Is blockchain a cure for peer-to-peer lending?

The blockchain, a decentralized ledger system, has been considered a revolutionary technology to transform businesses, including the financial markets. As peer-to-peer (P2P) lending is also known for decentralization in the sense that individuals borrow from and lend to each other directly, bypassing traditional banks, we explore the possibility and benefits of blockchains in P2P lending. We first provide an economic analysis of existing P2P lending problems, including herding and platform-borrower collusion, with and without the blockchain mechanism. We note that, compared with the existing markets, blockchain-backed P2P lending is highly effective in privacy preservation and borrower quality distinction. Since the role of intermediaries is eliminated in the blockchain world, the chance of platform-borrower collusion is also minimized. Moreover, we show that borrowers and lenders can expect additional surplus when the origination fee in traditional P2P lending is replaced with a smaller tokenization cost and when borrowers present a more accurate financial incentive in a smart contract. With the smart contract, borrowers are allowed to propose optimal interest rates based on their creditworthiness and capacity of repayment while detailed personal information is not required. Additionally, we demonstrate that small investors’ surplus can be further enhanced due to the elimination of herding.

billion USD in 2012 to 64 billion USD in 2015 and is expected to have a market worth 1,000 billion USD in 2025. 1 In the UK alone, the P2P lending in consumer markets has increased from US$0.79 billion in 2014 to US$2.5 billion in 2017, according to the International Monetary Fund (Bazarbash and Beaton, 2020). The growth of P2P lending as an alternative financing and investing market is attributable to its efficient funding process without involving official financial institutions (more details about the funding process will be provided in Sect. 3). One essential benefit of P2P lending is the financial surplus reducing borrowers' cost and increasing lenders' return compared with traditional financial services. According to Investopedia, borrowers and lenders in P2P lending receive a 7% margin on average compared with traditional banking services. 2 Additional benefits of P2P lending include faster funding process for borrowers and more diverse investment options for lenders.
The P2P lending business model, however, still sees underlying challenges. One of the biggest challenges is the high risk for investors due to moral hazards and adverse selection. Specifically, the default rate at Prosper.com, a leading P2P lending platform in the United States, was reported to be 2.6% for A-grade loans and 11.5% for D-grade loans as of May 2017, 3 in contrast to only 1.84% for consumer loans at commercial banks, according to the Federal Reserve Bank. 4 Similarly in China, approximately 250 P2P lenders default in merely two months in 2018. 5 The prevalence of risk in this market makes it essential for lenders to distinguish high-and low-quality loans, while these same lenders suffer from renown information asymmetry. Though not perfect, P2P lending has a great potential in the personal loans market. Therefore, we are interested in developing insights to overcome its drawbacks and fully utilize its benefits.
The blockchain, a decentralized, automatic ledger technique, has gained much attention in recent years, partly due to the spike in Bitcoin prices. The Bitcoins are a cryptocurrency based on the blockchain technology (Koutmos, 2019). Its unit price raised from $15 in May 2013 to a historical high of $67,139 in October 2021. According to Google Trends (see Fig. 1b), the search term "blockchain" raised much interest in 2016, whereas the term "personal loan" has been of constant interest. While cryptocurrencies like Bitcoins are important applications of the blockchain technology, the latter is not limited to cryptocurrencies and may have further implications for the financial market (e.g., personal loans). Since P2P lending is conceptually decentralized (although is practically still centralized via an online platform), we were interested in learning whether the blockchain could help bring more vitality to P2P lending since its decentralized nature well fits the goal of P2P lending.

Fig. 1
Trends about P2P lending and blockchain. a The P2P lending market evaluation and forecast from Statista; b the search interest (normalized to max 100) of two topics over past five years from Google Trends Worldwide Web Search demonstrated that the blockchain might be undesirable for financing. Even though the work by Malinova and Park (2017) was done in the context of P2P trading, it may not fit the P2P lending market since all liquidity requesters in their model settings have available valuable assets, while borrowers-liquidity requesters in P2P lending-do not commit assets before submitting loan requests. Thus, we further explore potential benefits of blockchain based on specific features of P2P lending.
In this study, we explore a theoretical model to explain the behavior of borrowers and lenders in the traditional world and the blockchain world. In P2P lending, a borrower submits a loan request, and an investor (or lender) can choose whether and how much to invest in the loan. 7 For borrowers, the significant concerns are personal privacy, charged origination fee, and paid interest. When it comes to lenders, we consider knowledge and investment heterogeneity among investors while simply such difference in two levels-small investors and large investors. A small investor may not well identify a loan's quality due to lack of financial knowledge and analytical capacity, and thus, choose to follow others' investment, which is renown as herding. Compared with small investors, large investors usually own richer financial knowledge and validate loan quality (i.e., reward-to-variability ratio) more accurately. However, they are still faced with the estimation uncertainty since there is information asymmetry in this market. Thus, there could be different effects of applying the blockchain technology on the two types of lenders.
Our work contributes to understandings of possible impacts of blockchains in P2P lending. First, by considering the loan quality estimation bias, we exploit an economic model to explain herding and fraud, and identify potential victim small investors in traditional P2P lending (see Sects. 3.1 and 3.2). Next, we theoretically analyze potential benefits of the smart contract based blockchain in P2P lending and show how the blockchain world may be superior to the conventional one. In the blockchain world, we first extend the decentralized consensus model from Cong and He (2019) to explain the requirement of honest majority in a blockchain (see Sect. 4.1). Then we explore the feasibility of eliminating intermediaries while motivating borrowers to maintain trustworthiness with a smart contract (see Sect. 4.2). In the permissioned blockchain, a borrower will automatically select an optimal interest rate himself based on the market competitiveness and his risk. The benefits of the blockchain technology are as follows. Most importantly, the blockchain technology eliminates intermediaries and reduces the intermediate transaction fee. As a result, borrowers will increase their interest rates but pay less ultimately, and lenders can expect more return from borrowers' paid interest (see Proposition 2). From borrowers' perspective, another direct benefit is the privacy protection and efficient distinction between high and low-quality loans (see Proposition 1). From lenders' perspective, they could increase surplus even if borrowers do not increase the interest rate. For small investors, the blockchain technology can prevent herding since no receiver's ID information is publicly released. Thus, they could avoid biased loan quality estimation and increase surplus in a Bertrand competition (see Proposition 3). For both small and large investors, they would estimate the loan quality with less variation since the blockchain technology could provide a direct financial incentive of borrowers. As a result, they could expect a higher expected return (see Proposition 4). In sum, the blockchain technology offers economic and social benefits to borrowers, small investors, and large investors simultaneously. To the best of our knowledge, this is a pioneer work modeling and analyzing the blockchain technology in the context of P2P lending to tackle its disadvantages.
The rest of this paper is organized as follows. In Sect. 3, we describe and model two significant problems in traditional P2P lending platforms. Then we conduct a literature review 7 In this paper, we use lender and investor interchangeably.
in Sect. 2 with a primer on the blockchain and smart contract in Sect. 2.1 as well as their applications focusing on the financial market in Sect. 2.2. Next, we apply the blockchain technology to overcome the problems in the traditional world that are stated in Sect. 3, and analyze the behavior of borrowers and lenders and benefits to them in Sect. 4. In Sect. 5 we perform a numerical study to illustrate the benefits of blockchain. In Sect. 6, we conclude the paper with discussions of limitations of this study and future research directions.

