minted, NFTs are owned (cryptographically protected by
private keys) by individuals/entities and stored in digital wallets. The
transfer operation allows for the seamless change of ownership of NFTs between
different wallets. Each transaction will be recorded on-chain, providing a
transparent and immutable history of ownership.

Earn money via NFTs? Due to their digital uniqueness, NFTs have gained
prominence in various industries, such as digital arts and games, enabling
creators to monetize their digital assets. We consider the following ways of
benefiting from NFTs. (i) A creator can create and sell NFTs by
minting/listing them on marketplaces (e.g., CryptoPunks and Ape Yacht Club are
the top collection list as per $\mathsf{DappRadar}$), which provides an
efficient method for creators to generate income. (ii) NFTs can be traded in
secondary markets, ideally by buying low and selling high based on market
trends and popularity. (iii) Owners can participate in play-to-earn (P2E)
(yu2022sok, ) NFT games to earn/sell in-game NFT items (e.g., Stepn and
Decentraland). (iv) NFTs can be staked in niche platforms (e.g., NFTX, BAND
Royalty, and Polychain Monsters) for rewards. (v) NFTs can be leased (as
specified in EIP-4907&5006) to others via secondary markets or DApps (e.g.,
Renfter, Vera, IQ Protocol, and Unitbox) for use in games. Other indirect
methods, such as investing in NFT-related companies, are excluded from this
work.

[1.3pt]$\triangle$!2ex In quest of a sustainable incentive. However, these
approaches typically concentrate on rewarding specific behaviors (e.g.,
minting, selling, trading, and staking) and are limited to generating static
(one-time) and fixed (predictable) income, lacking the potential to establish
a continuous revenue stream. Consequently, NFT users might be incentivized to
focus on selling as many newly created NFTs as possible, aiming to extract the
highest bid as long as the selling price exceeds transaction fees. This could
result in the creation of numerous meaningless NFTs and transactions, leading
to network congestion and high transaction fees. Moreover, such incentives
contradict practical scenarios wherein Intellectual Property (IP) creators
seek sustained benefits from their successful products. For instance, a singer
consistently earns royalties each time her songs are used for commercial
purposes. This discrepancy motivates our research question:

Is it feasible to devise an optimally sustainable incentive mechanism for
NFTs, or broadly, for larger decentralized IP-related production?

We present our efforts (i.e., contributions) step by step.

① Newly identified challenges in incentivizing NFTs. Building on the preceding
narrative, we noticed a previously overlooked constraint that significantly
impedes the growth of NFT incentives: their topology. Presently, while NFTs
may belong to a collection, each NFT is designed in isolation. Most existing
NFT implementations (cf. Table 2) develop their functionalities on an
individual NFT basis (e.g., defining roles as per EIP-7432, extending
functions as in EIP-5308, and adding parameters as per EIP-5007) without
direct connections (or capabilities of being attached) to broader NFT-formed
networks. The isolated nature of NFTs limits their effective relationships,
resulting in their inability to establish a dynamic income flow over time. As
a response, we dive into the intricacies of NFT networks to explore how
connections are established.

② Discovering existing ways of structuring NFTs. We have investigated
mainstream NFT networks (see Fig. 1) based on all existing NFT-related
standards (more in Table 2).

  * •

Chained design. Each NFT is linked to a regular transaction. Despite the
isolation of NFTs, an NFT retriever can find their history by searching the
associated transactions. Notably, these connections are inherently formed by
transactions in layer-one rather than direct links in L2222In the context of
blockchain, layer-one (L1) represents the base or foundational layer of a
blockchain network, including the main blockchain protocol and consensus
mechanism. Layer-two (L2) (gudgeon2020sok, ) refers to solutions built on top
of L1 blockchains, consisting of both scaling technologies (e.g., sidechains,
state channels, and off-chain protocols) and upper-layer decentralized
applications (DApps)..

  * •

Hierarchical design. The network adopts a structured hierarchy (as exemplified
in EIP-6150), where each level signifies a distinct degree of abstraction or
specialization, akin to scenarios in file storage. Ultimately, the network’s
topology in L2 takes on a tree-based shape.

  * •

DAG design. The network forms a directed acyclic graph in L2, where an NFT may
reference multiple ancestor NFTs or be referenced by multiple subsequent ones
(EIP-5521).

Figure 1. NFT formed network.

③ Establishing a uniform reference incentive model. It is evident that a DAG-
based topology maximizes NFT connections, allowing for increased references.
The more references an NFT builds, the greater its potential to generate or
extract revenues becomes. To step further, we accordingly formulate a generic
NFT incentive model, which we refer to as the reference incentive model. Our
model follows the straightforward recognition that is calculated by a
participant’s net income, i.e., payoff function as $\mathcal{U}$ = income as
$\mathcal{I}$ \- outcome as $\mathcal{O}$ (see Sec.2.1). However, due to the
inherent complexity of the network, we confront a series of difficulties.

Technical challenge (TC)-I: How to accurately measure complex connections or
references over time?

④ Reply TC-I: Crafting and refining the model (Sec.2.2-2.4). In formulating
the income aspect, our principles center around evaluating two key dimensions:
reference connections and stateful accumulator. Regarding the former, we
introduce two novel metrics tailored to the formed DAG network: participation
scale (horizontal level, count by in-degree and also referred to as the
reference list $\vec{\Theta}$) and depth (vertical level, represented as $d$).
These metrics serve to gauge the potential engagement within the NFT network.
For the former, an NFT publisher might have numerous followers (consider, for
instance, a hit song remixed by multiple direct producers). As for the latter,
we examine the publisher’s continuous income from an accumulated standpoint.
This perspective accounts for an NFT created by the publisher having
repetitive references over time (e.g., a hit song remixed successively by
multiple producers).

Regarding the outcome function (equiv. cost function), we incorporate a range
of parameters, such as descending rate $\sigma$ and interest rate $q$ (see
Sec.2.2 for details), to establish constraints that prevent perpetual payments
for any NFT, regardless of its value. Our aim is for the value of a published
NFT to appropriately diminish with increasing depth. This approach ensures
that a newcomer to the market can engage with a stepwise and fair pricing
structure: paying a premium for a recently popular NFT and less for an older
one, irrespective of its classic status333We operate under the assumption that
the majority of IP products will experience a natural decline in value over
time. Exceptional cases such as rare artworks, which tend to appreciate in
value, are not considered within the scope of this analysis.. Importantly, the
profit distribution and charging process can be concluded within a finite
number of rounds, akin to the concept that a patent becomes free after a
certain period.

Our proposed incentive model offers several additional advantages: (i) being
tailored to diverse strategies, with every parameter being adaptable; (ii)
facilitating the dynamic joining and departure of subscribed users over time,
as well as providing a real-time cumulative revenue reflection; and (iii)
being versatile for various incentive cases (either layer-two products or
layer-one consensus incentives) as long as their network structures involve
multi-agents and are formed in DAG.

However, the intricate reference dynamics between publishers and followers
pose difficulties in analyzing their best incentives.

Technical challenge (TC)-II: Does the optimal utility exist?

⑤ Reply TC-II: Theoretical analyses via game theory (Sec.2.5). We provide a
primary theoretical analysis via game theory (in particular, a Stackelberg
game (fang2021introduction, )) to determine the optimal utility for users in
decentralized services that is anchored on three key theorems: finality,
complexity, and solvability.

Concretely, finality ensures distribution processes within a finite number of
rounds, crucial for predictable and reliable transactions. Complexity shows
the non-convex and NP-hard nature of optimizing the payoff function,
highlighting the intricate challenges in distributed environments. Solvability
proves that users can eventually achieve optimal outcomes (namely, mixed
strategy Nash Equilibrium) in competitive, non-cooperative settings.

These theorems collectively demonstrate the existence of an optimal utility
for game players. However, obtaining such a corresponding solution is highly
complex (computationally infeasible), indicating its impracticality for
everyday users. We progress in different ways by leveraging AI-empowered
solutions to maximally approach the optimal solution.

Technical challenge (TC)-III: What could be the practical method for
approaching the optimal utility?

⑥ Reply TC-III: Practical training via deep reinforcement learning (DRL)
approaches (Sec.3-4). Building on TC-II’s response, we highlight the
advantages of using DRL for complex optimization challenges. DRL excels in
high-dimensional spaces and interactive learning, offering adaptability in
dynamic scenarios. Its strength lies in balancing strategy exploration and
exploitation, learning intricate policies that traditional methods may not
capture. We correspondingly define key DRL elements (agents, environment,
episodes, states, actions, policies, and reward functions) to simulate the
actual NFT competitive scenarios (Sec.3.1) and present its detailed approach
to training and operating (Sec.3.2).

However, given that our reference incentive model allows for an unrestricted
number of references (out-degree) in each round, we need to streamline the
training task for practical implementation.

We accordingly select a machine-learning (ML) resource marketplace (9796833, ;
9445602, ) as our focus (Sec.4), which (i) limits references to two (out-
degree set to 2): one representing a dataset and the other a
model444Represented as URLs when embedding to NFT fields.; (ii) aptly mirrors
the interest in ML markets during the era of AI, offering a viable case study
for decentralized intelligence.

Our practical use case presents a rich observation, wherein:

  * •

The system skillfully navigates NFT quality diversity, ensuring fairness
amidst varying distribution patterns.

  * •

Economic elements, notably interest rates, influence publisher tactics,
highlighting the need for balanced settings in the evolving NFT market.

  * •

Increasing publisher diversity and adjusting NFT settings foster fairer reward
distribution, essential for a competitive NFT environment.

