entities. These agents exhibit behaviour driven by their individual interests. Therefore, the consensus protocol must be designed to consider efective incentive compatibility constraints. The theoretical approach is based on the evaluation of incentive compatibility constraints for both honest and faulty nodes, according two diferent remuneration schemes. By extending the principles of incentive compatibility from non cryptocurrency blockchains to organizational structures modelled as DAOs, we explore how decentralized governance models can benefit from blockchain-based incentive mechanisms while addressing the inherent economic risks and legal challenges.
Blockchain technologies have received significant attention from economists, especially in the study of
non-fiat currencies and their impact on traditional monetary systems. Non-fiat currencies are those that
are not issued or regulated by a central government and lack physical backing like traditional currency.
Bitcoin [
However, it is important to acknowledge that blockchain is a valuable technology with diferent
applications, exerting significant influence across various sectors including environment, education,
health, financial services, trading, utilities, manufacturing, as well as both private and public
administrations. Beyond its origins in cryptocurrency, blockchain technology ofers innovative solutions in
numerous fields, such as supply chain management, healthcare, and digital identity management. For
instance, in supply chain logistics, blockchain provides a transparent and tamper-proof record system
that enhances traceability and accountability, thereby reducing fraud and ensuring product authenticity
[
Central to the success of these non-cryptocurrency applications are the incentive mechanisms that
encourage participation and ensure the integrity of the system. These mechanisms often involve
rewarding participants with tokens or digital assets for their contributions to the network, such as
validating transactions or providing storage space, which helps maintain the high-security standards
necessary for these applications. For example, in blockchain-based supply chains, participants including
suppliers and transporters may receive tokens as incentives for maintaining accurate and timely data
entries, which are crucial for the efectiveness and reliability of the supply chain [
This study aims to explore blockchain technologies in-depth, including the integration of fundamental blockchain features within economic theory and applications. It is important to note that applying an economic perspective to the functioning and attributes of blockchain may provide valuable insights to the extensive body of literature that has predominantly evolved within the realm of computer science. It is important to recognise the unique approach of economics in addressing problems and in choices making, which difers from the hypotheses and objectives typically used in computer science investigations.
Contribution of economic theory to computer science practice on blockchains is especially relevant in the realm of some potential applications of blockchain technologies where free-riding or other opportunistic behaviours may emerge. In the economic perspective, blockchain nodes are individuals, whose behaviours and objectives must be considered.
In contexts where blockchain is used outside of cryptocurrency - such as in digital supply chains, public
record management, or consensus models for collective decision-making - these issues become
particularly pronounced. Free-riding and opportunistic behaviors are crucial concerns in non-cryptocurrency
blockchain applications due to the decentralized nature and lack of a central authoritative entity which
in traditional systems often acts as a monitor or enforcer. For example, in a blockchain-based digital
supply chain, a participant may under-report sales to evade fees or engage in selective misreporting
to gain competitive advantages. Without the direct oversight typical in centralized systems, such
actions can undermine the integrity and trust upon which the blockchain operates. Real-world data
and theoretical analysis show that free riding can lead to significant ineficiencies and increase the cost
of maintaining blockchain systems, potentially making them economically unviable without proper
incentive mechanisms in place [
Agents often face complex and dynamic situations that involve rational, emotional, and social elements. Economics takes a unique approach to problem-solving and decision-making, based on a deep understanding of the behaviour, dynamics, and interactions among agents. In contrast, computer science is primarily focused on system design, algorithm optimization, and information management. The issues tackled in computer science are usually well-defined and structured, governed by clear logic and rules. The primary goal is to ensure the eficiency and accuracy of technical solutions. The integration of these perspectives is crucial in the development of blockchain solutions that are not only technically robust but also economically sustainable.