Literature review
In this section, we first provide an overview of blockchains and smart contracts, and then review research works about their economic benefits.

Blockchains and smart contracts
The history of blockchain can be dated back to 1991 when Stuart Haber and W. Scott Stornetta described a cryptographically secured chain of blocks (Haber and Stornetta, 1990). In 2008, Nakamoto (2008) officially proposed Bitcoin (BTC)-a blockchain-based, decentralized cryptocurrency. In the blockchain system, the ledger book consists of multiple blocks and is publicly available. In each block, all transaction information within a certain period (e.g., approximately 10 min in Bitcoin) including sender, receiver, and the transaction amount is recorded. Further, each block is linked to a previous block so that everyone can validate the trustworthiness of the block by tracking historical transactions. All miners 8 (i.e., record keepers) can verify transactions with a negligible verification cost and are required to prove their mining power. The first miner who verifies the transaction and proves the mining power can receive a certain amount of reward from a small transaction fee charged to the sender. This system will work as long as no one controls at least 51% of the mining power.
It should be noted that a blockchain can be classified into different types based on various criteria. A blockchain can be public or private based on user authentication (who are you). It can also be permissionless or permissioned based on user authorization (what can you do). Typically, permissionless blockchains such as Bitcoin are public, whereas permissioned blockchains such as Ripple are private. Each blockchain type has its own pros and cons. For instance, a permissionless blockchain has almost no requirement for participation but is difficult to control if it is attacked, while a permissioned blockchain is easy to manage but requires entrants to meet a preset standard. In P2P lending, it is important to control borrowers' quality via additional information since they overdraft the future. The credit score requirement is one type of quality indicators in existing platforms, for instance, the minimum score in SoFi and Marcus are 680 and 660, respectively. 9 Since a permissioned blockchain only accepts qualified users, it better satisfies the requirements of P2P lending.
Later in 2013, Vitalik Buterin introduced an improved platform named Ethereum (its corresponding cryptocurrency can also be called Ethereum) (Buterin, 2016). Compared with Bitcoin's primary purpose of supporting a decentralized currency, Ethereum was created mainly to help build and run distributed applications. Based on these applications, Ethereum further promotes P2P contracts. Due to the flexibility of building applications on the Ethereum platforms, many cryptocurrencies are developed upon it to improve the blockchain system. Since many investors and developers believe the future success of the appealing decentralized feature, cryptocurrencies have gained great success in the past five years. However, the underlying technique-blockchain-is not limited to cryptocurrencies, and could benefit a wider range of industries. For example, the smart contract, first proposed by Nick Szabo (Szabo, 1994), can be integrated into the Ethereum platform. A smart contract is a computer recognized protocol to automatically execute transactions and exchanges with predefined rules without involving a third party. In Buterin et al. (2014), Vitalik Buterin described the smart contract system and its algorithmic implementations in detail.
Blockchain technology development revolves around several issues. The first issue is to design mechanisms of trustworthy decentralized consensus. The most widely used ones are Proof-of-Work (PoW) (Nakamoto, 2008) and Proof-of-Stake (PoS) (Bentov et al., 2016). A miner (i.e., record keeper) can add transactions to a block by proving the computational power in the PoW blockchain or the involved stake in the PoS blockchain (more information about decentralized consensus mechanisms can be found in "Appendix A"). The second issue is privacy preservation. In many blockchain systems such as Bitcoin, all the users' transaction history and wallet balance are publicly known. This would be a problem for all borrowers and especially for large institutions. Business opponents of these large institutions may analyze their transaction behavior to identify business strategies that these institutions did not intend to disclose. Further, it may be undesirable that all you business relationship can be mined in these blockchain networks. To protect users' privacy, transaction senders' and recipients' key ownership is unidentifiable in newer blockchain systems, like Monero (Courtois, 2016). A more detailed overview of the blockchain's privacy preservation mechanism can be found in "Appendix B".