Further, we present further discussions on extended capabilities (Sec. 5.1)
and potential applications (Sec.5.2) of our incentive model to existing
scenarios in different dimensions.

♠ A very short summary of our deliveries in this study:

  * •

New structuring bottleneck in NFT incentives;

  * •

A generic referece incentive model;

  * •

Proved to be game-theoretically optimal;

  * •

Proved to be practically solvable via DRL;

  * •

Evidence from an implemented ML-based use case.

##  2\. The Reference Incentive Model

Our study concentrates on the incentive analysis within the established NFT
(DAG) network (cf. left in Fig.1). In this section, we present the reference
incentive model with theoretical analyses.

###  2.1. Our Reference Incentive Model

Design principles. In our model, an NFT publisher may act as both a leader and
a follower: they are the leader of the resources they provide and a follower
of other publishers’ resources. Each NFT, positioned as a node on the
DAG555Such an NFT network can be formed via EIP-5521., signifies a certain
type of unique resource (e.g., instantiated as dataset or model in Sec.4). The
directed edges of the graph embody the reference relationship among NFTs.
Intuitively, the incentive mechanism should operate under three orthogonal
guiding principles:

  * P1:

An NFT with a wider referencing bandwidth (horizontally, count by in/out
degree) should receive higher incentives.

  * P2:

An NFT with a deeper referencing depth (vertically, count by depth) should
accumulate more revenue.

  * P3:

The mechanism employs a weighted system for profit distribution to ensure
distribution is completed within a finite number of rounds.

Utility function. For any participant, his/her utility (equiv. payoff
function) is straightforwardly calculated by the gap between revenues (income)
and costs (outcome). From this, we formally define the payoff function
$\mathbb{U}$ for each NFT, with $\mathcal{I}$ representing the accumulated
income and $\mathcal{O}$ symbolizing the cost associated with minting this
NFT. To simplify the explanation, we omit the subscripts from the notations
while concentrating on one particular NFT $\mathcal{R}_{i,h,\Theta}$. More
parameters are defined in Table 1.

######  Definition 1.

The payoff function $\mathbb{U}$ of a publisher $j$ minting $i$-th NFT
$\mathcal{R}_{i,h,\Theta}$ at the block height $h$ with a reference list of
$\Theta$ is given by

$\mathbb{U}^{j}({\mathcal{R}_{i,h,\Theta}})=\mathcal{I}^{j}_{\mathcal{R}_{i,h,\Theta}}-\mathcal{O}^{j}_{\mathcal{R}_{i,h,\Theta}}.$

We then present how to construct the cost function
$\mathcal{O}^{j}_{\mathcal{R}_{i,h,\Theta}}$ and the income function
$\mathcal{I}^{j}_{\mathcal{R}_{i,h,\Theta}}$. For simplicity, we omit the
index $j$ unless differentiating between multiple publishers is necessary.

###  2.2. Outcome Function

$\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}$ denotes the costs borne by any NFT
publisher, where a unique NFT, $\mathcal{R}_{i,h,\Theta}$ (minted at the
$i$-th order during round $h$), has an initial minting fee of $p_{0}$. The
calculation for $p_{0}$ is as follows:

$\displaystyle p_{0}=$
$\displaystyle\hat{\mathcal{O}}\times[w_{0},w_{1},w_{2},\dots,w_{|\vec{\Theta}|}],\text{
with}\sum_{i=0}^{|\vec{\Theta}|}w_{i}=1\text{ and
}w_{i}\in\mathbb{R}_{0}^{+},$

here, $p_{0}$ includes a list of ratios, where $d$ previous NFTs are denoted,
and $w_{i}$ represents the profit-sharing ratio/weight for the $i$-th NFT in
the reference list $\vec{\Theta}$. Note that allocating the values $w_{0}$
requires an initial fixed expense $\hat{\mathcal{O}}>0$ for releasing each
NFT, independent of the size of the reference list $\vec{\Theta}$. To make it
clear, we further denote $w_{0}$ as the weight of self-references with $w_{i}$
being the weights of all other cross-references $\forall i>0$.

In practice, $p_{0}$ can be further expanded to:

$\displaystyle p_{0}=$
$\displaystyle\left(\hat{\mathcal{O}}+\mathcal{O}\right)\times[w_{0},w_{1},w_{2},\dots,w_{|\vec{\Theta}|}],$

where $\mathcal{O}$ is a variable top-up fee, acting as an additional payment
to those who previously contributed and own particular NFTs that the new NFT
refers to.

The publisher has the choice to immediately pay a portion of the total fee,
defined as the down-payment ratio $\lambda$, while the remaining is spread
across the next $\hat{d}$ rounds, with $\hat{d}=\phi(1-\lambda)$, where $\phi$
is a constant function. Additionally, an extra but optional payment
$\\{\pi_{r}:0\leq\pi_{r}\leq\bar{\pi_{r}}\\}$ can be done by any publisher who
is about to publish a new NFT. This payment $\pi_{r}$ is linked to the
following parameters by adjusting them accordingly to reap more profits:

  * •

Decay parameter ($d$): The decay parameter $d$ now becomes $\hat{d}+\Delta d$,
where $\hat{d}$ is the initial decay parameter, and $\Delta
d=f(\pi_{r}),\Delta d\in\mathbb{N}$, with $f$ being a monotonically increasing
function. Therefore, a larger $\pi_{r}$ leads to a larger decay parameter $d$,
extending the valid rounds of profit distribution.

  * •

Interest rate ($q$): The interest rate $q$ is modified from the initial
interest rate $\hat{q}$ based on the payment $\pi_{r}$. We define this
relationship as $(1+q)=g(\hat{q},\pi_{r})$, where $g$ is a monotonically
decreasing function in $\pi_{r}$. This means a higher $\pi_{r}$ leads to a
lower interest rate.

  * •

Descending rate ($\sigma$): The descending rate $\sigma$ is adjusted from the
initial descending rate $\hat{\sigma}$, according to the payment $\pi_{r}$. We
define this as $\sigma=l(\hat{\sigma},\pi_{r})$, where $l$ is a monotonically
decreasing function in $\pi_{r}$. Thus, a larger $\pi_{r}$ results in a lower
descending rate.

Table 1. Notation Definition

Notation |  Definition
---|---
$N$ |  The number of NFT publishers in the network.
$\vec{\Theta}$ |  The reference list generated by referrable links.
$\lambda$ |  The down-payment ratio of minting a new NFT.
$\vec{w}$ |  The list of weights assigned to each referring edge in a reference list $\vec{\Theta}$.
$d$ |  The measure of the maximum depth in the reference chain for a particular NFT, a.k.a., the decay parameter.
$q$ |  The interest rate in outcome with increasing depth towards the decay parameter $d$.
$\sigma$ |  The descending rate in income with increasing depth towards the decay parameter $d$.
$p_{0}$ |  The one-off payment to each owner of $\vec{\Theta}$ if a publisher decide not to pay by installment.
$\pi_{r}$ |  The optional payment in outcome that can be in favor of a longer $d$, a lower $q$, and a lower $\sigma$.
$\varepsilon$ |  The probability that an NFT $\mathcal{R}_{i,h,\Theta}$ gets referred by a new NFT $\mathcal{R}^{\prime}_{i,h,\Theta}\neq\mathcal{R}_{i,h,\Theta}$.
$\mathcal{R}_{i,h,\Theta}$ |  The $i$-th referrable NFT minted at round $h$ with $\vec{\Theta}$.
$\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}$ |  The accumulated cost of publishing an NFT $\mathcal{R}_{i,h,\Theta}$.
$\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}$ |  The accumulated income of publishing an NFT $\mathcal{R}_{i,h,\Theta}$.
$\Omega_{\mathcal{R}_{i,h,\Theta}}$ |  The NFTs candidate set for the new NFT $\mathcal{R}_{i,h,\Theta}$ to be selected, forming the reference list $\vec{\Theta}$.
$\hat{\mathcal{I}}$ |  The initial fixed reward granted to publishers if the performance outperforms the entire $\Omega_{\mathcal{R}_{i,h,\Theta}}$.
$\hat{\mathcal{O}}$ |  The initial fixed expense to publish a valid NFT.

The cost function ($\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}$) with compound
interest, which now depends on the payment $\pi_{r}$, is as follows:

$\displaystyle\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}=$ $\displaystyle\lambda
p_{0}+\pi_{r}+(1+q)^{1-\varepsilon}\frac{p_{0}(1-\lambda)}{d}+$
$\displaystyle(1+q)^{2-\varepsilon}\frac{p_{0}(1-\lambda)}{d}+...+(1+q)^{d-\varepsilon}\frac{p_{0}(1-\lambda)}{d}$
$\displaystyle=$ $\displaystyle\lambda
p_{0}+\pi_{r}+\sum_{j=1}^{d}g(\hat{q},\pi_{r})^{j-\varepsilon}\frac{p_{0}(1-\lambda)}{d},$

$\displaystyle\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}=$
$\displaystyle\begin{cases}\lambda
p_{0}+\pi_{r}+\sum_{j=1}^{d}g(\hat{q},\pi_{r})^{j-\varepsilon}\frac{p_{0}(1-\lambda)}{d},&\text{if}\
\lambda\neq 1\\\ p_{0}&\text{if}\ \lambda=1\end{cases}$

where the parameter $\varepsilon$ represents the probability that this NFT
gets referred when every time there appears a new NFT being published onto the
platform, i.e., $\varepsilon\in[0,1]$.

