Supply Chain Transparency and Blockchain Design

1. Introduction

Blockchain, a decentralized digital ledger technology that can record transactions between parties verifiably and permanently, was first developed as a cryptocurrency platform but is increasingly applied in supply chains (Carson et al. 2018). An increasing number of blockchain-based platforms are being developed to improve supply chain operations across industries (e.g., IBM Food Trust, Provenance, Dibiz, SkuChain, BlockVerify, Vechain, Factom, Bext360, Ripe.io, BartDigital, BeefChain, and OwlTing). According to Grand View Research, the global blockchain market was valued at $3.67 billion in 2020 and is poised to reach $394.6 billion in 2028 with a predicted annual growth rate of 82.4%.¹

One of the motivations to introduce blockchain in supply chain management is to enable trustworthy and efficient information exchange. Compared with traditional methods that enable information sharing, such as enterprise resource planning (ERP), electronic data interchange (EDI), and third-party intermediaries, blockchain offers new opportunities and advantages. First, ERP and EDI are often limited to one-to-one information sharing with immediate suppliers and customers because legacy issues make it expensive to integrate information systems across multiple organizations and the integration cost increases in the number of firms (Gaur and Gaiha 2020). Third-party intermediaries are similarly expensive. However, blockchain is agnostic to the number of participants and can significantly lower the cost of integration across multiple organizations. Second, when applied to supply chains, a blockchain’s data recording often involves the use of internet of things (IoT)—a network of connected devices embedded with autonomous sensors and software to record and transfer data with minimal human intervention. Because the data in the IoT are automatically generated, the combination of blockchain and IoT is well-suited for implementing smart contracts, which are self-enforcing protocols stored in the blockchain that automatically execute transactions (e.g., payment to the supplier) when a prespecified condition is satisfied (e.g., delivery of the product). According to recent industry studies, the global blockchain IoT market is projected to reach $2.4 billion by 2026, and the global smart contracts market is projected to reach $345.4 million by 2026.² The advancement of such transformative technologies can not only improve supply chain transparency, but also enable firms to design new ways to contract and collaborate with each other.

Despite these benefits, firms are reluctant to make information visible beyond immediate supply chain partners because it creates a dilemma: on the one hand, more information availability can improve operational decisions, and on the other hand, participants in a blockchain could take competitive advantage of the information shared by each other. As a result, many existing supply chain applications of blockchain are either limited to one-to-one information sharing or involve disintermediation. For example, Ripe.io shares growing conditions data from farms to food companies for fresh produce, DLT Labs shares GPS tracking data from third-party logistics providers to Walmart Canada for billing, and Ripple.io improves international funds transfer by disintermediating the banking system (Cui and Gaur 2023). Applications that require multiparty information sharing in the supply chain, such as in food safety and drug security, are yet to yield large-scale solutions.

When used for cryptocurrencies, blockchains are typically created as public blockchains (e.g., Bitcoin, Ethereum, and Litecoin) with permissionless entry, in which anyone can join and automatically gain access to the recorded data (Sharma 2019, Seth 2021). Such public blockchains naturally enable the highest degree of transparency. In contrast, when used in supply chains, blockchain is often required to be private and permissioned (e.g., Hyperledger Fabric, Quorum, and R3 Corda), in which only authorized participants can join. Such a blockchain enables firms to control access to data by selectively placing restrictions on the roles and activities of different participants through an access control layer (Seth 2021, Vitasek et al. 2022). Although an access control layer addresses firms’ concern about sharing own data with other participants (which could include competitors), it can compromise the degree of transparency, particularly when firms want to restrict data sharing to one-to-one (Jaeger 2018, Frankenfield 2020). To fully unlock the value of blockchain in supply chains, firms need to reach agreement on what degree of transparency it should enable, identify the types of data that need to be shared to achieve the requisite transparency, and implement it through the access control layer.

In this paper, we develop prescriptions to supply chain practitioners for blockchain adoption and design with regard to vertical and horizontal supply chain transparency across more than two participants. Specifically, we investigate the following research questions. (1) How does blockchain affect the supply chain by enabling transparency of different types of information, and when should it be adopted? (2) Who has the incentives to initiate a blockchain, and does the initiator need to compensate other firms? (3) What degree of transparency should the blockchain enable and should there be an access control to limit firms’ access to certain types of data? By answering these questions, our paper shows what supply chain characteristics create favorable conditions for the beneficial adoption of blockchain and what form of information sharing it should provide.

First, consider vertical cost transparency. A manufacturer often faces uncertainty in sourcing raw materials because a supplier may not be perfectly reliable. For example, the suppliers in agri-food supply chains are typically smallholder farmers who are vulnerable to disruptions (e.g., natural disasters, contamination, financial bankruptcy, and the COVID-19 pandemic). When facing such a risk, a common strategy used in the industry is to have an alternative, more reliable but more expensive, supplier as a backup when the primary supplier fails to deliver. Because the alternative supplier is more expensive, the manufacturer naturally wants to transfer the incremental sourcing cost to its buyers. However, firms are usually unable to change the wholesale price charged to downstream buyers because of the cost of renegotiating the wholesale price and revising the existing contract terms (Colias 2021, Steveni 2021). As a result, the manufacturer is restricted to charging a uniform wholesale price to absorb the resulting fluctuations in sourcing cost.³

Blockchain can remove this barrier to contracting flexibility. With real-time logistics data generated by IoT sensors, the manufacturer can credibly prove from which supplier it is currently sourcing. Thus, firms can design a smart contract that, based on the data recorded in the blockchain, automatically charges a wholesale price from the buyers and places the corresponding order quantities to the manufacturer depending on which supplier is providing the raw materials.⁴ Thus, by programming contingency into the smart contract, blockchain removes the need to renegotiate contract terms and allows firms to commit to a more flexible contract.