Economic benefits
The economic benefit of blockchain technology mainly derives from its decentralization nature. A direct outcome is the possibility of anonymizing transaction values and parties, which is critical for large traders in the financial market (Malinova and Park, 2017). Blockchain technology can also reduce verification cost and networking cost compared with the traditional world (Catalini and Gans, 2020). Further, The blockchain may benefit financial services in different periods of trading, including pre-trade, trade, post-trade, and custody & security servicing (Peters and Panayi, 2016;Trautman, 2016). For instance, the blockchain does not need central clearing for real-time cash transactions after trading occurs. Despite the potential benefits discussed above, some researchers show a dialectical attitude towards this emerging technique from different perspectives. For instance, Cai and Zhu (2016) admitted that the blockchain technology could prevent object information fraud (e.g., loan application) but did not function well in subjective information fraud (e.g., malicious rating). Further, there is a lack of a regulatory and legal framework to prevent potential attacks on the blockchain (Hileman and Rauchs, 2017). The authors also argued that the blockchain technology needed to solve the security and scalability issues to improve its performance. The requirement of external monitoring to the blockchain is further supported by the potential Bitcoin price manipulation found in (Griffin and Shams, 2020). In their work, empirical evidence was found that the purchases of Tether, a digital currency pegged to USD, occurred precisely during the Bitcoin price drop and quickly moved up the price. To address these challenges of applying the blockchain technology, Mendling et al. (2017) pointed out seven future research directions, such as the execution and monitoring system, the implementation of a redesigned blockchain-based process, and the impact of new business models.
There is a small number of recent works that explore the economic nature of the blockchain in different financial markets using mathematical modeling. For instance, Cong and He (2019) compared the blockchain world (both permissioned and permissionless) with the traditional world in the context of product trading with heterogeneous quality. They found that the permissioned blockchain could improve customer surplus and social welfare due to increased competition, while consumer surplus might be lowered in a public blockchain. To the best of our understanding, P2P lending is different from the context of product selling in the above work since borrowers overdraw future incomes while product sellers offer products with equivalent current values. In other words, product sellers obtain the liquidity after consumers receive products, while borrowers obtain the liquidity before lenders receive any product (i.e., principal and interest) in P2P lending. Another work from Malinova and Park (2017) investigated the market design comparing the intermediated and blockchain-based P2P trading, such as buying and selling a valuable asset for liquidity. They found that P2P trading did not require blockchain technology. By comparing the public blockchain with multiple IDs and the private blockchain with non-transparent single ID, they also found that the public blockchain has higher aggregated welfare but may lead to lower payoffs for large investors. Different from their framework, we include the investors' loan quality estimation uncertainty in our model settings. The loan quality estimation uncertainty, including bias and variance, can be used to explain P2P practice problems, such as herding and fraud. We further explore the blockchain technology as a solution to these problems.
Smart contract-a powerful digital tool to facilitate contracts-also attracts much attention due to the popularity of blockchain. As described in Szabo (1994), digital cash protocol can maintain paper cash characteristics such as unforgeability, confidentiality, and divisibility while performing online payment. Together with the blockchain technology, a smart contract can also promote sharing of services and properties in the Internet of Things domain (Christidis and Devetsikiotis, 2016). For instance, Slock.it 10 is conducting research on smart electronic locks that can be opened with tokens remotely, whereas LO3 Energy 11 is developing a platform to enable consumer P2P transactions on excessive energy in the blockchain automatically via a smart contract. Cong and He (2019) used the smart contract as a quality controller during the product selling process (i.e., money will not be transferred to the seller' account until the buyer receives a product with satisfactory quality) in the blockchain world.
Overall, the blockchain technology is an emerging and evolutionary technology that could reform the world economy. Currently, there is still a lack of relevant literature with mathematical and economic analysis on blockchain's applications in P2P lending. Our work is an attempt to employ the blockchain technology to facilitate P2P lending and explores potential benefits of blockchain to different market players.
provide an offer with a preset interest rate (based on the creditworthiness level). 12 Once the borrower accepts the offered loan, the platform will list it on the website (see Fig. 2a) and allow multiple lenders to invest into it. As we can see, for each loan, the website lists the critical investment information such as borrower rate, monthly interest, and historical return, as well as the borrower's credit profile, such as FICO score, bankcard utilization, and debt/income ratio (see Fig. 2b). These loans may have different quality, and thus, are rated from A to E by the platform with grade A being the highest rating. By comparing grade A loan with grade E loan (Fig. 2b vs. c), we can see that higher grade loans typically have smaller risk with lower return, and such information can be used by lenders to determine whether and how much to invest in these loans. If the loan is successfully funded, the loan will be leased to the borrower with an origination fee charged by the platform (e.g., approximately 5% in Prosper.com). Next, the borrower needs to make monthly repayment to lenders. If the borrower cannot repay the loan, the platform would notify the credit report agency and contact a collection agency.
In general, P2P lending platforms provide borrowers with a lower interest rate and lenders with a higher return compared with those offered by well-established financial institutions, such as major banks in the US. However, possessing less investment proficiency and information retrieval ability (compared to professional investors), lenders are still faced with high investment risks.
In the following subsections, we use a simple economic model to explain how herding and fabrication occurs in P2P lending. With this economic model, we provide a foundation of the loan quality estimation and use the estimation bias to further investigate drawbacks of the traditional world and benefits by applying the blockchain technology. In particular, we will discuss several long-lasting challenges of P2P lending. Suppose an investor j decides to invest w j to a loan with quality (i.e., the payoff for one unit of investment) h i . The lender can validate the loan quality with a cost λ j . We will use subscript {l, b} to represent lenders and borrowers, respectively. Our model reveals that in most cases, the victims from the herding and fabrication are small investors. In the following, we describe the challenges in P2P lending and our model settings in details.