If any publisher’s NFT is referenced by another publisher’s NFT, the interest
rate growth is delayed with a probability of $\varepsilon$, providing an
additional income source for the NFT owner. This allows any publisher to
adjust their payment $\pi_{r}$, thereby affecting both the decay parameter $d$
and the interest rate $q$. Therefore, the action for any publisher who is
about to publish their NFT $\mathcal{R}_{i,h,\Theta}$ becomes a tuple of three
elements, represented as

(1)
$\mathcal{A}_{\text{out}}=(\pi_{r},w_{1},w_{2},\dots,w_{|\vec{\Theta}|}),\text{
with}\sum_{i=1}^{|\vec{\Theta}|}w_{i}=1-w_{0},w_{i,\forall
i}\in\mathbb{R}_{0}^{+}.$

Furthermore, when a publisher publishes an NFT, the action of setting the
reference ratio for each component can reflect another characteristic of the
outcome action $\mathcal{A}_{\text{out}}$. This is mapped to:

$\Phi(w_{i})=\prod_{k=i}^{|\vec{\Theta}|}w_{k}\varpropto\varepsilon,\forall
i>0,$

where $\Phi(w_{i})$ exclusively serves as the income’s coefficient but also
correlates to the probability $\varepsilon$ of the NFT being referred each
time when a new NFT is published in the network. As a result, the equation
produces an income coefficient $\varepsilon$. In practice, we can regard the
income coefficient $\varepsilon$ as the quality of an NFT.

###  2.3. Income Function

The position of an NFT on the blockchain determines its income derived from
subsequent rounds. The set of freshly minted NFTs at round $h+1$, denoted as
$\mathcal{I}_{(h+1)}$, refers to $\mathcal{R}_{i,h,\Theta}$.

The income action $\mathcal{A}_{\text{in}}$ is represented by the unit price
being set for a subsequent one that references the current
$\mathcal{R}_{i,h,\Theta}$:

$\mathcal{A}_{\text{in}}=\psi_{\mathcal{R}},$

where $\psi_{\mathcal{R}}\in(0,\bar{\psi_{\mathcal{R}}}$] with
$\bar{\psi_{\mathcal{R}}}$ being the maximum value of the unit price, defined
as the cost for using a minimal fraction of a resource, e.g., 1% of the
resource.

The revenue for round $h+1$ is determined by
$k\sigma^{-1}|\mathcal{I}_{(h+1)}|$, where $k$ is a constant. The income
function now incorporates the income coefficient $\varepsilon$ as follows:

$\displaystyle\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}=$ $\displaystyle
k\sigma^{-1}|\mathcal{I}_{(h+1)}|\varepsilon+k\sigma^{-2}|\mathcal{I}_{(h+2)}|\varepsilon+...+k\sigma^{-d}|\mathcal{I}_{(h+d)}|\varepsilon+\hat{\mathcal{I}}$
$\displaystyle=$
$\displaystyle\varepsilon\sum_{j=1}^{d}kl(\hat{\sigma},\pi_{r})^{-j}|\mathcal{I}_{(h+j)}|+\hat{\mathcal{I}},$

where $\hat{\mathcal{I}}>0$ is an initial fixed reward if the item represented
by the new NFT $\mathcal{R}_{i,h,\Theta}$ is more performant than that of any
of the items contained in the candidate set
$\Omega_{\mathcal{R}_{i,h,\Theta}}$.

###  2.4. Back to Payoff Function

The publisher’s payoff function $\mathbb{U}$ now takes into account the unit
prices set by the publisher and their impact on the income coefficient,
calculated as follows:

$\displaystyle\mathbb{U}_{\mathcal{R}_{i,h,\Theta}}=$
$\displaystyle\varepsilon\sum_{j=1}^{d}k\sigma^{-j}|\mathcal{I}_{(h+j)}|+\hat{\mathcal{I}}-\lambda
p_{0}-\pi_{r}-\sum_{j=1}^{d}(1+q)^{j-\varepsilon}\frac{p_{0}(1-\lambda)}{d}$
$\displaystyle=$
$\displaystyle\varepsilon\sum_{j=1}^{d}k\sigma^{-j}|\mathcal{I}_{(h+j)}|+\hat{\mathcal{I}}-p_{0}\left[\lambda+\sum_{j=1}^{d}(1+q)^{j-\varepsilon}\frac{p_{0}(1-\lambda)}{d}\right]-\pi_{r}$
$\displaystyle\propto d[\sigma^{-d}|\mathcal{I}|-(1+q)^{d}].$

As a result, the optimization pricing problem can be reformulated over many
rounds, where each round corresponds to a publisher releasing a new NFT
$\mathcal{R}_{i,h,\Theta}$. This setup is illustrated as follows:

(2)
$\displaystyle\max_{\mathcal{A}_{\text{in}},\mathcal{A}_{\text{out}}}\quad\mathbb{U}=\sum_{\mathcal{R}_{i,h,\Theta}}\left[\varepsilon\sum_{j=1}^{d}k\sigma^{-j}|\mathcal{I}_{(h+j)}|+\hat{\mathcal{I}}\right.$
$\displaystyle\left.-p_{0}\left[\lambda+\sum_{j=1}^{d}(1+q)^{j-\varepsilon}\frac{(1-\lambda)}{d}\right]-\pi_{r}\right]$
$\displaystyle s.t.$
$\displaystyle(a):\sigma=l(\hat{\sigma},\pi_{r}),(1+q)=g(\hat{q},\pi_{r}),d=\hat{d}+f(\pi_{r}),$
$\displaystyle(b):\hat{d}=\phi(1-\lambda),$
$\displaystyle(c):0\leq\lambda,\sigma,\varepsilon\leq 1,$
$\displaystyle(d):d\in\mathbb{N},$
$\displaystyle(e):0\leq\pi_{r}\leq\bar{\pi_{r}}.$

The twofold benefits of this approach are clear. First, the publisher invests
more to generate a higher income due to the enhanced performance of the
resources that others obtain, coupled with the delay in the growth of the
outcome interest and the income descending. Second, if the publisher is
confident about the performance of their resources, they can choose to set a
higher unit price, resulting in increased profits during the income phase.

###  2.5. Game Analysis

We then provide theorems ensuring that the distribution process is completed
within a finite number of rounds. We consider the game to be a non-convex and
NP-hard problem, and Nash Equilibrium (NE) exists in the considered game.

######  Theorem 1.

(Finality) If $\sigma\in(0,1)$ and $d\in\mathbb{N}$, the distribution of
$\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}$ concludes within $d$ rounds.

###### Proof 0 (Theorem 1).

Given $|\sigma|<1$, the sum of a geometric series $\sum_{i=0}^{d}\sigma^{i}$
converges to $\frac{1-\sigma^{d+1}}{1-\sigma}$. Therefore, as $\sigma\in(0,1)$
and $d\in\mathbb{N}$, the sum of the series is a finite value, ensuring the
distribution of $\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}$ ends within $d$
rounds. ∎

Theorem 1 implies that revenue derived from each minted NFT within this
network is positively correlated to the total participants
($\sum_{d}|\mathcal{I}|$) or valid references ($|\Theta|$), and inversely
related to the round interest $q$. For instance, when an NFT is procured at a
higher initial price ($\lambda$), fewer rounds are needed to compensate the
preceding NFTs. Conversely, a higher descending rate ($\sigma$) results in a
reduced number of benefit-yielding rounds ($d$).

However, the comprehensive payoff function, encapsulating all parameters,
including $|\mathcal{I}|$, $\lambda$, $d$, $w$, and $\sigma$, is inherently
complex. Foreseeing the dominant parameter becomes increasingly difficult as a
sudden influx of participants ($|\mathcal{I}|$) could offset the influence of
other parameters. This abrupt increase could be due to external stimuli, which
are generally not known from the system’s perspective. Moreover, the selection
of $\sigma$ carries significant weight for the platform’s stability. A larger
$\sigma$ distributes more income to earlier rounds. Thus, it is imperative to
balance between platform growth and publisher engagement, leading to an
optimization problem to maximize publisher engagement while ensuring the
platform’s healthy development.

######  Theorem 2.

(Complexity) The optimization of the payoff function $\mathbb{U}$ for any NFT
minted is a non-convex, non-strict NP-hard problem.

###### Proof 0 (Theorem 2).

The proof, following the principles discussed in a previous study
(wang2023referable, ), involves examining the Hessian matrix of $\mathbb{U}$
with respect to $\sigma$ and $q$. We denote
$A=\frac{\partial^{2}\mathbb{U}}{\partial\sigma^{2}}$,
$B=\frac{\partial^{2}\mathbb{U}}{\partial\sigma\partial q}$, and
$C=\frac{\partial^{2}\mathbb{U}}{\partial q^{2}}$. The condition for convexity
requires the Hessian matrix to be positive semi-definite, which in turn
demands that all its eigenvalues be non-negative. This leads to the condition
$AC-B^{2}\geq 0$. However, we find that $AC-B^{2}\ngeq 0$ for $\sigma$ and $q$
in the range [0,1]. This indicates the non-convexity of the optimization
problem. In this case, we categorize the optimization as non-strict NP-hard,
acknowledging the complexity and potential computational challenges in finding
optimal solutions. Hence, traditional convex optimization methods are not
feasible for optimizing $\mathbb{U}$. ∎

The implications of Theorem 2 are profound in understanding the complexity of
the payoff function $\mathbb{U}$, where the complexity arises due to its
dependence on numerous parameters such as the number of participants
$|\mathcal{I}|$, initial price $\lambda$, round number $d$, weight $w$, and
descending rate $\sigma$. Moreover, the nature of this problem makes it
challenging to identify a dominant parameter, especially in scenarios
characterized by a sudden surge in participants.