The traditional paradigm in distributed computation categorises agents as either ’good’ or ’bad’ [
To understand the ethical and security challenges presented by blockchain technology, it is useful
to analyse a case study that clearly demonstrates the complex relationship between technological
vulnerabilities, ethical concerns, and the involvement of malicious actors in shaping the development
of blockchain technology. In 2016, a hacker exploited a vulnerability in the code of the Decentralised
Autonomous Organisation (DAO) and transferred 3.6 million Ether, valued at approximately 50 million
dollars, into a personal account. The DAO was a pioneering initiative in blockchain-based governance,
aiming to democratise investment in Ethereum-based start-ups by enabling investors to allocate funds
to proposed projects using Ethers. The breach not only highlighted vulnerabilities within such platforms
but also sparked a controversial debate over the blockchain’s immutable nature and the ethical principle
of ’code is law’. The Ethereum community’s decision to rectify the theft through a network fork resulted
in significant fallout, including the emergence of Ethereum Classic and a revaluation of hard and
soft fork applications in the blockchain domain [25]. Further complicating the situation, the hacker
communicated directly with the Ethereum and DAO communities after the attack through an open letter.
The hacker defended the extraction of funds as legal under the jurisdiction’s laws, exploiting a loophole
in the DAO’s smart contract code. The hacker claimed that exploiting a systemic flaw was not a crime
and threatened legal action against any attempts to recover the stolen Ether. This increased tensions
within the community. In addition, the hacker’s eforts to sabotage soft fork proposals by ofering
significant bribes to Ethereum miners highlight the dificulties in implementing technical solutions
to ethical violations. This controversial exchange resulted in the abandonment of a soft fork due to
identified vulnerabilities, ultimately requiring a hard fork. The division of the Ethereum blockchain into
Ethereum (ETH) and Ethereum Classic (ETC) resolved the immediate crisis and sparked a significant
discussion on censorship resistance and the principle of blockchain immutability [
Other contributions draw attention to the contrasting methodologies employed in computer science
and economics within the context of blockchain technology [
A practical example of this dynamic is Dogecoin, a cryptocurrency conceived purely ironically in 2013.
Contrary to the rational expectations of game theory, Dogecoin gained popularity and market value
despite its unconventional origin [
In the context of blockchain and consensus protocols, it is crucial for nodes to adhere to the established protocol to ensure network consistency and security. The use of the ’Byzantine’ concept recognises the possibility of non-compliant actions by certain nodes. Therefore, it is necessary to develop consensus algorithms that can handle such deviations in behaviour, ensuring the security and integrity of the system, even in the presence of defective or malicious nodes.
A specific investigation delves into numerous economic implications and challenges within the realm
of economic science [
Non-cryptocurrency applications of blockchain are often private blockchains, due to limitations
observed in public blockchains when applied to industrial use cases. It is important to note that public
blockchains exhibit constraints that prove detrimental to corporate and administrative applications [
Another research has highlighted that incentive-compatible mechanisms widely employed in existing
blockchain systems are not seamlessly applicable to non-cryptocurrency scenarios [
Contribution of the paper is the analysis of diferent rewarding schemes ensuring the compatibility of
incentives for self-interest agents maximizing their utility functions. As also emphasised recently [
In blockchain, incentivization mechanisms play a crucial role in motivating miners to participate in validation processes, contributing significantly to the system’s overall maintenance. While efective in cryptocurrency applications, extending existing blockchain systems to non-cryptocurrency domains with distinct business models poses a significant challenge. The lack of efective incentives can be a significant obstacle to the wider adoption of blockchain technology.
An incentive compatibility mechanism characterizes a process where participants would not find
it advantageous to violate the rules of the process [
The main challenge is to create an incentive mechanism that can be easily adapted to
noncryptocurrency applications. The need for a compatible incentive mechanism becomes evident in
the context of non-cryptocurrency blockchain applications that employ ’Voting-based’ consensus
algorithms. Research in this domain is currently limited and mostly focused on incentive mechanism
design for cryptocurrency applications that use ’Proof-based’ consensus algorithms [
It is essential to point out that the ‘Voting-based’ consensus algorithms are used also in cryptocurrency
permissionless blockchains, where probabilistic consensus can be achieved due to the large numbers of
not identified nodes. In this framework, fast probabilistic consensus protocols [
It is important to note that studies on incentive compatibility for Proof-of-Work (POW) are not applicable to PBFT-based blockchains due to the inherent disparity between ’Proof-based’ and ’Votingbased’ consensus algorithms. Bridging this gap is essential for the successful integration of blockchain technology into non-cryptocurrency applications.