Irrational herding
The P2P lending, essentially a credit marketplace, suffers from the problems of information asymmetry and adverse selection (Lin et al., 2013). In the P2P lending market, borrowers have much more information about the loan quality than lenders, especially small investors. In P2P lending platforms (e.g., Prosper), one common phenomenon resulted from the information asymmetry is herding (Herzenstein et al., 2011), where investors often observe and follow others' investment and participate in loans that are close to be successfully funded. 13 Possible explanations to this irrational behavior are lack of resources (e.g., time) or expertise (e.g., financial knowledge) and opportunity cost (e.g., selecting an excellent but less popular listing while it does not get funded finally.) Such irrational investment decision can hurt lenders' surplus due to the inability of effective diversification, high system risk from the mono investment portfolio, and insufficient money resource allocation (Wang and Greiner, 2010). The herding also exists in the emerging cryptocurrency market, and generates significant impact that can be either positive or negative depending on the market (King and Koutmos, 2021).
Here we use an economic model to explain herding and its impact. An investor has two choices: The first choice is to devote effort to validate all loans' quality and choose the best one (h (1) ). Such effort would lead to a validation cost λ j . The second choice is using some simple information, such as credit score and friends' recommendation, to estimate a loan i's quality h i . Then the utility from the first choice is Thus, compared with the first choice, the utility gain in the second choice is, where (1) we can obtain that the investor j should carry out the validation process (choice one) if w j > w = λ j c i . However, the investor j may overestimate the quality of a "popular" loan i due to the herding effect in the second choice. In this case, the estimation of loan i's quality becomes h i + d j G(η i ), where d j is the belief that others make good choices, η i is the percentage of funded for loan i, G(·) is a function linking probability of successful loan and percentage of funded. It is obvious that G(·) is an increasing function with 0 ≤ G(0) < G(1) ≤ 1. Then the estimation of the utility difference between the two choices becomes, Solving Eq. (2), we can obtain that the threshold w increases to w = λ j c i −d j . That is, the investor j should validate all loans' quality (choice one) for the optimal utility gain but may proceed to use some simple information only (choice two) due to the herding when her investment is, Further, for such an investor j, she will invest in a loan i in the second choice if and only if Note that Eq. (3) represents the majority of lenders, whose investment amount is at a moderately small level. For these lenders, their real utility gain in the second choice E[ΔU l ] is negative while the estimated utility gain E[ΔU l ] is positive. In sum, the herding will lead to more investors' investment without thorough loan quality validation. As a result, it may harm lenders' surplus and finally lower the market efficiency.

Investment risk due to borrower default and borrower-platform collusion
The primary risk lenders face in P2P lending platforms are from malicious borrowers. It is not rare that borrowers default on loans due to lack of repayment capacity and sometimes intentional fraud (Jiang et al., 2018). Further, even if the platform requests a third party to collect the debt, lenders rather than the platform are responsible for the entire cost occurred in the debt collection process. The frequent occurrence of such phenomenon may come from the insufficient financial incentive for borrowers to obey the rule.
Another source of investment is from the platform itself. It is possible that the platform colludes with borrowers to attract lenders' investment. It is difficult for lenders to distinguish whether a loan is fabricated or not due to information asymmetry. A famous example is the Ezubao incident that occurred between 2014 and 2016 (Gough, 2016), resulting in $7.6 billion dollars stolen from victim investors. The platform attracted follow-up investment by a high delusive return with fabricated projects. Similar problems happened in the United States, such as the Lending Club scandal discovered in April 2016 that involved fraud and nondisclosure (Rudegair, 2016).
Here we use an economic model to explain the mechanism of such investment risk from the borrower and platform collusion. Consider the case where collusion happens-the loan has extremely low quality (h i < 0). If an investor j can obtain an unbiased estimation of h i , she will not invest into it due to the expected negative payoff. However, since the loan may be packaged and promoted due to collusion between the borrower and platform, the investor j would over-estimate h i as,ĥ where i j is a random term with mean zero and a i j is the fabrication level with a i j = g i (w j ). Moreover, g i (·) is a decreasing function with respect to w j , that is, large investors are less likely to become victims due to their richer financial knowledge. Here we use the functional form g i (w j ) = a i w j . Then the investor j's estimation of expected payoff would be, Solving E[Û l ] = 0 we can obtain that w = a i −λ j −h i . When w j > w, lender j will not invest due to estimated negative payoff. However, for those lenders with w j < w (i.e., small investors), they would invest and receive a negative payoff ultimately. Note that lim a i →+∞ w = +∞, which indicates all the lenders may become victims if the fabrication level is sufficiently high (e.g., the platform fraud in Ezubao).

Information disclosure and privacy leakage in public listings
Further, from the borrowers' perspective, their privacy cannot be guaranteed since they submit their personal information to a third party. Even a trusted third party such as Equifax may suffer from the data breach (Mathews, 2017). Moreover, high-quality borrowers cannot distinguish themselves from low-quality borrowers by providing more financial incentive since all the borrowers' creditworthiness are determined by their credit profiles. The platform may set up a high interest rate for a borrower if his credit profile is not good enough, though the borrower could repay the loan timely.
Since the blockchain technology could generate decentralized consensus without intermediaries and protect market players' personal information, it is deemed to be a good solution to overcome the above-mentioned drawbacks of traditional P2P lending platforms.

Peer-to-peer lending in the blockchain world
In this section, we explore the viability of a P2P lending system supported by the blockchain technology. Figure 3 contrasts the P2P lending process in the traditional world and the blockchain world. In the traditional world, the borrowers submit loan applications (i.e., listings) by disclosing personal information. Investors assess the quality of listings and allocate small amounts of funds on listings they prefer. Once a listing receives enough fund, it automatically becomes a loan. When the borrowers pay back the loans with interest, the investors receive returns of investments. When the borrowers fail to pay back the loans (e.g., default), the investors cannot recover the investment amount and bears a loss. In the blockchain world, 14 a borrower first needs to obtain tokens from a trusted third party with his real-world asset collateral (e.g., auto vehicle). It would not have any impact on the asset unless they cannot repay the loan. Then the borrower could submit a loan request with the token commitment rather than the personal information. An investor will review his commitment and determines the investment with his proposed interest rate and risk. Finally, the collateral will be returned (forfeited) if the repayment is successful (failed). In the blockchain world, borrowers undertake the risk of failed repayment, which is different significantly from the traditional world where lenders take the majority of the risk. Thus, borrowers have more incentive to submit a trustful loan and make repayment timely in the blockchain world. Further, since lenders have involved investment, we could apply the PoS and Delegated Proof-of-Stake (DPoS, a variation of PoS) mechanisms to guarantee the decentralized consensus on the transaction verification and blockchain maintenance. 15 In the following, we will discuss how blockchain and smart contract can benefit borrowers and lenders compared with the traditional world. First, the blockchain world helps protect personal information, attract high-quality borrowers, and increases users' surplus by eliminating the role of intermediaries (i.e., P2P lending platforms). Second, the multiple ID setting in the blockchain world can prohibit herding among small investors and increase lenders' surplus. Third, by delivering a direct financial incentive, large investors increase their payoffs as the estimation of loan quality has less uncertainty.