######  Theorem 3.

(Solvability) The considered NFT pricing game can be transformed from a
stochastic optimization problem into a repeated $N$-player non-cooperative
game (fujiwara2015non, ) with finite actions $a_{\mathcal{R}_{i,h,\Theta}}$
that satisfies Mixed Strategy Nash Equilibrium (MNE) (reny1999existence, ).

###### Proof 0 (Theorem 3).

As proved in Nash’s theorem (nash-1, ), a finite non-cooperative game has at
least one NE solution for agents taking mixed strategies. This is expressed
as:

$\Delta(\mathcal{A}_{j})=\left\\{p_{j}=\\{p_{j,1},\dots,p_{j,k}\\},p_{j,k}\geq
0,\sum_{k}p_{j,k}=1\right\\},$

where $\Delta(\mathcal{A}_{j})$ denotes the probability distribution of
publisher $j$’s action space $\mathcal{A}_{j}$ for all possible actions, and
$p_{j,k}$ is the probability of the $j$-th publisher taking the $k$-th action.
This implies that an MNE point can be eventually found in the considered
pricing game. Let $a_{\mathcal{R}_{i,h,\Theta}}^{j,\star}$ denote the optimal
outcome and income actions of publisher $j$ regarding her NFT published on
$h$-th round with a ratio list of $\Theta$. The point
$a_{\mathcal{R}_{i,h,\Theta}}^{j,\star}$ can be considered as an MNE if it
satisfies:

$\mathbb{U}^{j}_{\mathcal{R}_{i,h,\Theta}}(a_{\mathcal{R}_{i,h,\Theta}}^{j,\star})\geq\mathbb{U}^{j}_{\mathcal{R}_{i,h,\Theta}}(a^{j}_{\mathcal{R}_{i,h,\Theta}}),\forall
i,j,h,\Theta.$

∎

Reaping profits while setting prices against unknown competitors and solving
the optimization problem are challenging for any publisher $j$. Any
adjustments of its strategy of $\mathcal{A}_{\text{in}}$ and
$\mathcal{A}_{\text{out}}$ regarding an NFT $\mathcal{R}^{j}_{i,h,\Theta}$ are
intricately coupled with an unknown number of the strategies applied by
different publisher $j^{\prime}$. It is a dynamic pricing environment in which
any publisher $j$ needs to solve the payoff function and work out the most
profitable pricing strategy independently.

To this end, we propose that each publisher can implement Theorem 3 by running
a decentralized DRL algorithm to play this non-cooperative game, as outlined
in the following section.

##  3\. Approaching Optimal Utility via DRL

While achieving equilibrium as described in Theorem 3 entails high
computational complexity (NP-hard), practical methods can still approach an
approximate solution (stably converged to a value, which we consider as
practically solvable in this study).

DRL approach. Model-free reinforcement learning (RL) offers a dynamic solution
for effective machine learning (ML)-based decision-making, capable of tackling
intricate optimization problems in changing environments, including the
pricing problem discussed in Sec.2.5. DRL extends this capability, leveraging
deep neural networks to manage intricate data within large state-action spaces
and to execute complex function approximation tasks effectively. This makes it
particularly proficient in handling the decentralized Stackelberg problem, a
type of sequential decision-making challenge. To operationalize Theorem 3, the
preferred approach is policy-based deep reinforcement learning (DRL)
algorithms.

###  3.1. DRL Model

We present the necessary components in such a DRL model:

Agents. The entities that execute a learning process and maintain a local
prediction model are the agents. We suppose each publisher $j$ who
participates in the NFT network or has performed some actions is an agent in
this paper.

Episode. The determination of a concluded episode hinges on whether the
learning progression employs a Monte-Carlo update or a Temporal-Difference
update, as referenced in the literature (rl-survey, ). In the context of this
paper, the pricing contest within the network is depicted as a recurrent game
with no predefined termination point. During an episode, a complete cycle
takes place in which a publisher prepares to release their NFT after examining
the current state. As soon as the NFT gets published, the publisher determines
the subsequent actions based on the new state. The interval between
identifying two successive states can be set at a specific duration, e.g., the
full cycle of a block’s height that stores NFTs.

States ($\mathcal{S}$). Each agent (or publisher) obtains the continuous
observation of the environment, denoted by $s\in\mathcal{S}$. Each publisher
maintains a current state in a given episode, specifically in relation to the
NFT that is about to be sent, as given by $s_{\mathcal{R}_{i,h,\Theta}}$. The
set of allowable states for each impending NFT release is closely associated
with a predetermined NFT candidate set $\Omega_{\mathcal{R}_{i,h,\Theta}}$.
This candidate set is defined by a specific quantity of NFTs that have not yet
expired and are sampled according to the quality $\varepsilon$ of
$\mathcal{R}_{i,h,\Theta}$. This state consists of two elements:

  * •

the unit price of the candidate NFTs previously published666We consider that
“one gets what one pays for” is applied during the sharing. This indicates
that the proportional mapping correlation between the unit price and the
resource quality can be established.. $[\psi]_{i^{\prime},h^{\prime},\Theta}$
where $i^{\prime}\neq i$ and $h^{\prime}<h$; and

  * •

the resource demands from the previous observation of other NFTs
$[\pi_{r},w]_{i^{\prime},h^{\prime},\Theta}$ where $i^{\prime}\neq i$ and
$h^{\prime}<h$.

These two components together define the publisher’s valid state set, as given
by

$s_{\mathcal{R}_{i,h,\Theta}}=\\{\psi,[\pi_{r},w]\\}_{i^{\prime},h^{\prime},\Theta}.$

Policy $\pi(\cdot)$. The local policy is persistently trained and updated over
time. In this process, each NFT publisher supplies their local learning model
with his/her observed state $s$ from the environment across various episodes.
Consequently, a probability distribution over valid actions by any publisher
can be derived, which aids in making decisions in subsequent episodes. This
relationship is represented as $\pi(s,a):\mathcal{S}\to\mathcal{A}$.

Actions ($\mathcal{A}$). In reference to the action definition in the non-
cooperative game involving $N$ agents, every agent forms its decision
$a\in\mathcal{A}$ based on its local policy. This policy is generated by the
agent’s local learning model during the ongoing episode. The set of
permissible actions for publisher $j$ has three components:

  * •

the decision $\mathcal{A}_{\text{trigger}}$ of triggering to publish an NFT or
not in the current episode;

  * •

the outcome action, which includes the sum of payment designed to adjust the
interest and descending rate favorably for the publisher, as well as the
segments of a previous NFT that his NFT is set to reference;

  * •

the income action, which is the unit price specified for his NFT in
anticipation of it being referred by others.

These three components together define the publisher’s valid action set, as
given by

$\displaystyle a_{\mathcal{R}_{i,h,\Theta}}=\\{$
$\displaystyle\mathcal{A}_{\text{trigger}},\mathcal{A}_{\text{down-
pay}},\mathcal{A}_{\text{out}},\mathcal{A}_{\text{in}}\\},$

where $\mathcal{A}_{\text{trigger}}$ is a Boolean value;
$\mathcal{A}_{\text{down-pay}}$ reflects the down-payment ratio
$\lambda\in[0,1]$.

Reward function ($\mathsf{R}$). A crafted reward function provides valuable
insights about the mapping $\mathcal{S}\to\mathcal{A}$, thereby enhancing the
effectiveness of the local policy. Taking into consideration the optimization
problem outlined in (2), any NFT publisher has two primary goals in an
episode: to minimize the cost of publishing an NFT related to its resource,
and to maximize the income from the potential usage of this resource by others
in the network. Hence, the reward function is constructed as

$\mathsf{R}(a_{\mathcal{R}_{i,h,\Theta}})=\mathbb{U}_{\mathcal{R}_{i,h,\Theta}}.$

All NFT publishers are considered rational. Their objective is to maximize
their rewards throughout the process of resource trading.

Environment. An environment is viewed as a black box that takes as input the
actions of the agents and outputs the states. In our paper, the NFT network is
the environment shared by all miners (in PoW contexts) or validators (PoS).

###  3.2. Operation Sketch

1

Initialization

2Initialize DRL parameters; Reset DRL replay memory; Clean caches of
$(\mathcal{O}_{\mathcal{R}_{i,h,\Theta}},\mathcal{I}_{\mathcal{R}_{i,h,\Theta}})$.