To tackle the issue of creating digital identities on a blockchain and implementing an anonymous
voting system to prevent the creation of fictitious digital identities, an approach is needed where the
blockchain is used as an immutable ledger to securely store digital identities [
To ensure anonymity in the voting system, cryptographic techniques such as zero-knowledge proofs
and homomorphic encryption voting systems can be implemented. These techniques allow participants
to prove they possess a certain piece of information without revealing it. The proposed zero-knowledge
proofs and homomorphic encryption voting system ensures integrity, confidentiality, and authenticity
of votes while preserving voter anonymity [
To prevent the creation of fictitious digital identities, identity validation is performed before voting
through ofline verification procedures or interactions with certification authorities. Anti-Sybil
mechanisms can be implemented that require approval by existing members before assigning an identity [
Despite the shift in consensus algorithms from ’Proof-based’ to ’Voting-based’, concerns about
incentive compatibility remain, particularly in PBFT-based consensus algorithms. Free riders within
peer-to-peer networks exploit benefits to the detriment of honest actors [
Acknowledging the rational and self-interested nature of participants, the design of incentive
mechanisms rooted in game theory proves indispensable in addressing these challenges [
Several studies have analysed the compatibility problems that arise in blockchain systems based
on Practical Byzantine Fault Tolerance (PBFT), particularly regarding incentive mechanisms. One
notable endeavour, the SmartCast system [
A fundamental process in blockchain functioning is the broadcast process, implying a problem
concerning asymmetric information, because nodes have private information on the content of the message they
receive. The message content may be a dichotomous variable, as in the retrieve/attack message of the
Byzantine problem [
To comprehend and enhance the incentive mechanisms in such a system, an understanding of game
theory is indispensable. The concept of Nash equilibrium, where each player, recognizing the strategies
of others, has no incentive to unilaterally change their strategy, can be crucial in designing systems
where honest behaviour is maintained [
Consider a non-crypto currency blockchain with n=3k+1 validators, including faulty/malicious validators who are interested in blockchain malfunctioning and/or wrong certifications. In a PBFT protocol the block is accepted if at least 2k+1 validators agree on the block acceptance. The agreement of each validator i is expressed through a vi vote (i=1,..,n), which can take two values: Therefore, the final decision on the block can be summarized as follows: = {︃1 if the validator agree,
0 if the validator does not agree.
If ∑︁ > =1
If ∑︁ ≤ =1 {︃1 if the content is true
0 if the content is false {︃1 if the message reaches the consensus
0 if the message does not reach the consensus
Furthermore, we assume that a reputation grade > 0, or another kind of non-monetary reward, is associated with the voting (consensus) process.
Finally, we assume that the validators have the capability to access the data encapsulated within the blocks, although they cannot comprehend or interpret the contents. From the validator’s perspective, the data housed within the block is simply construed as uncomplicated sequences of bits, even singular bits. The validator’s role is emphasised as impartial through this abstraction, with a focus on the binary nature of the data rather than its semantic interpretation.
The following behavioral hypotheses are adopted: H1: Validators can read the message content as either true or false.
H2: Honest validators receive positive satisfaction from the acceptance of true blocks and the rejection of false blocks (with the same satisfaction gain). Faulty validators receive positive satisfaction from the acceptance of false blocks and the rejection of true blocks (with the same satisfaction gain).
H3: Honest and faulty validators receive positive satisfaction for positive .