An extended framework of decentralized consensus
Cong and He (2019) developed a model of decentralized consensus and demonstrated that record keepers will always choose to report the true state of a transaction, even when the number of record keepers goes to infinity. However, their model is based on the assumption that the majority of miners are honest. In this subsection, we modify the miner's utility function to explain this rule.
Suppose there is a transaction w to be verified. w = 1 if the transaction happens and 0 otherwise. In the network, there are K record keepers to validate the transaction and broadcast their validation result y = {y 1 , . . . , y k , . . . , y K } with y k ∈ {0, 1}. The consensus of the transaction z(y) = 1 with probability 1 K k y k and 0 otherwise. The record keeper k needs to consider the following benefit: First, creating a deviated consensus ( z(y) = w) could bring him/her a benefit b k (e.g. recording a non-existing transaction); Second, he/she could receive a reward r k (e.g., a certain amount of cryptocurrency) if the report is accepted by the whole network (y k = z(y)); Third, he/she has a willingness h k to be honest (y k = w), or equivalently, a reputation cost (−h k ) if misreporting (y k = w). Thus, each risk-neural record keeper k needs to maximize the following utility function: Note that in (7) the risk-neutral record keeper will receive cryptocurrency r k if and only if his reported transaction aligns with the consensus (the second term on the RHS). That is, no matter whether the record keeper is honest or not, to receive cryptocurrency, the only thing is to be consistent with the majority.
Further, we consider the case where all the record keepers submit their reports simultaneously (e.g., ignoring the network speed difference). In this case, each one has a prior probability p = Pr(y k = w) to report the true record. The prior p can be understood as the percentage of the honest record keepers among all. Without losing generality, we discuss the situation when w = 0. 16 We can obtain the utility of reporting the truth and misreporting as follows, Thus, the record keeper k will report the truth (y k = w) if and only if Note that lim K →∞ E[ΔU ] = r k (2 p − 1) + h k , a sufficient condition to guarantee the decentralized consensus is that p > 1 2 and there are sufficiently many record keepers (K > K = b k −h k (2 p−1)r k +h k + 1). In blockchain, when the token price increases (e.g. see the Ethereum price trend), the reward r k becomes larger, and consequently, the minimum number of record keepers required (K ) is reduced. When the reward r k is low, a small increase in the reward may lead to a significant reduction in the required number of record keepers, whereas the impact diminishes when the reward becomes large. In the rest of this paper, we focus on the case where perfect consensus is reached, that is, most stakeholders are honest.

Permissioned blockchain to protect privacy and prevent fraud
In this subsection, we consider and show how a permissioned blockchain can help resolve the privacy and safety issues in the traditional world. To enter the blockchain, a borrower i needs to commit a collateral in the smart contract. What a borrower needs to do regarding collateral commitment is signing an agreement such that in the absence of timely repay, the collateral will be forfeited to pay the principal.
Compared with the traditional world, the penalty process for failed repayment is brought forward to the beginning of a loan request. The trusted third party does not need to bear the financial risk since they do not lend out any cash and the liquidity is still with investors, which is dramatically different from a traditional loan. Suppose a borrower needs one unit liquidity and offers an interest rate R i , the commitment would be i = {1 + R i , ξ i }(ξ i ≥ 0) with R i and ξ i being money charged upon successful and failed repayment. Note that R i and ξ i are time-discounted values. The commitment ξ i can be accomplished by an valuable collateral in a trusted third party. After collateral, borrowers receive a certain amount of tokens, which can be used as the commitment ξ i in the smart contract.
With this smart contract setting, borrowers can enter the blockchain with more financial incentive and privacy preservation. First, they are not required to submit any personal information to the P2P lending network. Their loans will be evaluated based on their commitments. The higher the commit (both successful one R i and failed one ξ i ), the more chance the loan becomes funded. Second, borrowers' quality will be reflected on their commitment upon failed repayment (ξ i ). On one hand, a high-quality borrower can propose a high ξ i to convince lenders his creditworthiness. On the other hand, a low-quality borrower can still attract more lenders with a high commitment ξ i . However, the borrower may receive a great loss since he is lack of repayment capacity and the asset value ξ i will be forfeited by the trusted third party upon failed repayment. Thus, a borrower will propose a commitment ξ i based on his capacity of repayment to minimize the potential loss. In sum, with smart contract borrowers propose interest rates based on their credit worthiness, and we summarize the corresponding benefitsas follows,

Proposition 1 With smart contracts, high-quality borrowers tend to propose a lower interest rate, R i , and a higher commitment upon failed repayment, ξ i , than low-quality borrowers do.
Since borrowers' personal information is not submitted, a natural problem is how to determine their creditworthiness. We further model how borrower i will choose his interest rate R i given his creditworthiness and market competitiveness. Considering the case where borrower i's maximum acceptable interest rate is x i (the interest rate from banks minus the processing fee charged by the platform). Given an interest rate R i , the probability of his loan being funded is f where R is the minimum interest rate lenders will accept. The probability of being funded, f (R i ), is lower if β is large (high market competitiveness) or ξ i is low (high risk of borrower i). Then a risk-neural borrower i's problem is, Here we use the functional form f (R i ) = (R i − R) β/ξ i . Taking derivative with respect to R i , we can obtain the optimal interest rate proposed by the borrower i is, It is easy to verify that R < R i < x i and R i increases as the market competitiveness β increases and decreases as ξ i increases. For a borrower i with high risk, he may propose a commitment close to zero if he fails to complete the repayment (ξ i → 0). In this case, the optimal choice for borrower i is to propose the highest interest rate (R i → x i ). For those borrowers with low risk, they could offer a high commitment upon failed repayment to increase their chances of being funded while reducing the paid interest. The results in (12) has several practical implications. In particular, exogenous factors may affect the borrowers' optimal interest rate through parameters such as x i and R. For instance, with an expansionary monetary policy the interest rate x i will be reduced, and thus, the optimal interest rate R * i will be lower, whereas political conflicts may raise the overall risk of market players, and thus, the minimum interest rate R may be higher, leading to an increased R * .
Further, in the traditional world, the platform needs to charge a considerable origination fee to maintain the ledger and its team. However, in the blockchain world, the cost would occur during the tokenization with a trusted third party. Here we make the following assumption,