Second, consider horizontal order transparency. In practice, it is common for multiple buyers to source from the same manufacturer. When the manufacturer experiences a capacity shortfall, buyers compete for the manufacturer’s limited capacity, resulting in a rationing game. Such a phenomenon is frequently witnessed in fashion goods, pharmaceuticals, telecommunications, automotive, electronics, and many other industries. Further, this challenge of competing for the upstream production capacity can be worsened when the supply chain lacks transparency (Whelan 2015, Hobbs 2019). For example, a buyer may not need to purchase from the manufacturer in every period for various reasons: random market demand, time-varying product assortments, or randomness caused by the disruption in the supply of other components (Colias 2021). Such factors make it difficult to know exactly how many buyers are competing for capacity in a particular period. Even though buyers want to coordinate by sharing the ordering information with each other, such a collaborative partnership can be difficult to form without a credible way to guarantee the truthfulness of the shared information.

Blockchain can facilitate the requisite collaboration between competitors by securely providing them access to each other’s ordering information. A buyer can verify whether a competing buyer is also ordering from the same manufacturer through the logistics data credibly recorded in the blockchain. Firms can, thus, include another layer of contingency in the smart contract such that, depending on the number of buyers ordering in a period, the smart contract automatically places the corresponding order quantities to the manufacturer. In this way, blockchain can change the competitive environment between firms and may help firms match supply more efficiently to demand in uncertain markets.

We examine these applications of blockchain and the interaction between them using a stylized model of a supply chain that consists of one manufacturer and two buyers. The manufacturer has limited production capacity and uses dual sourcing for raw materials. Its primary supplier has a lower sourcing cost but may suffer from a random disruption; if the primary supplier is disrupted, the manufacturer sources from an alternative, higher cost supplier. The two buyers face random demand in their respective markets and have a probability of needing to order. They place orders simultaneously and compete with each other for the manufacturer’s capacity in a rationing game. The manufacturer allocates its production quantity to each buyer according to a preannounced linear allocation policy. To uncover the impact of blockchain, we compare two cases. First, without blockchain, the manufacturer offers a uniform wholesale price regardless of the supplier used, and the buyers make ordering decisions without knowing each other’s ordering status (i.e., needing to order or not). Second, with blockchain, the manufacturer offers dynamic wholesale prices contingent on the realized supplier (i.e., cost transparency), and the buyers make ordering decisions contingent on the realized number of buyers who order (i.e., order transparency). The contracting equilibrium in this case provides the contingent wholesale prices and order quantities that can be implemented by programming them into a smart contract. We first examine a blockchain that enables both cost and order transparency, and then consider the optimal design of a blockchain that enables either or both types of transparency.

Our first main result is that blockchain improves the supply chain profit when the manufacturer’s capacity is large and reduces the supply chain profit when the manufacturer’s capacity is small. The manufacturer’s capacity critically determines which type of transparency dominates, whether the net effect is beneficial, and whether the firms’ incentives for blockchain adoption can be aligned. When the capacity is large, the buyers’ competition is not intense regardless of blockchain. Thus, the impact of blockchain is mainly driven by cost transparency. In this case, the manufacturer is enabled to use a dynamic wholesale price contract to facilitate the entire supply chain to act together by ordering more when facing a lower sourcing cost and ordering less (and, hence, selling at higher retail prices) when facing a higher sourcing cost. Thus, the supply chain benefits from cost transparency, and blockchain should be adopted. When the manufacturer’s capacity is small, the buyers have a strong incentive to overorder. Thus, the impact of blockchain is mainly driven by order transparency. The information advantage of blockchain can alleviate this competitive pressure and mitigate the buyers’ overorder incentive. As a result, double marginalization is exacerbated, and the supply chain profit is hurt. Therefore, blockchain should not be adopted in this case.

Our second set of results relates to incentives. In the case when blockchain is profitable for the supply chain, vertical cost transparency interacts with horizontal order transparency, and the resulting outcome may or may not be a win–win–win. We find that, when the manufacturer’s capacity is sufficiently large such that the buyers are freed from the rationing game (i.e., they each order their monopolistic optimal quantities), blockchain leads to a win–win–win. It can be initiated by any firm in the supply chain, and all firms are willing to join the blockchain without any compensation scheme in place. Here, the benefit of vertical cost transparency acts in the same direction for both the manufacturer and the buyers. However, when the manufacturer’s capacity is not sufficiently large to eliminate the rationing game, cost transparency induces the manufacturer to charge a much lower wholesale price to sell out its capacity when the sourcing cost is low, making the buyers compete more intensely. Further, order transparency also plays a role, and blockchain improves the manufacturer’s profit at the expense of hurting the buyers’ profits. Resolving this incentive conflict and initiating the blockchain requires the manufacturer to compensate the buyers. Here, horizontal order transparency impacts the manufacturer and the buyers in the opposite directions, creating a challenge in blockchain adoption.

Our final results relate to the design of the information sharing functionality of the blockchain. We find that, when the manufacturer’s capacity is small, an alternative way of implementing the blockchain to provide cost but not order transparency can improve supply chain profit. Contrary to order transparency, cost transparency enhances the buyers’ overorder incentive in a highly capacitated supply chain. It allows the manufacturer to selectively charge a lower wholesale price to intentionally intensify the buyers’ overorder incentive when the sourcing cost is low. Thus, double marginalization is alleviated, and the supply chain profit is improved through the blockchain. Further, both the manufacturer and the buyers can be better off. Implementing such a blockchain requires an access control layer for the logistics data recorded in the blockchain, which prevents firms from viewing the data records of other firms within the same tier but grants them permission to access the data content from other tiers.