With these basic elements of the blockchain, we can describe the utility functions of the faulty ( ) and honest () validators as , = (, ) as follows:
⎧ ⎨⎪> 0 if = ′ = ⎪⎩= 0 otherwise {︃(1, 1) a true message is accepted
(0, 0) a false message is rejected ′ =
⎧ ⎨⎪> 0 if = ⎪⎩= 0 otherwise {︃(1, 0) a true message is accepted
(0, 1) a false message is rejected
In other words, these utility functions imply that the honest validator receive positive satisfaction from the acceptance of a true block or the rejection of a false block, whereas the faulty validator pursue the objective of false blocks accepted and true blocks rejected (H2). Note that the derivatives are independent from the vote expressed by the validators. As to the reputation grade, both types of validators have increasing utility from the reward (H3).
′ = > 0 ′ = > 0 (6)
The remuneration scheme is fundamental in a mechanism design. Two diferent remuneration schemes will be analysed, considering alternatively the payofs for all types of validators at the end of the consensus process (final payofs), or in the while the consensus process is still running (expected payofs), that is when the y value is still unknown. The final payofs are described in a strategic form, the matrix representation of a simultaneous (two players) non cooperative game, with the validator as row player and the State of Nature as column player, who selects the message proposed to validator. Payofs are quantified only for the row player (the validator). Validator has two available actions/strategies when receiving the message, corresponding to the values (1,0) chosen for the vote expressed with vi. For each strategy, resulting payofs are reported according to the diferent States of Nature. (3) (4) (5)
Scheme A: the validator receives a positive if the block is accepted, and the vote is = 1. No reward is provided for the ’no agreement’ vote.
Nevertheless, when validators give their vote, they know if the message content is true or false, but they do not know if the message will be added to the block or not. They may have an expected result , based on the PBFT hypothesis on faulty/honest nodes. If all faulty nodes vote 0 to true blocks and 1 to false block, whereas honest nodes do the opposite, the probability of each type of block to be accepted/rejected are:
If they can recognize the true/false feature of the block, they can evaluate the expected payofs as follows. Let’s consider first the expected values for honest nodes ( ) when facing true blocks. {︃( 23 + 1)(′ + ′) if = 1 ( 23 + 1 − 1)′
From the above descriptions it easy to verify that = 1 is a dominant strategy for an honest node facing true blocks. When coming at false blocks, the expected values are as follows. {︃( 23 + 1 − 1)′ + ( 13 − 1 + 1)′ Here, one would expect that = 0 is a dominant strategy, but this is true only if ′ > 1 ′ 3 (7) (8) (9) (10) (11)
Consequently, the false block rejection will depend on the specific form of the utility function (the validator preferences for honest behaviours and reward) and on the blockchain dimension n.
When coming at the expected values for faulty nodes ( ), for true blocks it would be: (1, ) =
( 13 − 1)′ {︃( 32 + 1 + 1)′ + ( 13 − 1 − 1)′ Whereas for false blocks, the faulty node has a dominant strategy in = 1 {︃( 13 − 1)(′ + ′ ) if = 1 ( 13 − 1 − 1)′
The results for the scheme put in evidence that for honest nodes facing true blocks the agreement strategy is always dominant, but the rejection of false blocks is conditioned. Vice versa, faulty nodes will always agree on false blocks, but the rejection of true blocks is conditioned. In this scheme more likely could happen that both true and false blocks will be accepted, compared with the previous scheme.
Scheme B: the validator receives a positive wi when the block is accepted and the vote is vi=1; a positive wi is also received when the block is rejected, and the vote is vi=0.
It easy to verify that = 1 is a dominant strategy for an honest node facing true blocks. When coming at false blocks, the expected values are as follows. {︃( 23 + 1)(′ + ′) ( 23 + 1 − 1)′ + ( 13 − 1 + 1)′ if = 0 {︃( 23 + 1 − 1)′ + ( 13 − 1 + 1)′ if = 1 ( 23 + 1)(′ + ′) if = 0 (12) (13) (14) (15) (16) ′ > 1 ′ 3
+ 3 ′ > 1 ′ 3 + 3
It easy to verify that = 0 is a dominant strategy for an honest node facing false blocks. When coming at the expected values for faulty nodes ( ), for true blocks it would be: {︃( 32 + 1 − 1)′ + ( 13 − 1 − 1)′
Whereas for false blocks, the faulty node has a dominant strategy in vi=1, if the same conditions as above holds.