Assumption 1
The fees (tokenization fee plus transaction fee) in the blockchain world is smaller than the origination fee in the traditional world.
Take a car as an example asset. Such tokenization is different from the auto loan since the trusted third party is not required to release any cash but only need to verify the car ownership with the CarFax report. Since the blockchain technology eliminates intermediaries with smart contract, it saves an enormous amount of human resource fee. A proportion of the saved origination fee could be distributed to the trusted third party as a participation incentive.
Under Assumption 1, the maximum acceptable interest rate for borrower i becomes larger in the blockchain world (Δx i = x blockchain i − x traditional i > 0). Based on Eq. (12), the interest rate proposed by borrowers will increase in the blockchain world. From lenders' perspective, they gain more return from an increased interest rate proposed by borrowers (ΔR i = β ξ i +β Δx i ). From borrowers' perspective, their paid fee, which equals to the interest rate plus the origination fee, decreases by an amount ( ξ i ξ i +β Δx i ). Further, since borrowers pay more interest, more lenders will be attracted and the probability of getting funded is increased. In sum, we have the following proposition,

Proposition 2
The blockchain approach can save borrowers' ultimate payment by ξ i ξ i +β Δx i after eliminating origination fee and increase lenders' expected return by β ξ i +β Δx i from higher interest rates proposed by borrowers.
Proposition 2 mainly comes from the significant advantage of the blockchain technology to eliminate intermediaries. The saved transaction cost would benefit borrowers and lenders simultaneously. It should also be noted that the higher the market competitiveness (β), the more benefit lenders can gain. Further, given the market competitiveness (β), a borrower with a higher commitment (ξ i ) would save more debt cost compared with those with less commitment.
After borrowers enter the blockchain, they may not want to commit their valuable asset every time. Further, they may request a lower interest rate given their excellent performance of repayment. To address this concern, we can apply a DPoS mechanism to select witnesses. Top borrowers selected as witnesses need to maintain the blockchain and can gain reputation score if they perform well. Since witnesses could be replaced with low-quality performance, they are incentivized to keep correct records. Then they can use these tokens to serve as the commitment. Further, witnesses can be changed by the stakeholders (i.e., lenders) if they do not perform a high-quality service securing the network. As the blockchain grows, it is more and more competitive for a borrower to become a witness and he has financial incentive to deliver an excellent service (i.e., make repayment timely and secure the blockchain).

Multiple public IDs to prevent herding for small investors
One approach to eliminate the effect of "herding instinct" is to make η i unobservable while completing loan funding process given certain conditions (i.e., η i > η threshold ). It is infeasible for P2P platforms in the traditional world to hide the "% Funded" since lenders need to make sure that their investments are not attacked by fraud, such as malicious use by the platform.
There are several approaches in the blockchain to make η i unobservable while lenders' every investment is on track. One approach is using the stealth address and ring signature adopted by Monero. 17 All outsiders can only observe the occurrence of the transaction but have no idea about the sender's and receipt's information. Another approach is based on the multiple-public-ID setting. For each user in the platform, he/she will be assigned multiple private and public IDs using the hash function. The number of public IDs of user k is determined by the number of units of liquidity requested/invested. For instance, if a borrower requires a loan $1,000 and one unit be $25, the number of public IDs assigned to him will be 40. In this setting, all outsiders can only observe the transactions among these public IDs but cannot link them to their corresponding users.
Further, borrowers are guaranteed to receive their requested loan with the smart contract. All the invested liquidity (in the form of cryptocurrency such as Ethereum) will be stored in a smart contract. Any borrower can enter his password (master private key) to see if his loan satisfies the releasing conditions. Once the conditions are met, the cryptocurrency will transfer from the smart contract to the borrower's account, and this process will be broadcasted to the whole network. Otherwise, the money will be returned to lenders' accounts.
By prevent herding using blockchain, small investors can estimate the loan quality (h i ) without the belief that others make good choices (d j ). Thus, they can obtain a quality estimation with less bias. From the perspective of lenders' surplus, we have the following proposition,

Proposition 3 The blockchain increases the lenders' surplus if the lenders' preference distribution over loans with different quality is sufficiently right skewed.
Proposition 3 reveals the importance of avoiding herding in the P2P lending. It is beneficial for the market to keep away from the excessive demand for "popular" loans that may have low quality since herding could lower the market efficiency, not to mention the possibility that malicious market players (even the platform) may manipulate popular loans. By strategically hiding the funding status of each loan, lenders can invest more rationally with their financial analysis of each borrower's commitment.

Additional benefit for both large and small investors
In this subsection, we explore the benefit in the blockchain world due to a stronger financial incentive from a borrower. After eliminating herding and fabrication, an investor j's unbiased estimation of loan i's quality can be expressed as, 17 More details about blockchain's privacy protection techniques can be found in "Appendix B".
where i j is an error term with mean zero. Following existing operations research literature (e.g., Terwiesch andXu, 2008, Ales et al., 2017), we assume that i can be approximated using a Gumbel distribution with mean zero and scale parameter μ due to the flexibility of Gumbel distribution. In fact, the Gumbel distribution is typically used to model the distribution of random variable for maximum, and leads to a closed form expression. The larger the scale parameter μ, the higher the variance of estimation uncertainty. As discussed in Sect. 4.2, the permissioned blockchain provides a different incentive for borrowers to repay the loan timely. In the traditional world, the incentive is guaranteed using the personal credit profile. However, the incentive is financial in the blockchain world. Here we make the following assumption regarding the estimated loan quality, Assumption 2 With a financial incentive, investors can estimate the loan quality more accurately. That is, the loan quality estimation error has a smaller variance in the blockchain world compared with the traditional world. Mathematically, μ blockchain < μ traditional .
Assumption 2 reveals a critical difference between the traditional world and the blockchain world. In the traditional world, borrowers are not required to provide any monetary commitment upon failed repayment. Such requirement corresponds to ξ i = 0 in the smart contract (or a small ξ i for those who value their credit profiles). Thus, the difficulty of identifying borrowers' quality is massive from investors' perspective. On the contrast, high-quality borrowers in the blockchain world can reveal their quality with a high commitment ξ i as discussed in Sect. 4.2. Since the incentive in the blockchain world is more directly related to the personal risk, it is reasonable to generate a reduced quality estimation variation.
After validating n different loans, the large investor j will pick up the one with the highest estimated quality, that is, According to the discrete choice model, the expected utility of the investor j is, where P i = 1 Z exp{h i /μ} and Z = n i=1 exp{h i /μ}. Comparing the expected utility in the traditional world and the blockchain world, we obtain the following proposition,