Our paper yields the following managerial implications. First, it shows that a blockchain that provides transparency to not only immediate trading partners, but also across nonadjacent tiers can be beneficial to a supply chain and can be implemented with incentive alignment. Second, it shows that sometimes a blockchain should only enable selective information transparency, and the manufacturer’s capacity determines which type of blockchain is value-adding. Third, it shows that, all else constant, sometimes a blockchain should not be implemented in a supply chain because existing imperfections counter each other to provide an efficient supply chain, and the removal of those imperfections can exacerbate double marginalization.

2. Literature Review

Our paper is related to three streams of literature: (1) blockchain operations, (2) information sharing in supply chains, and (3) rationing games. First, a rising literature is investigating blockchain as a disruptive technology to operational systems. When used as a technology to facilitate financing and token transactions for platforms, blockchain is typically constructed as a public (or permissionless) blockchain. Researchers focus on the decentralized features of such public blockchains on platform financing (i.e., decentralized finance) and operations. For example, Gan et al. (2021, 2023) study the optimal token issuance policies for initial coin offerings (ICOs) and the implications of ICOs on platform operations and regulation. Chod et al. (2022) examine moral hazard issues in token financing and show that raising capital by issuing tokens rather than equity can alleviate under-provision of noncontractible entrepreneurial effort. Tsoukalas and Falk (2020) study the effectiveness of token-weighted voting to crowdsource information on blockchain-based platforms and show that it can discourage truthful voting and erode the platform’s predictive power.

However, when applied to supply chains, a private (or permissioned) blockchain is needed. Babich and Hilary (2020) identify the key strengths and weaknesses of blockchain and propose directions for operations management research. Chod et al. (2020) demonstrate the efficiency of signaling a firm’s quality to lenders through inventory transactions in the blockchain compared with loan requests. Cui et al. (2022) and Dong et al. (2022) study the value and design of traceability-driven blockchains to improve product quality under different supply chain structures. Pun et al. (2021) show that blockchain can be used to combat counterfeits and can be more efficient than a pricing strategy in eliminating postpurchase regret and improving social welfare. Sumkin et al. (2021) show that blockchain adoption can exacerbate nonresponsible sourcing in the diamond supply chain. Iyengar et al. (2023) study firms’ incentives to join a permissioned blockchain, which can enable consumers to have more visibility over the quality level of firms. Our work contributes to this literature by studying different types of information transparency enabled by blockchain and smart contract implementation to automate transactions when more information becomes transparent.

Our paper is also related to the literature on information sharing in supply chains, which studies both vertical and horizontal information sharing. In vertical information sharing, previous papers analyze firms’ incentive to share private demand information (e.g., Lee et al. 2000, Raghunathan 2001, Simchi-Levi and Zhao 2003, Gaur et al. 2005, Li et al. 2014, Chen et al. 2016), inventory information (e.g., Roy et al. 2019), and new product reliability information (e.g., Bakshi et al. 2015). Besides vertical information sharing, a set of papers, primarily in the economics literature, investigates firms’ incentives to exchange their private information horizontally in oligopoly markets (e.g., Novshek and Sonnenschein 1982, Clarke 1983, Vives 1984, Gal-Or 1985, Li 1985, Shapiro 1986, Kirby 1988, Raith 1996, Zhu 2004). These papers consider various competitive settings, such as regarding the content of information shared (demand signal or production cost), the type of products (substitutes or complements), and the structure of production costs (homogeneous or heterogeneous).

Another stream in the information sharing literature considers a supply chain comprising a selling firm and multiple buying firms. Under such a supply chain structure, Shamir and Shin (2018) focus on horizontal information sharing between the buying firms and study their exchange of private signals on a common demand shock. They show that the buying firms will not share information when there exists information leakage to those firms who do not share. Other papers in this stream study one-to-one vertical information sharing between the uninformed selling firm and each informed buying firm. Li (2002) finds that buying firms have no incentive to share information with the selling firm about their private signals on the common market demand but have an incentive to share information about their private marginal production costs. Zhang (2002) further considers the impacts of complementary, substitutable, and independent products in this setting. Investigating the impact of different levels of confidentiality, Li and Zhang (2008) show that the buying firms will not share their information without confidentiality. Jain et al. (2011) and Jiang and Hao (2016) study the selling firm’s differential pricing strategy in order to gain access to the buying firms’ private signals. Gal-Or et al. (2008) study two-sided information sharing between the upstream and the downstream in a scenario in which both the selling and the buying firms possess private signals on demand shock. Anand and Goyal (2009), Kong et al. (2013), and Chen and Özer (2019) study information leakage from an incumbent buying firm to an entrant buying firm through a common selling firm.

While we consider a similar supply chain structure with one selling firm and multiple buying firms, our work differs from these papers in two ways. First, these papers consider demand-side competition between buying firms, for which the value of information sharing comes from the increased precision of market conditions because of pooling of signals. Differently, we focus on supply-side competition between buying firms with respect to the selling firm’s capacity. In this context, we show that the value of information sharing depends on the buying firms’ incentive to overorder to fight for the selling firm’s capacity as well as how the selling firm takes advantage of the buying firms’ overorder incentive by strategically adjusting the wholesale price. Second, these papers focus on either vertical or horizontal information sharing. In contrast, we propose a modeling framework to capture both vertical (i.e., cost transparency) and horizontal (i.e., order transparency) information sharing in order to study how they collectively impact firms’ decisions on whether to adopt blockchain.