3

4 Procedure  _$\mathsf{MainFunc}$(__)_

5 while  _True_ do

6 foreach  _publisher $j$ in the network, concurrently_ do

7 $\Omega_{\mathcal{R}_{\text{raw}}}$ $\leftarrow$
$\mathsf{RetrieveResources}$(__) , $\forall j$ omitted;

8

9 $s_{\mathcal{R}_{\text{raw}}}$ $\leftarrow$
$\Omega_{\mathcal{R}_{\text{raw}}}$;

10 $a_{\mathcal{R}_{\Theta}}$ $\leftarrow$
$\text{DRLAgent.ChooseAction}(s_{\mathcal{R}_{\text{raw}}})$;

11
$(\textit{TX}_{id},s_{\mathcal{R}_{i,h,\Theta}},s^{\prime}_{\mathcal{R}_{i,h,\Theta}},a_{\mathcal{R}_{i,h,\Theta}},\mathcal{O}_{\mathcal{R}_{i,h,\Theta}},\mathcal{I}_{\mathcal{R}_{i,h,\Theta}})$
$\leftarrow$ $\text{DRLAgent.Execute}(a_{\mathcal{R}_{\Theta}})$, where
$\text{Quality}_{i}$ and $\text{Price}_{i}$ $\in$
$a_{\mathcal{R}_{i,h,\Theta}}$;

12 if  _$a_{\mathcal{R}_{i,h,\Theta}}.\mathcal{A}_{\text{trigger}}$ is
$False$_ then

13 $\mathsf{MemorizeExperience}$(__) , $\forall j$ omitted;

14

15 end if

16 else

17 while  _current block height $<(h+d)$, non-blockingly_ do

18 $\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}$.Update($q,d$) and
$\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}$.Update($\sigma,d$);

19 end while

20 if  _current block height $\geq(h+d)$_ then

21 $\mathsf{MemorizeExperience}$(__) , $\forall j$ omitted;

22

23 end if

24

25 end if

26

27 DRLAgent.UpdateParameters($\mathsf{SampleExperience}$(__)), $\forall j$
omitted;

28

29 $\mathsf{ObserveNetwork}$(__) , $\forall j$ omitted;

30

31 end foreach

32

33 end while

34

35

36end

37 Procedure  _$\mathsf{RetrieveResources}$(__)_

38 while  _$|\Omega_{\mathcal{R}_{\text{raw}}}| <|\Omega_{\textit{MAX}}|$_ do

39 $\Omega_{\mathcal{R}_{\text{raw}}}.$append(($\text{Quality}_{i^{\prime}}$,
$\text{Price}_{i^{\prime}}$)), $\forall i^{\prime}$-th NFTs in a sliding
window that adjusts with the growth of the blockchain tip;

40 end while

41

42

43end

44 Procedure  _$\mathsf{MemorizeExperience}$(__)_

45
$\text{DRLAgent.Memorize}((\textit{TX}_{id},s_{\mathcal{R}_{i,h,\Theta}},s^{\prime}_{\mathcal{R}_{i,h,\Theta}},a_{\mathcal{R}_{i,h,\Theta}},\mathcal{O}_{\mathcal{R}_{i,h,\Theta}},\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}))$;

46

47end

48 Procedure  _$\mathsf{SampleExperience}$(__)_

49
$(\textit{TX}_{id},s_{\mathcal{R}_{i,h,\Theta}},s^{\prime}_{\mathcal{R}_{i,h,\Theta}},a_{\mathcal{R}_{i,h,\Theta}},\mathcal{O}_{\mathcal{R}_{i,h,\Theta}},\mathcal{I}_{\mathcal{R}_{i,h,\Theta}})\leftarrow\text{DRLAgent.Sample}(\textit{BATCH\\_SIZE})$;

50
$\mathsf{R}(a_{\mathcal{R}_{i,h,\Theta}})\leftarrow\mathcal{I}_{\mathcal{R}_{i,h,\Theta}}-\mathcal{O}_{\mathcal{R}_{i,h,\Theta}}$,
with
$\mathsf{R}(a_{\mathcal{R}_{i,h,\Theta}})=\mathbb{U}_{\mathcal{R}_{i,h,\Theta}}$;

51 return
$(s_{\mathcal{R}_{i,h,\Theta}},s^{\prime}_{\mathcal{R}_{i,h,\Theta}},a_{\mathcal{R}_{i,h,\Theta}},\mathsf{R}(a_{\mathcal{R}_{i,h,\Theta}}))$;

52

53end

54 Procedure  _$\mathsf{ObserveNetwork}$(__)_

55 while  _blockchain is growing_ do

56 Observe the network to identify interesting NFTs, publish own NFTs based on
these findings, and trigger the next iteration inside $\mathsf{MainFunc}$(__)
for each publisher $j$.

57 end while

58

59

60end

61Notice: “DRLAgent.Execute($\cdot$)” in the context of our reference
incentive model, represents the action where publisher $j$ releases their new
rNFT $\mathcal{R}_{i,h,\Theta}$ to the blockchain. This includes the available
rNFT index $i$, block height index $h$, and reference list $\Theta$.

Algorithm 1 Implementing the (DRL-based) reference incentive model

Algorithm 1 operates autonomously for each publisher, ensuring the system’s
effective convergence to a stationary point even in a fully decentralized
setup. Each publisher begins by setting up their experience replay memory,
initializing predefined hyperparameters, weights, and any cumulative counters
associated with an NFT (Line 2). At the outset, publisher $j$ selects an
action $a$ at random. During the commencement of each workflow, the publisher
scans the network for appealing NFTs within a sliding window linked to the
blockchain’s tip, assessing the data quality and pricing of these NFTs (Line
6). When a decision is made to publish an NFT, i.e.,
$\mathcal{A}_{\text{trigger}}$ is set to true, the publisher also determines
the down-pay ratio ($\mathcal{A}_{\text{down-pay}}$), references to preceding
NFTs ($\mathcal{A}_{\text{out}}$), and sets the price for the new NFT
($\mathcal{A}_{\text{in}}$) (Line 9). Note that the references to preceding
NFTs undergo a normalization process to ensure that the total payment ratio
distributed among the referred NFTs sums up to one, in accordance with
Equation (1). The cumulative outcome and income for this NFT are updated along
with the reference payment over time (Line 15). The reward for this new NFT
might be immediate or might require waiting until the decay parameter $d$
concludes (Lines 10–20), depending on the publisher’s decision. This event is
then recorded in the replay memory. Consequently, each publisher’s DRL agent
updates its parameters by sampling from the memory. This training cycle
continues indefinitely or until a specified maximum number of block heights is
reached.

Algorithm’s complexity. The computational complexity of this model can be
expressed as $O((N+1)\times(101\times 10^{k}))$, where $N$ represents the
number of NFTs to be referenced, and $k$ signifies the decimal precision. This
complexity accounts for scenarios where the number of NFTs ranges from 0 to
$N$, each NFT possesses a reference rate varying from 0% to 100%. This
intricate calculation poses significant challenges, particularly in contexts
demanding continuous states and actions, especially when computational
resources are limited. To this end, it becomes imperative to constrain $N$
within practical bounds while maintaining a high level of accuracy denoted by
$k$. This is crucial for the effective deployment of the model in real-world
applications where resource constraints are prevalent. To illustrate the
efficacy of our approach within these constraints, we focus our attention on a
specific use case: limiting the number of references from an unlimited set to
just two. This targeted scenario not only showcases the practicality of our
approach but also provides a tangible example of its effectiveness. We present
experimental results in the following part to practically substantiate the
utility and performance of our proposed DRL method.

##  4\. Evaluation

In this section, we experimentally assess the DRL-based solutions by applying
our incentive model to a use case. We examine convergence performance and
stability under a variety of different environment settings. Several insights
are also shed and discussed.

###  4.1. Experiment Design

In our reference incentive model, we specifically focus on references between
NFTs representing datasets and models within an ML resource marketplace (see
Fig.2). To address the complexity of multiple datasets/models, a pre-merging
mechanism can be applied to align with the EIP-998 standard for composability.
The mechanism allows an NFT to represent a composite of multiple datasets
and/or models. Thus, each NFT can encapsulate a variety of dataset and model
resources as a single entity for reference777This enables the recursive
finalization of profit distribution by sequentially decapsulating bundled
resources. The specifics of inner profit distribution, however, fall outside
the scope of our study, as they can be implemented by Apps behind the scenes..
This mechanism is especially beneficial for Federated Learning (FL) scenarios.
It facilitates a streamlined approach by representing datasets and models as a
single composable NFT entity and allowing underlying applications to
deconstruct and process the bundled resources efficiently for critical FL
operations such as Federated Averaging.

Parameter settings. Our experiments include a series of parameters: the number
of publishers $N$, the quality distribution of the initial NFTs, the initial
raw interest $\hat{q}$, the size of the candidate set
$\Omega_{\mathcal{R}_{i,h,\Theta}}$ of any NFT $\mathcal{R}_{i,h,\Theta}$, the
initial decay parameter $d$, the initial fixed reward $\hat{\mathcal{I}}$, and
the initial fixed expense $\hat{\mathcal{O}}$.

For the purpose of proof-of-concept, $p_{0}$ is converted to:

$\displaystyle p_{0}=$
$\displaystyle\left(\hat{\mathcal{O}}+\mathcal{O}\right)\times[w_{0},w_{d},w_{m}],\text{
with }\mathcal{O}\propto\\{w_{d},w_{m}\\},$

where $w_{d}$ and $w_{m}$ are the reference weights for a dataset and a model,
respectively. Note that the term “bundle” is omitted for simplicity in the
presentation.

The outcome action is accordingly converted to:

$\mathcal{A}_{\text{out}}=(\pi_{r},w_{d},w_{m}),\text{ with
}w_{0}+w_{d}+w_{m}=1,\forall w\in\mathbb{R}_{0}^{+}.$

where $w_{d}$ and $w_{m}$ correspond to a portion of a dataset and a model
that is being shared, respectively.

Assumptions. In the context of the ML resource marketplace where our incentive
reference model is applied, we assume that each user knows which is most
suitable for the whole platform, and each NFT uses at most one dataset and one
model as its basis. A portion of a model might be pruned or compressed, and a
dataset might be a partial dataset. For example, 50% of a dataset might
represent half the data size, and 50% of a model might mean pruning half of
the parameters. Both the dataset and model resources are formatted as 256-bit
hash values, serving as URIs that redirect to decentralized data storage
platforms such as IPFS.

Hardware settings. Experiments are conducted on nodes in a high-performance
computing server with the following specifications:

  * •

CPU. 2 x Intel(R) 6138 CPU @ 2.00GHz, 2 × 40 cores

  * •

GPU. 8 × NVIDIA PCIe A100

  * •

RAM. 250GB

  * •

Disk. 2TB

Software settings. We carry out the experiments upon the Ubuntu 20.04 OS
environment with PyTorch 2.0.1 in Python 3.10.13.