Proposition 4 For large investors, E[U blockchain
Proposition 4 indicates that the less uncertainty when estimating the loan quality, the higher utility an investor can expect to gain. Intuition is that if an investor can estimate the loan quality perfectly, she will pick up the best loan for sure. Thus, lenders' choices will be wiser in the blockchain world as a result of a better distinction between high-and lowquality borrowers compared with the traditional world. there is a loan with a quality of h = 1.39 and a funding percentage 24.56%. An investor would like to invest w on this loan. He is endowed a level of trust in others' choices, d, which is lower in the blockchain world due to reduced herding. Here we assume that d traditional = 1 in the traditional world, and d blockchain = 0.3 in the blockchain world. His cost of validating the loan quality is λ = 0.5. Figure 4 shows his expected utility, E[U ], for different investment amount, w. For each figure, the solid and dashed line represents the investor's actual and optimal choice, respectively. The shadow part, then, measures the sub-optimality of the choice. As we can see, the investor makes an optimal choice in regions (I) and (III) but a sub-optimal choice in region (II). Comparing Fig. 4b with a, we can see that the area of (II) is reduced, and thus, promotes this investor's optimality of investment.
Then we check how will the market players make decisions, i.e., the optimal interest rate in the contract, in the blockchain world, and what the potential benefits can be. Assume that in the market there are two borrowers with high and low quality. Their maximum acceptable interest rate is x 1 = 0.1 and x 2 = 0.15, respectively. There is also an investor with a reservation rate R = 0.03. Here we show two results of interest. First, we compare their optimal interest rate with a fixed identical failed commitment ξ 1 = ξ 2 = 0.12. Figure 5a shows how the optimal rate R * i , changes when the market competitiveness, β, increases. As we can see, with blockchain a borrower with a higher quality will propose a larger interest rate, and this rate increases with the market competitiveness. Second, we examine the relationship between the optimal interest rate and the failed commitment under given market competitiveness. Figure 5b shows the indifference curve for the two investors when the market competitiveness β = 0.2. For any given R i , the low-quality borrower needs to offer a higher ξ i than the high-quality borrower, and vice versa. Therefore, the blockchain market is sufficient in the sense that borrowers need to offer rates based on their creditworthiness.
Next, we examine the potential benefits of using blockchain for both sides of the market with a reduced origination fee, which is assumed Δx = 3% in this numerical study. Figure 6 presents the gain from this reduced fee for both borrowers and lenders, given that the market competitiveness β = 0.2. As we can see, the reduced fee is distributed between the borrower and lender. The borrower's (lender's) gain increases (decreases) with the commitment upon failed repayment, because a higher commitment indicates a lowered interest rate, and thus, the corresponding lender's gain. The gains of the two sides become equivalent if and only if the commitment upon failed repayment equals the market competitiveness.
Finally, we show the potential benefits of lenders in addition to that from reduced transaction cost. Assume that there are ten loans in the market with their quality sampled from a uniform distribution. A lender wants to invest one dollar into the market, and his expected payoff is shown in Fig. 7. As we can see, the expected payoff decreases with the market volatility. Since blockchain can lower the market volatility by making the transaction more transparent, we can expect an increased payoff for lenders.