(0, ) = {︃( 13 − 1)(′ + ′ ) ( 13 − 1 − 1)′ + ( 23 + 1 + 1)′
If the remuneration scheme award both positive votes for accepted blocks and negative votes for rejected blocks, the honest validators are always incentivized to behave correctly, by agreeing on true blocks and rejecting the false ones. On the other hand, the faulty nodes will be incentivized to behave maliciously only if their motivation is strong enough, that is if (17) (18) (19) (20)
The above discussion shows that the remuneration scheme A is not incentive compatible for honest nodes, who will prefer to accept also false blocks, also when considering expected payofs. The false block rejection will depend on the validator’s preferences and on the blockchain dimension. Conversely, the second scheme (B) is incentive compatible for honest nodes, who have a dominant strategy in accepting true blocks and rejecting false blocks. Faulty nodes will always agree on false block acceptance, whereas the rejection of true blocks is conditioned.
This paper starts from the idea that, to widely employ non-cryptocurrency permissioned blockchain in business and organizational applications, it is important to consider that nodes are not abstract entities, but economic agents who behave pursuing their own interests.
With this perspective, the consensus protocol must be designed considering efective incentive compatibility constraints, at least for those currently defined as honest nodes. The proposed analysis of individual behaviour is based on two diferent types of agents, with diferent objective function. It compares two diferent remuneration schemes, showing that the design of mechanisms may be relevant for addressing individual choices toward protocol integrity and secure network environment.
The model we consider for incentive compatibility constraints is inherently static, as the decisionmaking of each validator is contingent solely upon its conduct within the current round, without regard to its past performance or prevailing network conditions. Such a static approach may entail potential ineficiencies and vulnerabilities within the system. Transitioning from a static to a dynamic model necessitates several adjustments to accommodate the evolving dynamics of validator participation, potentially fortifying the consensus system within the framework of voting-based blockchains. The dynamic model permits the system to adapt to changing conditions or alterations in validator engagement, thereby enhancing the system’s resilience and adaptability.
Within the dynamic model, the reputation of validators becomes subject to fluctuations over time based on their actions and performance. Active participation, consistent voting patterns, and constructive contributions to consensus can lead to an augmentation of a validator’s reputation. Conversely, unethical behaviour, erratic voting, or inadequate participation may result in a deterioration of reputation. Dynamic reputation is contingent upon metrics such as voting consistency, adherence to consensus commitments, and overall participation. This framework creates incentives for validators to cultivate a positive, enduring reputation, fostering trust within the network.
Furthermore, the dynamic model takes into consideration the interactions among validators during various consensus phases. For instance, a validator altering its vote during the preparation phase without a valid justification might incur a reputation penalty. Interactions among validators can shape the interpretation of votes and decisions during the consensus process.
Should the incentive compatibility constraints model evolve into a dynamic framework, mechanisms could be implemented to assess the trustworthiness of each validator based on historical behaviour, network participation, quality of service, reputation, and other relevant factors. This augmentation could bolster the security and eficiency of the protocol, rendering it more resistant to potential attacks and scalable. The dynamic model, by incorporating the evolution of validators’ actions and decisions over time, introduces a temporal and adaptive component into the consensus system. Time assumes a pivotal role in this model, as past and present actions of validators influence their reputation and, consequently, their future rewards, thereby encouraging consistent and reliable conduct over time.
Situations characterized by a framework akin to the one recently delineated find representation in
game theory through repeated games [
Within an infinitely repeated prisoner’s dilemma, the "grim trigger strategy" has been identified as
a mechanism to encourage cooperation among players [