We have a predefined number of agents operating concurrently on nodes, with a
decentralized pricing game running in the same cluster for simplicity and
generality. The solution employs a continuous version of Proximal Policy
Optimization (PPO), known for its effectiveness in DRL. It is important to
note that our solution is adaptable; it works seamlessly with various DRL
algorithms, including the classical Deep Deterministic Policy Gradient (DDPG),
ensuring transparency and flexibility in implementation.

Figure 2. Use Case: An ML Resource Marketplace

###  4.2. Experiment Results

The rewards in all figures (Fig.3-Fig.9) are normalized to keep the reward
values in a specific convenient range and obtain the best value approximation
since the value distribution function could significantly affect the gradients
(c51-settings, ). The occurrence of fewer result values for a particular
setting across all epochs can be attributed to the dynamics of the ML resource
marketplace, where the income from published NFTs is only realized at the end
of their expiry height $d$. If an NFT fails to be referenced before the
maximum epoch, its reward value is set to null.

Fig.3 illustrates the convergence trend of rewards across $100$ epochs for
various configurations of publisher numbers. The analysis reveals that as the
number of publishers increases from $10$ to $40$, their rewards tend to
converge. The majority of publishers settle at a moderate reward level,
approximately around the normalized reward of $0$. Only a small fraction
achieve high normalized rewards close to $1$, and similarly, few reach low
normalized rewards of $-1$. This trend becomes more pronounced with an
increase in the number of publishers, suggesting that employing a DRL-based
approach in the pricing game results in relatively fair outcomes when the
number of publishers is reasonable and resources are approximately uniformly
distributed.

(a) $N=10$

(b) $N=20$

(c) $N=30$

(d) $N=40$

Figure 3. Comparison between different settings of the number of publishers
$N$ in terms of normalized reward with a setting of uniform-distributed
initial NFTs, $\hat{q}=0.01$, $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$,
$\hat{d}=10$, $\hat{\mathcal{I}}=2$, $\hat{\mathcal{O}}=0.1$.

Fig.4 shows how different statistical distributions impact the rewards of
initial NFTs. In the uniform distribution, we observe a general equilibrium
among publishers, with most displaying similar rewards and a few outliers
adjusting to fit the common trend, which can be found in
Figs.3(a),4(a),5(a),6(b),7(b),8(a),9(a) under the same setting. The normal
distribution aligns with the expected bell-curve shape, showing a central
clustering of rewards. In contrast, the Pareto distribution deviates from the
anticipated 80-20 rule, with most publishers having uniform-like rewards and
only a few falling behind, indicating a lesser effect of resource
concentration. The Poisson distribution, however, presents a more varied
pattern with noticeable fluctuations among publishers, while collectively
maintaining a reward range between -0.5 and +0.5. This unexpectedly close
alignment to the uniform distribution, but with even more balance, suggests
our system’s proficiency in managing the randomness of the Poisson
distribution and maintaining equilibrium.

(a) Uniform Distribution

(b) Normal Distribution

(c) Pareto Distribution

(d) Poisson Distribution

Figure 4. Comparison between different settings of the quality distribution of
initial NFTs in terms of normalized reward with a setting of $N=10$,
$\hat{q}=0.01$, $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$, $\hat{d}=10$,
$\hat{\mathcal{I}}=2$, $\hat{\mathcal{O}}=0.1$.

Fig.5 illustrates the impact of different initial raw interest rates
($\hat{q}$) on publisher behaviors. At $\hat{q}=0.01$, we observe moderate
fluctuations, with most publishers settling around a -0.25 reward. Increasing
the rate to 0.05 results in a stabilization of rewards around 0.2, though some
publishers choose not to participate, likely to avoid costs. At a higher rate
of 0.1, similar behaviors are evident, but with an approximate decrease in
rewards from 0.2 to -0.2, indicating cost-conscious strategies. At the highest
rate of 0.5, there is a marked convergence of rewards within -0.5 to -0.2,
showing a collectively cautious approach in response to higher costs. It
suggests that as financial risks increase, publishers tend to focus more on
minimizing losses than maximizing gains, demonstrating the significant role of
economic factors in shaping strategies within NFT ecosystems.

(a) $\hat{q}=0.01$

(b) $\hat{q}=0.05$

(c) $\hat{q}=0.1$

(d) $\hat{q}=0.5$

Figure 5. Comparison between different settings of the initial raw interest
$\hat{q}$ in terms of normalized reward with a setting of $N=10$, uniform-
distributed, $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$, $\hat{d}=10$,
$\hat{\mathcal{I}}=2$, $\hat{\mathcal{O}}=0.1$.

Fig.6 and Fig.7 collectively demonstrate the influence of candidate set size
$|\Omega_{\mathcal{R}_{i,h,\Theta}}|$ and initial decay parameter $\hat{d}$ on
publishers’ reward patterns. In both scenarios, with smaller candidate set
sizes or lower decay parameters, there’s a significant fluctuation in rewards
among some publishers, indicative of a highly competitive or unbalanced
environment. This volatility is particularly pronounced when the candidate set
size is limited to $|\Omega_{\mathcal{R}_{i,h,\Theta}}|$ or $\hat{d}$ is low,
reflecting the intense competition and rapid shifts in the landscape of
reference fees and incentives due to shorter effective NFT durations. As both
the candidate set size and $\hat{d}$ increase, these fluctuations decrease,
leading to stabilization and convergence of rewards. This pattern suggests a
movement towards a more equitable distribution, mirroring the expected
outcomes of a uniform distribution. The increase in diversity and options
within the candidate set, along with the extended lifespan of NFTs due to a
higher decay parameter, both contribute to a fairer, more predictable, and
harmonious environment for publishers, emphasizing the crucial role these
parameters play in shaping the dynamics of competitive interactions and reward
distribution in NFT ecosystems.

Fig.8 and Fig.9 reveal the interplay between initial fixed reward
$\hat{\mathcal{I}}$ and initial fixed expense $\hat{\mathcal{O}}$, and their
impact on publishers’ reward behaviors in NFT ecosystems. The initial fixed
reward $\hat{\mathcal{I}}$, granted for superior performance in newly
published NFTs, induces notable variations in rewards among publishers when
set low. However, as $\hat{\mathcal{I}}$ increases, these fluctuations
diminish, leading to a more uniform reward distribution. Interestingly, at
higher $\hat{\mathcal{I}}$ values, most publishers opt for inactivity,
reflected in consistently zero rewards, with only a few active publishers
earning similar rewards, indicating a strategic shift towards non-
participation in publishing due to the high reward benchmark. Conversely, the
initial fixed expense $\hat{\mathcal{O}}$, a preventive measure against
malicious attacks, shows a less pronounced impact on publisher behavior at
lower levels. Yet, as $\hat{\mathcal{O}}$ escalates, it becomes a critical
factor, potentially fostering monopolistic trends within the NFT space, as
evidenced in Fig. 9(d). This suggests a delicate balance in setting
$\hat{\mathcal{O}}$: too low, and it is ineffectual as a deterrent; too high,
and it risks centralizing power and stifling diversity in publishing. These
observations underline the need for judicious calibration of
$\hat{\mathcal{I}}$ and $\hat{\mathcal{O}}$ to maintain a dynamic,
competitive, yet fair NFT environment, encouraging active participation while
safeguarding against disruptive behaviors.

(a) $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=5$

(b) $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$

(c) $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=20$

(d) $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=100$

Figure 6. Comparison between different settings of the candidate set size
$|\Omega_{\mathcal{R}_{i,h,\Theta}}|$ in terms of normalized reward with a
setting of $N=10$, uniform-distributed, $\hat{q}=0.01$, $\hat{d}=10$,
$\hat{\mathcal{I}}=2$, $\hat{\mathcal{O}}=0.1$.

(a) $\hat{d}=5$

(b) $\hat{d}=10$

(c) $\hat{d}=20$

(d) $\hat{d}=30$

Figure 7. Comparison between different settings of the initial decay parameter
$\hat{d}$ in terms of normalized reward with a setting of $N=10$, uniform-
distributed, $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$, $\hat{q}=0.01$,
$\hat{\mathcal{I}}=2$, $\hat{\mathcal{O}}=0.1$.

(a) $\hat{\mathcal{I}}=2$

(b) $\hat{\mathcal{I}}=4$

(c) $\hat{\mathcal{I}}=8$

(d) $\hat{\mathcal{I}}=16$

Figure 8. Comparison between different settings of the initial fixed reward
$\hat{\mathcal{I}}$ in terms of normalized reward with a setting of $N=10$,
uniform-distributed, $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$, $\hat{q}=0.01$,
$\hat{d}=10$, $\hat{\mathcal{O}}=0.1$.

(a) $\hat{\mathcal{O}}=0.1$

(b) $\hat{\mathcal{O}}=0.2$

(c) $\hat{\mathcal{O}}=0.4$

(d) $\hat{\mathcal{O}}=0.8$

Figure 9. Comparison between different settings of the initial fixed expense
$\hat{\mathcal{O}}$ in terms of normalized reward with a setting of $N=10$,
uniform-distributed, $|\Omega_{\mathcal{R}_{i,h,\Theta}}|=10$, $\hat{q}=0.01$,
$\hat{d}=10$, $\hat{\mathcal{I}}=2$.

Takeaways. We provide the following key experimental results.

① Adaptability in diverse distribution environments. Our system demonstrates
remarkable adaptability and resilience across different initial NFT quality
distributions, effectively managing variations in resource concentration. The
deviation from the 80-20 rule in Pareto distributions and the unexpected
equilibrium in Poisson distributions underline the system’s capacity to
maintain balance and fairness, irrespective of the underlying distribution
characteristics.