Conclusion and discussion
In this paper, we explore how the smart contract based blockchain technology could advance market efficiency and improve surplus for borrowers and lenders simultaneously in P2P lending. Liquidity requesters in general contract based business activities, such as product selling and trading, deliver products on or before receiving funds. However, borrowers who need funds but do not have enough liquidity obtain investors' trustiness via their commitment of future repayment, that is, they overdraft the future. With a smart contract involving a trusted third party, borrowers can reach an agreement on the collateral, which is executed automatically when the repayment fails. In this case, borrowers can obtain lenders' trust more easily by providing a high commitment upon failure. Thus, high-and low-quality borrowers can be well distinguished with their risk (i.e., the capacity for making timely repayment). Further, by eliminating intermediaries and requesting borrowers' financial incentives, the blockchain world can provide economic surpluses to borrowers and lenders. The surplus comes from reduced transaction fee (i.e., no origination fee), eliminated herding risk, and reduced uncertainty in loan quality estimation. Borrowers could also avoid potential personal information leak. Our theoretical analysis informs how the intrinsic features of the blockchain technology make it superior to the conventional method. Our proposed model and its results also have some policy implications. First, the regulatory should force the execution of the smart contract. In our model, it is critical that the collateral amount is sufficiently high to incentivize the borrowers to propose interest rates based upon their private creditworthiness. Second, the occurrence of the dishonest majority should be prevented from the regulatory perspective. The regulatory may implement a monitoring system to detect possible dishonest majority occurrence. A possible approach is to set up an external channel for investors to report misbehavior. Finally, the regulatory should maintain the price level of the tokens, that is, the market volatility should be lowered, so that the blockchain system is stable.
There are several limitations to this work. First, the blockchain technology generally requires a vast network of users to guarantee the decentralized consensus. Thus, it is necessary to develop a mechanism to attract sufficiently many investors in P2P lending, as shown in Sect. 4.1. Further, a critical requirement for maintaining trustworthiness in blockchains is the "honest majority", that is, more than 50% of users in the chain need to be honest. This requirement may not be satisfied, and thus, leading to 51% attacks. Several possible solutions are available from existing research. For instance, the weight of each user in this chain is determined by their reputation instead of mining power or investment amount (Han et al., 2019). Our model specified in (7) also provides a possible solution to the "honest majority" problem: By providing sufficient willingness, e.g., connecting to the real world credit profile, the "honest majority" can then be guaranteed because everyone would believe that others report the truth to maximize their utility. Second, though the permissioned blockchain could deliver stronger incentive from borrowers, it sets up a higher entry barrier compared with the permissionless blockchain. It would be interesting to investigate the potential permissionless blockchain benefit-disruption trade-off to further explore the feasibility of the permissionless blockchain in P2P lending. Finally, blockchain applications are often faced with scalability issues. In this study, we have not investigated how the blockchain network size may affect economic outcomes.
As an emerging technology, blockchains pose many future research directions. From the theoretical perspective, the economic impact of imperfect consensus should be integrated into the blockchain design to assure a low risk. Next, it would be interesting to analyze the borrowers and lenders' behavior when they could autonomously choose to disclose personal information. Further, it would be beneficial to investigate if some mechanisms, such as new user promotions, could be integrated into the blockchain world to attract more investors. Finally, as there are different types of blockchain mechanisms, a more viable way to apply this technology in P2P may be available with a comprehensive effort. From the empirical perspective, there is still a lack of real-world data to test the effectiveness and efficiency of the blockchain technology. Overall, it requires coadjutant effort from multiple discipline experts (i.e., computer scientists, economists, and mathematicians) to implement the blockchain and smart contract technology and analyze its effectiveness and efficiency.
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A Major decentralized consensus mechanisms
In the blockchain world, each miner (i.e., record keeper) can announce their transaction verification results (i.e., whether the transaction occurs or not and is the transaction amount correct). The verification process is easy to implement, and thus, the associated cost is often negligible. Here we describe three popular approaches to prevent fraudulent reports. Proof-of-Work and Proof-of-Stake PoW requires miners to demonstrate their computational power, whereas PoS requires them to prove their stake. PoW blockchain is widely used in cryptocurrencies such as Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), Bitcoin Cash (BCH), and Monero (XMR). Compared with PoW, PoS can save much computational resource (i.e., electricity) and keep more stable cryptocurrency price, which determines miners' involved stake value. Example PoS cryptocurrecies include Cardano (ADA), Nxt (NXT), and Peercoin (PPC). In both mechanisms, to attack the blockchain, attackers need to control at least 51% of computational power or stake. Though it is difficult to achieve, the 51% attack did happen several times, for instance, in two ETH based blockchains-Krypton and Shift-in August 2016, and in a Bitcoin fork -Bitcoin Gold (BTG) in June 2018.
Delegated Proof-of-Stake Recently, DPoS was created to increase the speed of block creation and the scalability of the blockchain. In DPoS, users vote for witness and their voting power is proportional to their stakes. Top witnesses (typically top 101) have the right to validation transactions, create blocks, and receive a certain amount of reward. Note that the witnesses are not required to have large involved stakes. Moreover, all witnesses are faced with the risk of being replaced if they behave maliciously. Thus, they are motived to keep their reputation among the voters. At the same time, delegates are also voted to supervise the work of witnesses and can propose any changes except transaction validation and block creation. For instance, they can recommend to change the reward amount to witnesses. Example cryptocurrencies include EOS.IO (EOS), Bitshares (BTS), and Steem (STEEM).

B Blockchain technology to support privacy
In the blockchain world, an essential approach to protecting the user privacy is the asymmetric cryptography technique (Antonopoulos, 2014). Each user may have multiple pairs of keys: public keys are visible to all the users in the network, whereas private keys are only known to the owner. By using the hash function (Rogaway and Shrimpton, 2004), public keys can be obtained easily with private keys, but not vice versa. Further, users are not required to disclose any identifiable information or the ownership of public keys. Thus, the crowd in the network can only observe transactions among these public keys but cannot identify their owners.
Based on the basic concepts of public and private keys, several approaches are created to support users' privacy. For instance, Monero uses two techniques, namely stealth address and ring signature, to protect recipients' and senders' information, such as their public keys (Courtois, 2016). In Monero, each user has a spend key and a view key. Each time a transaction occurs, a stealth address for the transaction output is generated via a hashing function involving the receiver's public view key and public spend key. The other users in the blockchain can only observe the stealth address but cannot link it to any other address. Further, the receiver can still allocate and spend the received cryptocurrency using his private spend key and view key. With the "stealth address" method, receipts' privacy is protected. Next, the "ring signature" method can protect senders' privacy. It creates a signature for a transaction using a combination of the sender's public address and a group of past transaction output. It is computationally impossible for any outsider to identify which one is the genuine address. Further, miners can still verify the transaction (e.g., preventing double-spending) with a key image (Wong and Memon, 2001). In addition to the above two techniques, "zk-Snarks" (Bitansky et al., 2012), a variation of zero-knowledge proof, is adopted by a cryptocurrency named Zcash (ZEC). The zero-knowledge proof is a method of proving valid transaction without revealing the sender, receiver, and transaction amount (Goldwasser et al., 1989). Consequently, the problem "front-running" (Malinova and Park, 2017) no longer exists.

C Derivations and proofs
Proof of Proposition 3 Suppose each small investor plans to make one unit investment and there are multiple loans with heterogeneous quality h i . Following Cong and He (2019), an investor j's surplus in a Bertrand competition is j ∝ E[h (2) ]. In the traditional world, lenders may be promoted to invest in "popular" loans due to herding. That is, the lenders' preference distribution over different loans is skewed. It shifts the demand curve for these "popular" loans. In this case, the "popular" loans count more weight in determining the lenders' surplus. If these "popular" loans have relatively low quality, it is possible that the second-order statistic are lowered.

Proof of Proposition 4
Denote y i = exp{h i /μ traditional } and α = μ traditional /μ blockchain . It is easy to see that y i increases as h i increases and α > 1.
It is equivalent to prove that,