Because we focus on the supply-side competition of buying firms, our model captures the rationing game (Lee et al. 1997) that ensues when the buying firms’ total order quantity outstrips the selling firm’s supply and causes the buying firms to strategically determine their order quantities in a noncooperative game. Several capacity allocation mechanisms are used in practice and extensively studied in the literature, including linear, proportional, uniform, and lexicographic allocation (e.g., Cachon and Lariviere 1999a, b; Bakal et al. 2011; Liu 2012; Cho and Tang 2014; Rong et al. 2017). Under both linear and proportional allocation, the buying firms can have an incentive to inflate their order quantities so as to receive larger allocations, which is referred to as the gaming effect (Lee et al. 1997, Cho and Tang 2014). Liu (2012) examines whether uniform allocation can eliminate the gaming effect. Cho and Tang (2014) further establish the exact conditions under which uniform allocation fails to eliminate the gaming effect and construct a competitive allocation that can eliminate the gaming effect. These papers assume an exogenous wholesale price. Chen et al. (2013) endogenize the selling firm’s wholesale price decision and compare the equilibria under proportional and lexicographic allocation. Qi et al. (2015) study how the buying firms would invest to improve the selling firm’s capacity level. Qi et al. (2019) compare two capacity reservation policies depending on whether the unused reserved capacity of one buying firm can be utilized to serve another buying firm. To the best of our knowledge, our paper is the first to study the impact of information transparency in rationing games, and we complement the literature by studying how information transparency can impact both the buying firms’ ordering policies and the selling firm’s wholesale price decision.

3. The Model

We consider a supply chain that consists of a manufacturer M and two buyers, B₁ and B₂. The manufacturer sources raw materials from its suppliers with dual sourcing and sells finished products to the buyers at wholesale price w (see Figure 1). The manufacturer has a production capacity limitation K,⁵ and the unit production cost is constant and normalized to zero. Throughout this paper, we refer to the manufacturer’s sourcing from the suppliers as the upstream supply chain and the buyers’ ordering from the manufacturer as the downstream supply chain. We present our model as follows; Online Appendices A–C provide the proofs of all the results, and Online Appendices D–H provide the analyses of five extensions and alternative formulations of our main model.

3.1. Upstream Supply Chain

The manufacturer faces an uncertain supply. It normally sources raw materials from a low-cost supplier S_l, who is not perfectly reliable and may suffer from a random disruption. When the primary supplier is disrupted, it fails to provide anything, and the manufacturer sources the raw materials from an alternative supplier S_h, which is always reliable but has a higher unit sourcing cost. For simplicity, we normalize the unit sourcing cost from supplier S_l to zero and supplier S_h to c > 0 (i.e., the incremental sourcing cost). We denote $\beta \in (0,1)$ as the probability that a disruption does not occur to supplier S_l. Because the disruption to supplier S_l is random, whether the manufacturer is sourcing from the primary or the alternative supplier may not be observable to the buyers. The manufacturer sources raw materials in a just-in-time fashion and orders the quantity it needs to fulfill the buyers’ orders.

3.2. Downstream Supply Chain

Each buyer faces an uncertain demand and needs to place an order with the manufacturer with probability $\alpha \in (0,1)$. Specifically, the (uncertain) maximum market demand potential for buyer B_i, $i\in \{1,2\}$, is denoted as A_i, which can take value a > 0 with probability α and zero with probability $1-\alpha$. Thus, whether a buyer is placing an order is random and may not be observable to the other buyer. The two buyers, B₁ and B₂, simultaneously choose their order quantities, y₁ and y₂. If the manufacturer’s capacity K is sufficient to fulfill both orders, each buyer receives the amount it orders. Otherwise, the manufacturer allocates quantity q_i (i.e., the sales quantity) to buyer B_i according to a preannounced linear allocation policy, which is standard in the literature and characterized as follows:

Here, and in the rest of the analysis, we refer to the focal buyer as index i and the other buyer as j. Based on the quantity each buyer receives, the buyers produce their final products (with a constant unit production cost that is normalized to zero) and sell in their own end markets.⁶ The retail price for buyer B_i is determined by the inverse demand function $p_i=A_i-q_i$.⁷ We assume $a⩾4c$ for analytical convenience; the case of $a<4c$ does not generate additional insights but overcomplicates the equilibrium analyses.

3.3. Justification of Allocation Rule

Linear allocation is an individually responsive (IR) mechanism, under which a buyer receives more allocation by ordering more unless it is allocated all of the capacity (Cachon and Lariviere 1999a, Liu 2012, Cho and Tang 2014).⁸ Because each buyer’s allocated quantity depends on the other buyer’s order quantity, buyers compete with each other for the manufacturer’s capacity in a rationing game. Without loss of generality, we restrict the buyers’ order quantities to $y_i⩽K$ (Cachon and Lariviere 1999a, Chen et al. 2013). When the buyers compete intensely to exhaust the manufacturer’s capacity, the capacity allocation depends on the difference between the buyers’ order quantities; thus, both buyers have the incentive to increase the order quantity above that of the opponent. However, as long as $y_i⩽M$, where M can be any constant that is no less than K, the equilibrium capacity allocation remains the same. Thus, order quantities larger than K are uninformative.

3.4. Case Without Blockchain

To study the impact of blockchain, we compare cases with and without blockchain. Figure 2(a) illustrates the sequence of events for the case without blockchain. The game consists of two stages of decision making. First, the manufacturer offers a uniform wholesale price to the buyers (i.e., the pricing stage) regardless of from which supplier it is sourcing. When there is a change of suppliers because of a random disruption of the primary supplier, the manufacturer is unable to increase the wholesale price charged downstream because of the cost of renegotiating the wholesale price and revising the existing contract terms.⁹ Then, each buyer decides whether to participate, and if so, chooses an order quantity (i.e., the ordering stage) without observing whether the other buyer orders. Without blockchain, the buyers cannot credibly communicate their ordering status to each other. Thus, each buyer chooses the order quantity based on the prior probability that the other buyer orders.