② The Interplay of economic factors and publisher behavior. Economic factors
(e.g., initial raw interest rate, fixed expenses) significantly influence
publisher strategies within NFT ecosystems. As financial risks heighten,
publishers focus more on risk mitigation than gain maximization, leading to
strategic shifts like reduced participation or monopoly formation.

③ Equilibrium and fairness in reward distribution. Increasing the number of
publishers, along with adjustments in candidate set size and NFT lifespan,
contributes to a more equitable reward distribution. This phenomenon aligns
with uniform distribution principles, suggesting that a larger, more diverse
candidate set and extended NFT lifespans promote a fairer and more stable
environment.

##  5\. Discussion

###  5.1. Additional Capabilities

Flexibility for customized requirements. The considered ML resource
marketplace accommodates the provision of additional customized services.
Users registered with the marketplace might be interested in customized
preprocessing or privacy-sensitive datasets and models. Such preferences can
be related to various attributes, such as the quality of training resources,
fairness, bias mitigation, privacy enforcement, and accountability. Users can
optionally request all these aspects for an additional charge. These
attributes can also enhance the coherence of regulatory compliance.

Mathematically, we represent the normalized service demands as
$\varphi_{\dagger}\in[0,1]$, and the unit price of offering customized
services as $\psi_{\dagger}\in[0,\bar{\psi_{\dagger}}]$. This leads to two
updates to the system:
$\mathcal{A}_{\text{out}}\Longleftarrow\varphi_{\dagger}\cup\mathcal{A}_{\text{out}}$
and
$\mathcal{A}_{\text{in}}\Longleftarrow\psi_{\dagger}\cup\mathcal{A}_{\text{in}}$.

Adaptability for multiple conditions. The reference incentive model seamlessly
interplays with the marketplace’s dynamics. The model’s resilience in various
NFT quality distributions showcases its ability to adapt to different market
conditions, maintaining fairness and resource balance. This adaptability is
critical in managing the economic factors influencing publisher strategies
within the NFT ecosystem. As financial risks escalate, the model’s framework
can further accommodate strategic shifts in publisher behavior, emphasizing
the importance of setting balanced economic parameters.

Fairness in resource/profit distribution. The model’s approach to reward
distribution, by increasing publisher numbers and adjusting NFT parameters,
aligns with uniform distribution principles. This strategy ensures equitable
rewards and fosters a stable environment, highlighting the model’s role in
sustaining a harmonious and competitive NFT marketplace.

###  5.2. Broader Adoption

Compatibility with NFT standards. The proposed framework demonstrates
extensive compatibility with various NFT standards, enhancing its adoption
potential in diverse scenarios:

  * •

Composability and hierarchical relationships: EIP-998, 6150, and 7510 focus on
composability and hierarchical NFT structure. Our model complements these by
effectively managing and tracking the complex inter-NFT relationships, which
enriches the depth of interactions within these frameworks.

  * •

Utility and ownership: EIP-5006, 6059, and 5528 emphasize flexible utility,
ownership models, and financial transactions in NFTs. Our model can augment
these standards by providing robust mechanisms for tracking ownership and
utility changes and facilitating transparent financial dealings.

  * •

Extended functionalities: EIP-4519, 5023, and 5606 introduce use cases such as
physical asset linkage and multiverse asset management. Our model can enhance
these use cases by offering a structured system for tracking and incentivizing
interactions, thus adding value to these applications.

  * •

External standards: While our design originates from the Ethereum ecosystem,
our overarching reference incentive model can be extended to L2 NFTs on other
public chains that incorporate reference functions in the future.

Integration with NFT Marketplaces. Our model allows straightforward
integration into platforms such as OpenSea, Rarible, and Binance, enriching
their diverse collections with advanced relationship tracking and analysis
capabilities. This integration is designed to be unobtrusive, ensuring the
maintenance of existing marketplace functionalities and user experiences.
Users have a strong inherent motivation to earn continuous profits. This model
ensures a transparent and efficient way to track and reward contributions
within the NFT ecosystem and amplifies their profit potential from sharing
NFTs and data. Our approach aligns well with the evolving needs of the digital
asset community, offering a balanced advantage for both marketplace operators
and users.

Extension to any resource marketplace. As discussed in the case study, our
model can be applied to any (ML-)resource marketplace scenario. Here, models
and datasets are openly shared and developed through mutual referencing,
forming a DAG-based network within the marketplace. However, the framework’s
potential extends beyond the resource marketplace to other areas with
different complexities. For instance, it can be used for joint ventures
involving data-driven investment strategies in finance, which creates a
transparent network of contributions and rewards. Similarly, in the metaverse,
this model can be crucial for managing the creation and sharing of virtual
assets. It can trace and incentivize contributions in the virtual economy,
which ensures fair reward distribution among digital artists, developers, and
users.

##  6\. Related Work

NFT-related standards. Since the advent of NFTs in 2021 (wang2021non, ), a
plethora of sub-domains have emerged, consisting of new applications
(vidal2022new, )(wang2022exploring, )(cetinic2022understanding, ), system
security (das2022understanding, ), and addressing anti-law activities such as
wash trading (wen2023nftdisk, ) and rugpulls (huang2023miracle, ). Instead of
relying on nebulous topic classifications, we orthogonally explore the
foundational elements — the token standards. Specifically, we review all up-
to-date (Jan. 2024) NFT-related token standards within the Ethereum ecosystem
(cf. Table 2), selectively presenting their primary functions, distinctive
features, and potential applications. To our surprise, the landscape of NFT
standards has experienced a remarkable expansion, skyrocketing from approx. 10
(mid-2021) to 50+, surpassing the pace observed in other standard tracks that
are assumed to progress at a slower rate.

Recent incentive analysis. The recent wave of incentive analyses has
predominantly focused on the Ethereum ecosystem and PoS protocols following
its transition. Deb et al. (possafety2023, ) proposed a model for analyzing
the cryptoeconomic safety of PoS blockchain (Ethereum 2.0) and observed the
bounds between cost and profit from malicious corruption. Cortes et al.
(cortes2023autopsy, ) systematically studied Ethereum’s post-merge incentive
mechanism and empirically analyzed the performance of the corresponding
network. Huang et al. (huang2021rich, ) observed the diverse incentive models
implemented in current PoS blockchains and provided an in-depth analysis of
various PoS representatives. More incentive studies also apply to broader
areas such as DeFi products (auctions (wu2023strategic, )(bahrani2023bidders,
), AMM (kulkarni2022towards, )(bartoletti2022theory, ), DEX
(hasbrouck2023economic, )), MEV (chionas2023gets, ), transaction fees (post-
EIP1559, (ferreira2021dynamic, )(leonardos2023optimality, )), NFTs
(heimbach2023defi, )(chen2022absnft, )(bao2023herding, ), etc.

DAG formation in L1. DAG topology has been widely applied in blockchain
systems (wang2023sok, ) for improving scalability and performance
(wang2021weak, )(yu2020ohie, )(bagaria2019prism, )(benvcic2018distributed, ),
followed by a cascade of supplementary analyses, including security
(amores2023we, )(kiayias2019trees, )(wang2020security, ), fairness
(raikwar2023fairness, ), simulation (zander2019dagsim, )(lin2023tanglesim, )
and optimizations/protection (malkhi2022maximal, ). Most L1 protocols utilize
DAG to reshape their data structures (silvano2020iota,
)(churyumov2016byteball, )(baird2016swirlds, )(li2020decentralized, ) and
reform consensus progress (keidar2023cordial, )(keidar2021all,
)(schett2021embedding, )(danezis2022narwhal, )(spiegelman2022bullshark, ),
which requires highly adaptive modifications to their corresponding
foundational systems.

DAG adoption for L2. Diverging from applying DAG to blockchain
structure/consensus, several studies have embraced the DAG philosophy to
construct upper-layer decentralized applications that operate independently of
their L1 counterparts. Wang et al. (wang2023referable, ) introduced the
utilization of DAG topology in building an NFT-rewarding market, as expounded
in this paper. Yu et al. (10174882, ) stepped further by leveraging Graph
Neural Networks (GNNs) to develop a prediction and recommendation framework.
Simultaneously, DAGs can also be used in the closely related domain of
decentralized federated learning, aiding in the parallel processing of task
workers (ironforge, ).

Game theory in blockchain. Various game theory models have found application
in blockchain systems (liu2019survey, ) such as utilizing stochastic games
(kiayias2016blockchain, ), cooperative games (lewenberg2015bitcoin, ),
evolutionary games (kim2019mining, ), Stackelberg games (chen2022absnft, ),
subgame perfect Nash equilibrium (qin2022bdts, ). They serve to analyze
practical scenarios at different levels, such as staking/mining pools
(gersbach2022staking, )(zhang2022insightful, )(li2020mining, )(wang2019pool,
), mining participation (chaidos2023blockchain, ), validator selection
(zhang2023rationally, )(gavzi2023fait, ), mining behaviors (eyal2015miner,
)(bai2021blockchain, )(cheung2021griefing, ), off-chain transactions
(rain2023towards, ) and adversarial strategies (estradabreaking,
)(heimbach2022eliminating, )(negy2020selfish, )(kwon2017selfish, ).

DRL-assisted applications. Many areas realize the superiority of applying deep
reinforcement learning to solve complex problems, including blockchain L1
solutions (10201805, ; zhang2024tbdd, ), IoT and telecommunication (8657779, ;
8231220, ), microchip design (liang2020adaptive, ), robotic design
(gu2017deep, ), gaming (lample2017playing, ), healthcare (yu2021reinforcement,
), economics and finance (Charpentier2023, ; math8101640, ),
training/jailbreaking ML models (hu2023enabling, ; zou2023universal, ) and
more (wang2022deep, ).

##  7\. Conclusion

In this paper, we study how to make NFT rewards better. After checking
existing NFT standards and projects, we noticed that current reward systems
are one-time and separate. In response, we propose a reference incentive
model, where NFTs are structured as DAG, for deep analyses. Our model allows
each token to grow its connections, earning more rewards from future
transactions. We also prove that this model works better both in theory and
practice.

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Table 2. Ethereum NFT-related Standards: Categorized by Final-LastCall-Review-
Draft (Updated on Feb. 2023)

EIP- | Title | Main (new) functions/events/metadata | Feature | Application
---|---|---|---|---
721 | Non-fungible token | $\mathsf{tokenID}$ | Artwork/IP |
1155 | Multi token standards | $\mathsf{batchProcessing}$ | Adding attributes for groups | Game
2309 | ERC-721 Consecutive Transfer Extension | $\mathsf{ConsecutiveTransfer}$ | Upgrading events | Authorization
2981 | NFT Royalty Standard | $\mathsf{royaltyInfo}$ | Retrieving the royalty payment infomation | Royalty payments
3525 | Semi-Fungible Token |  $\mathsf{SlotChanged}$, $\mathsf{slotOf}$ | Additional attribute for semi-fungible | Financial market
4519 | Non-Fungible Tokens Tied to Physical Assets |  $\mathsf{ownerEngagement}$, $\mathsf{userEngagement}$ | Representing physical assets | IoT indusrty
4906 | EIP-721 Metadata Update Extension | $\mathsf{MetadataUpdate}$ | Upgrading events |
4907 | Rental NFT, an Extension of EIP-721 | $\mathsf{userExpires}$ | Adding a new role and timer | Rental market
4910 | Royalty Bearing NFTs | CRUD (RoyaltyAccount), $\mathsf{royaltyPayOut}$ | Upgrading royalty account management | Royalty payment
4955 | Vendor Metadata Extension for NFTs | namespaces | Upgrading metadata | Metaverse 3D modelling
5006 | Rental NFT, NFT User Extension | UserRecord | Adding the new role of user | Rental Market
5007 | Time NFT, ERC-721 Time Extension |  startTime, endTime | On-chain time management | Lending market
5023 | Shareable Non-Fungible Token | share | Enabling assets to be sharable | Collaborative projects
5192 | Minimal Soulbound NFTs | locked | Bound to a single account | Soulbound Items
5375 | NFT Author Information and Consent | authorInfo | Adding authorship and consent | Authorization
5380 | ERC-721 Entitlement Extension |  entitle, entitlementOf | Adding entitlement for users | Rental market
5489 | NFT Hyperlink Extension |  authorizeSlotTo, revokeAuthorization | Adding hyperlinks |
5528 | Refundable Fungible Token | escrow (Fund/Refund/Withdraw) | Enabling refund | Rental market
5570 | Digital Receipt Non-Fungible Tokens |  | Adding digital receipts for physical purchases |
5606 | Multiverse NFTs |  bundle, delegateTokens | Enabling one-to-many asset mapping | Metaverse, Game
5615 | ERC-1155 Supply Extension | totalSupply | Fetching token supply data |
5725 | Transferable Vesting NFT |  claimedPayout, vestedPayout | Vesting tokens | Financial market
5773 | Context-Dependent Multi-Asset Tokens |  acceptAsset, acceptAsset, setPriority | Adding context-dependent output |
6059 | Parent-Governed Nestable Non-Fungible Tokens |  DirectOwner, Child | Adding parent-governed nestable relationship | File system
6066 | Signature Validation Method for NFTs |  sign, isValidSignature | Verifying signature | E-voting
6105 | No Intermediary NFT Trading Protocol |  listItem, buyItem | Adding a marketplace functionality | Marketplace
6147 | Guard of NFT/SBT, an Extension of ERC-721 |  changeGuard, transferAndRemove | Adding a new role for new management scheme | Soulbound Items
6150 | Hierarchical NFTs |  parentOf, childrenOf | Adding hierarchical structure | File system
6220 | Composable NFTs utilizing Equippable Parts |  Equipment, IntakeEquip, equip | Adding parts via equipping | Certification
6381 | Public Non-Fungible Token Emote Repository |  emote, emoteCountOf | Enabling emote repository | Feedback system
6454 | Minimal Transferable NFT detection interface | isTransferable | Identifying transferability |
6672 | Multi-redeemable NFTs |  redeem, getRedemptionIds | Enabling redemption | Financial market
6808 | Fungible Key Bound Token |  addBindings, allow (Transfer/Approval) | Upgrading security to fungible | Financial market
6809 | Non-Fungible Key Bound Token |  addBindings, allow (Transfer/Approval) | Upgrading security to non-fungible | Financial market
5008 | ERC-721 Nonce Extension | nonce | Adding nonce |
5114 | Soulbound Badge |  CollectionUri, badgeUri | Bound to one-off transferring | Soulbound Items
5216 | EIP-1155 Approval By Amount Extension |  approve, allowance | Upgrading approval functions |
5496 | Multi-privilege Management NFT Extension |  setPrivilege, privilegeExpires | Adding shareable privileges | Marketplace
5585 | ERC-721 NFT Authorization |  authorizeuser, transferUserRights | Enabling cross-users authorization | Authorization
6982 | Efficient Default Lockable Tokens | locked | Enabling locks to reduce gas consumption |
7066 | Lockable Extension for ERC-721 |  lock, transferAndLock | Enabling locks to management trading | Authorization
7160 | ERC-721 Multi-Metadata Extension |  tokenURIs, pinTokenURI | Upgrading metadata URIs | File system
7231 | Identity-aggregated NFT |  setIdentitiesRoot, verifyIdentitiesBinding | Integrating Web2 and Web3 identities | Metaverse
4973 | Account-bound Tokens |  unequip, give, take | Bound to an account | Game
5521 | Referable NFT |  referringOf, setNodeReferring | Enabling reference relationship | Literature market
6065 | Real Estate Token |  debtOf, managerOf, geoJsonOf, legalOwnerOf | Adding real estate functions | Real estate market
6120 | Universal Token Router |  exec, pay, discard | Upgrading tranfer calls to reduce gas consumption |
6551 | Non-fungible Token Bound Accounts |  account, token, state | Account bound to tokens |
6997 | ERC-721 with transaction validation step |  ValidateTransfer, ValidateApproval | Upgrading security to non-fungible | Financial market
7432 | Non-Fungible Token Roles |  grantRoleFrom, roleExpirationDate | Adding expirable role management | Rental market
998 | Composable Non-Fungible Token |  rootOwnerOf, transferChild | Enabling composability between tokens | Metaverse, Game, Marketplace
4883 | Composable SVG NFT | renderTokenById | Extending composability to SVG tokens | Marketplace
5173 | NFT Future Rewards |  releaseFR, retrieveFRInfo | Enabling future earnings | Financial market
5700 | Bindable Token Interface |  bind, boundBalanceOf | Tokens bound to other tokens | Game, Rental market
5727 | Semi-Fungible Soulbound Token |  issue, revoke, verify | Additional attribute for semi-fungible soulbound token | Soulbound Items
5791 | Physical Backed Tokens | transferTokenWithChip | Linking physical items | IoT industry
6604 | Abstract Token | AbstractTokenMessage | Abstracting tokens | Identification, Access credentials
6682 | NFT Flashloans |  flashFeeToken, availableForFlashLoan | Enabling flashloans | Real Estate, Financial market
6785 | ERC-721 Utilities Information Extension |  setUtilityUri, utilityHistoryOf | Adding utility to tokens |
6786 | Registry for royalties payment for NFTs |  payRoyalties, getPaidRoyalties | Upgrading royalties | Royalty payments
6806 | ERC-721 Holding Time Tracking |  getHoldingInfo, _afterTokenTransfer | Adding holding time | Rental market
6823 | Token Mapping Slot Retrieval Extension | getTokenLocationRoot | Enhancing precision of off-chain transaction simulations |
6956 | Asset-bound Non-Fungible Tokens |  tokenByAnchor, OracleUpdate | Bound to assets authorized by oracle | Digital twin
7303 | Token-Controlled Token Circulation | _grantRoleBy (ERC721, ERC1155) | Enabling token-controlled token circulation | Authorization
7507 | Multi-User NFT Extension |  userExpires, setUser | Bound to multiple users | Rental market
7015 | NFT Creator Attribution |  _validateSignature, _isValid | Securing creator attribution | Authentication, Authorization
7085 | NFT Relationship Enhancement |  setRelationship, setAttribute | Enhancing reference relationship | Literature market
7496 | NFT Dynamic Traits |  getTraitValue, TraitUpdated | Enabling trait values | Marketplace
7498 | NFT Redeemables |  getCampaign, redeem | Extending redeemablility | Marketplace
7510 | Cross-Contract Hierarchical NFT |  parentTokenOf, setParentTokens | Enabling cross-contracts hierarchy | Metaverse
7513 | Smart NFT - A Component for Intent-Centric |  execute, validatePermission | Enabling executable NFTs | Metaverse
7531 | Staked ERC-721 Ownership Recognition | rightsHolderOf | Adding staking interface for Legacy NFTs | Game
7548 | Open IP Protocol built on NFTs |  isParent, isSibling, Component | Merging multiple IPs | Rental market
7590 | ERC-20 Holder Extension for NFTs |  TransferERC20ToToken, …From… | Extending exchange of different token types | Marketplace