3.5. Case with Blockchain

Blockchain technology plays a role in our model by enabling information transparency in two ways: (1) enabling the manufacturer to credibly prove to the buyers from which supplier it is sourcing (i.e., cost transparency) and (2) enabling the buyers to verify each other’s ordering status (i.e., order transparency). A smart contract is designed to include two layers of contingency arising from these two types of transparency. Figure 2(b) illustrates the sequence of events for the case with blockchain. First, the participants create a smart contract including the various contingencies, and then the random factors are realized and the smart contract executes automatically. In the smart contract, the manufacturer chooses different wholesale prices contingent on whether it is sourcing from the primary or the alternative supplier.¹⁰ Then, each buyer decides whether to join the smart contract, and if so, chooses different order quantities contingent on whether only one buyer or both buyers order and whether the primary or the alternative supplier is used. Thus, the participating firms decide the wholesale prices and order quantities in all scenarios up-front and program these decisions into the smart contract.

The execution of the smart contract starts with the realization of random factors and the setting of the wholesale price. Then, in the ordering window (e.g., the first day of every week), each buyer decides whether to place an order. To place an order, a buyer clicks a button (without entering an order quantity as the order quantities are programmed into the smart contract), and when the ordering window ends, the smart contract automatically transfers an order quantity to the manufacturer depending on how many buyers order.¹¹ It is easy to see that, if a buyer has agreed to the wholesale prices chosen by the manufacturer, its equilibrium strategy is to place an order as long as it is realized to have market demand. Thus, we focus the equilibrium analysis on the game of smart contract creation. Similar to the case without blockchain, this game consists of pricing and ordering stages. Throughout the paper, we use superscript $\mathcal{N}$ to represent the equilibrium for the case without blockchain and $\mathcal{B}$ for the case with blockchain.

4. Equilibrium Analyses

We now proceed to the equilibrium analyses. We use backward induction to find the subgame perfect equilibrium of the game played by the manufacturer and the buyers for the case without blockchain in Section 4.1 and with blockchain in Section 4.2. We focus on $\alpha =\beta =1/2$ (i.e., the degree of information asymmetry is maximum) in our theoretical analyses because of tractability.¹²

4.1. Equilibrium Without Blockchain

In this case, the manufacturer offers a uniform wholesale price w to the buyers regardless of from which supplier it is sourcing, and each buyer B_i chooses an order quantity y_i without observing whether the other buyer B_j orders. In the ordering stage, because each buyer has private information about its own ordering status, we derive the Bayesian Nash equilibrium. We solve for a buyer’s order quantity given that it orders; the scenario in which a buyer does not order is ignored from the equilibrium as the order quantity is zero. Buyer B_i’s problem is formulated as follows, in which it needs to consider if buyer B_j orders (with probability α) or not (with probability $1-\alpha$):

where and are the expected profits of buyer B_i if the total order quantity from both buyers does not exceed or exceeds the manufacturer’s capacity, respectively. The following lemma characterizes the Bayesian Nash equilibrium of the buyers’ ordering stage.

Lemma 1

(Buyers’ Equilibrium Order Quantities Without Blockchain). In the case without blockchain, for any w > 0 chosen by the manufacturer, the buyers’ equilibrium order quantities are

$$y_i^{\mathcal{N}}(w)=y_j^{\mathcal{N}}(w)=y^{\mathcal{N}}(w)=\{\begin{array}{ll}K\hfill & if \hspace{0.17em}w⩽a-\frac{5}{3}K,\hfill \\ \frac{1}{4}(3a-3w-K)\hfill & if \hspace{0.17em}a-\frac{5}{3}K<w⩽a-K,\hfill \\ \frac{1}{2}(a-w)\hfill & if \hspace{0.17em}w>a-K.\hfill \end{array}$$

Let $Q=q_i+q_j$ denote the total sales quantity. Based on the equilibrium of the ordering stage, the manufacturer’s expected total sales quantity is as follows:

In the pricing stage, without knowing which supplier will be used, the manufacturer chooses the wholesale price to maximize its expected profit:

where $\mathbb{E}{Q}^{\mathcal{N}}(w)$ is given by (2). The following proposition characterizes the manufacturer’s equilibrium wholesale price and the buyers’ equilibrium order quantities in the case without blockchain.

Proposition 1

(Equilibrium Without Blockchain). In the case without blockchain, the manufacturer’s equilibrium wholesale price, $w^{\mathcal{N}}$, and the buyers’ equilibrium order quantities, $y_i^{\mathcal{N}}=y_j^{\mathcal{N}}=y^{\mathcal{N}}$, are

$$(w^{\mathcal{N}},y^{\mathcal{N}})=\{\begin{array}{ll}\left(a-\frac{5}{3}K,K\right)\hfill & if \hspace{0.17em}K⩽\frac{3}{22}(2a-c),\hfill \\ \left(\frac{1}{12}(6a+3c+2K),\frac{3}{16}(2a-c-2K)\right)\hfill & if \hspace{0.17em}\frac{3}{22}(2a-c)<K⩽\frac{3}{14}(2a-c),\hfill \\ \left(a-K,\frac{1}{2}K\right)\hfill & if \hspace{0.17em}\frac{3}{14}(2a-c)<K⩽\frac{1}{4}(2a-c),\hfill \\ \left(\frac{1}{4}(2a+c),\frac{1}{8}(2a-c)\right)\hfill & if \hspace{0.17em}K>\frac{1}{4}(2a-c).\hfill \end{array}$$

Furthermore, $w^{\mathcal{N}}>c$.

Proposition 1 shows that, in the case without blockchain, the manufacturer’s equilibrium wholesale price and the buyers’ equilibrium order quantities behave differently depending on the manufacturer’s capacity level K. This indicates that the factors driving the equilibrium are dependent on the manufacturer’s capacity level, and we also observe that the firms’ equilibrium decisions do not have to be monotonic in K. Furthermore, the firms’ equilibrium decisions are not always dependent on the manufacturer’s incremental sourcing cost c, implying that the manufacturer does not always have the ability to transfer the incremental sourcing cost to the buyers. The equilibrium in the case without blockchain is characterized by four regions, which we describe as follows.

If the manufacturer’s capacity K is extremely large (i.e., $K>\frac{1}{4}(2a-c)$), a rationing game does not arise in equilibrium. In this case, a buyer orders $y^{\mathcal{N}}=\frac{1}{8}(2a-c)$, which is the unconstrained monopolistic optimal order quantity without capacity rationing. Without the need to compete for the manufacturer’s capacity, a buyer does not need to take into account the ordering status of the other buyer because it is guaranteed to receive the quantity it orders. Moreover, the equilibrium wholesale price, $w^{\mathcal{N}}=\frac{1}{4}(2a+c)$, is independent of the manufacturer’s capacity level K so that it is not capacity-constrained and is increasing in the manufacturer’s incremental sourcing cost c so that the manufacturer is able to transfer part of the incremental sourcing cost to the buyers.

As long as the manufacturer’s capacity is not extremely large, a rationing game arises in equilibrium. Consider first the case in which the manufacturer’s capacity K is extremely small (i.e., $K⩽\frac{3}{22}(2a-c)$). In this case, the buyers compete intensely for the manufacturer’s limited capacity and have the strongest incentive to overorder. In equilibrium, each buyer overorders to the maximum level K. Correspondingly, a buyer receive half of the manufacturer’s capacity if the other buyer orders and receives the entire capacity if the other buyer does not order. Even though a buyer receives the entire capacity of the manufacturer if the other buyer does not order, a buyer is still willing to overorder to the maximum level K in this case because the resulting retail price, a − K, is still high. Moreover, the manufacturer’s equilibrium wholesale price, $w^{\mathcal{N}}=a-\frac{5}{3}K$, is capacity-constrained, which indicates that it is completely governed by the buyers’ overorder incentive and is not affected by its incremental sourcing cost c. In fact, the manufacturer increases the wholesale price to the highest level possible such that it can sell out its entire capacity K even when only one buyer orders. As K increases, because the buyer’s overorder incentive is weakened, the manufacturer needs to reduce its wholesale price to sell out the capacity.

As the manufacturer’s capacity K becomes larger (i.e., $\frac{3}{22}(2a-c)<K⩽\frac{3}{14}(2a-c)$), the buyers still have the incentive to overorder, but it is unprofitable for them to overorder to the maximum level K. This is because, if a buyer orders K but the other buyer does not order, this buyer suffers from a low retail price by selling the entire capacity in the end market. Thus, the buyers resort to a moderate overorder quantity that is below K but above $\frac{1}{2}K$. Such a moderate overorder quantity allows a buyer to maintain a retail price that is not too low if the other buyer does not order yet competing to obtain half of the total capacity if the other buyer does order. Furthermore, a buyer is less afraid to overorder if the manufacturer charges a lower wholesale price. Anticipating this, the manufacturer has an incentive to deliberately reduce the wholesale price so that it can stimulate the overorder incentive of the buyers to a greater extent and sell disproportionately more. However, by reducing the wholesale price, the manufacturer loses profit margin for the entire K units if both buyers order, the total loss of which is higher when K is higher. Thus, the manufacturer has less incentive to reduce the wholesale price when K is higher, which is why the equilibrium wholesale price, $w^{\mathcal{N}}=\frac{1}{12}(6a+3c+2K)$, is increasing in K. This also indicates that the buyers’ overorder incentive is weakened when K is higher; hence, the equilibrium order quantity, $y^{\mathcal{N}}=\frac{3}{16}(2a-c-2K)$, is decreasing in K. Therefore, when the manufacturer’s wholesale price is not capacity-constrained as in the preceding case, the way that the equilibrium responds to the capacity can be reversed. In addition, the equilibrium wholesale price is increasing in the manufacturer’s incremental sourcing cost c so that it can transfer part of the incremental sourcing cost to the buyers.

As the manufacturer’s capacity K further increases (i.e., $\frac{3}{14}(2a-c)<K⩽\frac{1}{4}(2a-c)$), the buyers have the weakest incentive to overorder. In this case, each buyer overorders only to the minimum level $\frac{1}{2}K$ and receives half of the manufacturer’s capacity in equilibrium regardless of whether the other buyer orders. Although a buyer still wants to receive half of the manufacturer’s capacity if the other buyer orders, it has no incentive to order more than $\frac{1}{2}K$ because it is worried about the very low retail price resulting from selling more than $\frac{1}{2}K$ in the end market if the other buyer does not order. Moreover, as long as the manufacturer slightly increases the wholesale price, the buyers are completely freed from the rationing game, and the manufacturer does not benefit from the buyers’ competition to sell out its capacity when both buyers order. Thus, similar to the case of an extremely small capacity, the manufacturer’s equilibrium wholesale price, $w^{\mathcal{N}}=a-K$, is capacity-constrained (hence, it is decreasing in K) and completely governed by the buyers’ overorder incentive (hence, it is independent of the incremental sourcing cost c). The difference is that, in this case, the manufacturer increases the wholesale price to the highest possible level such that it can sell out its entire capacity K only when both buyers order.

4.2. Equilibrium with Blockchain

Blockchain changes when firms choose wholesale prices and order quantities as they commit to these decisions when they create the smart contract before random factors are realized. In this case, the manufacturer offers different wholesale prices contingent on the realized supplier, and given each wholesale price, the buyers choose different order quantities contingent on the realized number of buyers who order. We denote the manufacturer’s contingent wholesale price as w_k and buyer B_i’s contingent order quantity as $y_{i|kn}$, where $k\in \{l,h\}$ represents the realized supplier and $n\in \{1,2\}$ represents the realized number of buyers who order. In the ordering stage, because blockchain removes the information asymmetry between buyers, we derive the Nash equilibrium. When both buyers order, buyer B_i’s equilibrium order quantity depends on that of buyer B_j, and its problem is formulated as

where andare the profits of buyer B_i if the total order quantity from both buyers does not exceed or exceeds the manufacturer’s capacity, respectively. When only one buyer orders, buyer B_i’s problem (which does not depend on buyer B_j) is formulated as

Combining these two scenarios, buyer B_i’s expected profit is

The following lemma characterizes the Nash equilibrium of the buyers’ ordering stage.

Lemma 2

(Buyers’ Equilibrium Order Quantities with Blockchain). In the case with blockchain, for any $w_k>0$ (where $k\in \{l,h\}$) chosen by the manufacturer, the buyers’ equilibrium order quantities are

1. If both buyers order,

   $$y_{i|k2}^{\mathcal{B}}(w_k)=y_{j|k2}^{\mathcal{B}}(w_k)=y_{k2}^{\mathcal{B}}(w_k)=\{\begin{array}{ll}K\hfill & if \hspace{0.17em}{w}_k⩽a-K,\hfill \\ \frac{1}{2}(a-w_k)\hfill & if \hspace{0.17em}{w}_k>a-K;\hfill \end{array}$$

2. If only one buyer orders,

   $$y_{i|k1}^{\mathcal{B}}(w_k)=y_{j|k1}^{\mathcal{B}}(w_k)=y_{k1}^{\mathcal{B}}(w_k)=\{\begin{array}{ll}K\hfill & if \hspace{0.17em}{w}_k⩽a-2K,\hfill \\ \frac{1}{2}(a-w_k)\hfill & if \hspace{0.17em}{w}_k>a-2K.\hfill \end{array}$$

Based on the equilibrium of the ordering stage, when the realized supplier is k, the manufacturer’s expected total sales quantity is as follows:

In the pricing stage, the manufacturer chooses the wholesale prices to maximize its expected profit:

if it sources from the primary supplier andif it sources from the alternative supplier, where $\mathbb{E}{Q}^{\mathcal{B}}(w_k)$ is given by (6). The manufacturer’s expected profit is The following proposition characterizes the manufacturer’s equilibrium wholesale prices and the buyers’ equilibrium order quantities in the case with blockchain.

Proposition 2

(Equilibrium with Blockchain). In the case with blockchain, if the manufacturer sources from the primary supplier, its equilibrium wholesale price, $w_l^{\mathcal{B}}$, and the buyers’ equilibrium order quantities, $y_{i|l2}^{\mathcal{B}}=y_{j|l2}^{\mathcal{B}}=y_{l2}^{\mathcal{B}}$ if both buyers order and $y_{i|l1}^{\mathcal{B}}=y_{j|l1}^{\mathcal{B}}=y_{l1}^{\mathcal{B}}$ if only one buyer orders, are

$$(w_l^{\mathcal{B}},y_{l2}^{\mathcal{B}},y_{l1}^{\mathcal{B}})=\{\begin{array}{ll}(a-2K,K,K)\hfill & if \hspace{0.17em}K⩽\frac{1}{5}a,\hfill \\ \left(\frac{1}{2}(a+K),K,\frac{1}{4}(a-K)\right)\hfill & if \hspace{0.17em}\frac{1}{5}a<K⩽\frac{1}{3}a,\hfill \\ \left(a-K,\frac{1}{2}K,\frac{1}{2}K\right)\hfill & if \hspace{0.17em}\frac{1}{3}a<K⩽\frac{1}{2}a,\hfill \\ \left(\frac{1}{2}a,\frac{1}{4}a,\frac{1}{4}a\right)\hfill & if \hspace{0.17em}K>\frac{1}{2}a;\hfill \end{array}$$

if the manufacturer sources from the alternative supplier, its equilibrium wholesale price, $w_h^{\mathcal{B}}$, and the buyers’ equilibrium order quantities, $y_{i|h2}^{\mathcal{B}}=y_{j|h2}^{\mathcal{B}}=y_{h2}^{\mathcal{B}}$ if both buyers order and $y_{i|h1}^{\mathcal{B}}=y_{j|h1}^{\mathcal{B}}=y_{h1}^{\mathcal{B}}$ if only one buyer orders, are

$$(w_h^{\mathcal{B}},y_{h2}^{\mathcal{B}},y_{h1}^{\mathcal{B}})=\{\begin{array}{ll}(a-2K,K,K)\hfill & if \hspace{0.17em}K⩽\frac{1}{5}(a-c),\hfill \\ \left(\frac{1}{2}(a+c+K),K,\frac{1}{4}(a-c-K)\right)\hfill & if \hspace{0.17em}\frac{1}{5}(a-c)<K⩽\frac{1}{3}(a-c),\hfill \\ \left(a-K,\frac{1}{2}K,\frac{1}{2}K\right)\hfill & if \hspace{0.17em}\frac{1}{3}(a-c)<K⩽\frac{1}{2}(a-c),\hfill \\ \left(\frac{1}{2}(a+c),\frac{1}{4}(a-c),\frac{1}{4}(a-c)\right)\hfill & if \hspace{0.17em}K>\frac{1}{2}(a-c).\hfill \end{array}$$

Furthermore, $w_l^{\mathcal{B}}⩽w_h^{\mathcal{B}},\hspace{0.17em}{w}_l^{\mathcal{B}}>0$, and $w_h^{\mathcal{B}}>c$; $y_{l2}^{\mathcal{B}}⩾y_{l1}^{\mathcal{B}},\hspace{0.17em}{y}_{h2}^{\mathcal{B}}⩾y_{h1}^{\mathcal{B}},\hspace{0.17em}{y}_{l2}^{\mathcal{B}}⩾y_{h2}^{\mathcal{B}}$, and $y_{l1}^{\mathcal{B}}⩾y_{h1}^{\mathcal{B}}$.

Blockchain-enabled transparency changes both the ordering and pricing stages of the game by enabling firms to make decisions contingent on the realization of random factors. In the ordering stage, a buyer orders a larger quantity if the other buyer also orders ($y_{l2}^{\mathcal{B}}$ or $y_{h2}^{\mathcal{B}}$) and a smaller quantity if the other buyer does not order ($y_{l1}^{\mathcal{B}}$ or $y_{h1}^{\mathcal{B}}$). In the pricing stage, the manufacturer can transfer the incremental sourcing cost to the buyers only when it is sourcing from the alternative supplier. Thus, the manufacturer charges a lower wholesale price $w_l^{\mathcal{B}}$ when sourcing from the primary supplier S_l and a higher price $w_h^{\mathcal{B}}$ when sourcing from the alternative supplier S_h. Correspondingly, the equilibrium order quantity under the primary supplier ($y_{l2}^{\mathcal{B}}$ or $y_{l1}^{\mathcal{B}}$) is higher than that under the alternative supplier ($y_{h2}^{\mathcal{B}}$ or $y_{h1}^{\mathcal{B}}$). As Proposition 2 shows, given the realized supplier, the equilibrium can fall into one of four scenarios parallel to the four scenarios in the case without blockchain, but there is a notable difference in how the equilibrium order quantities behave.

For instance, the moderate overorder quantity between $\frac{1}{2}K$ and K is eliminated under blockchain-enabled transparency. Recall from Proposition 1 that, without blockchain, the buyers can choose a moderate overorder quantity that is between $\frac{1}{2}K$ and K when the manufacturer’s capacity is moderately small. Such a moderate overorder quantity never arises with blockchain when both buyers order, indicating that this equilibrium is completely driven by the information asymmetry in the rationing game. In Proposition 1, this moderate overorder quantity arises because the buyers need to factor in both the need to compete for more capacity if the other buyer also orders and the need to maintain a higher retail price if the other buyer does not order. However, if a buyer can choose the order quantity contingent on whether the other buyer orders, these two considerations are decoupled. If the other buyer is ordering, then the buyer’s order quantity is uniquely driven by the need to compete for more capacity, which pushes the order quantity up to the maximum overorder level K. If the other buyer is not ordering, then the buyer’s order quantity is uniquely driven by the need to maintain a higher retail price, which pushes the order quantity down to the monopolistic optimum given the manufacturer’s wholesale price. Thus, the moderate overorder quantity is eliminated, and as a result, a buyer’s equilibrium order quantity in the rationing game (i.e., when both buyers order) is always increasing in K. This is in contrast to the case without blockchain in which a buyer’s equilibrium order quantity can be nonmonotonic in K because of the moderate overorder quantity. Such changes in the rationing game have implications for how blockchain can impact the supply chain efficiency, which we examine next.

5. Implications for Blockchain Adoption

In this section, we examine the conditions for blockchain adoption when considering both functionalities of blockchain in enabling cost and order transparency. In Section 5.1, we determine when blockchain should be adopted by analyzing its impact on the supply chain profit. In Section 5.2, we further study the alignment of firms’ incentives for blockchain adoption.

5.1. Adoption from the Supply Chain Perspective

Theorem 1 summarizes the comparison of the total supply chain profit and firms’ decisions in the cases with and without blockchain using the equilibria characterized in Propositions 1 and 2. Theorem 1(a) shows that blockchain should not be adopted in the supply chain when the manufacturer’s capacity is small (i.e., $K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$) and should be adopted when the manufacturer’s capacity is large (i.e., $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$). Theorem 1, (b-c), provides additional insights regarding how blockchain impacts the firms’ operational decisions by analyzing the changes in the expected wholesale price and total sales quantity. We explain these results as follows.

Theorem 1

(Impact of Blockchain on Supply Chain).

1. Blockchain reduces the total supply chain profit if $K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$ and increases the total supply chain profit if $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$.

2. Blockchain reduces the expected wholesale price if $K⩽\frac{3}{26}(2a-c)$ and increases the expected wholesale price if $K>\frac{3}{26}(2a-c)$.

3. Blockchain always reduces the expected total sales quantity.

Theorem 1 uncovers that the manufacturer’s capacity is an important factor that governs which type of transparency plays a dominating role and whether the dominating effect alleviates or amplifies inefficiencies in the supply chain. First, consider the case when the manufacturer’s capacity is large (i.e., $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$). In this case, the buyers’ competition for the manufacturer’s capacity is not intense; regardless of whether the buyers observe the ordering status of each other, they are likely to order the unconstrained monopolistic optimal quantities. Thus, order transparency does not play a dominating role. Instead, the impact of blockchain is primarily driven by cost transparency. Recall that cost transparency provides a credible way for the manufacturer to share information about the upstream sourcing cost to the buyers and enables the manufacturer to adopt a more flexible dynamic wholesale price contract. Furthermore, an ample capacity allows the manufacturer to more freely adjust its dynamic wholesale prices according to which supplier is currently used as opposed to being restricted to set the wholesale prices at the capacity-constrained optimum. Thus, the entire supply chain can act together by ordering more when facing a lower sourcing cost and less when facing a higher sourcing cost. In this way, the average per-unit sourcing cost is reduced, which improves the efficiency of the supply chain. As shown in Theorem 1(a), when the manufacturer’s capacity is sufficient, blockchain improves the total supply chain profit and, hence, should be adopted. Because the total supply chain profit is improved, even if blockchain does not improve the profit for all firms, the firm(s) who benefit from blockchain may be able to compensate the other firm(s) so that they are also willing to adopt the blockchain.

Furthermore, cost transparency changes the equilibrium to one in which the expected wholesale price is increased and the expected sales quantity is reduced. Theorem 1(b) shows that blockchain increases the expected wholesale price if $K>\frac{3}{26}(2a-c)$, which is smaller than the threshold of $a-\frac{1}{4}\sqrt{4a^2+6c^2}$; this implies that the expected wholesale price is increased for values of capacity for which blockchain improves total supply chain profit. With an ample capacity, the manufacturer’s wholesale price decision is unlikely to respond to the buyers’ overorder incentive but is predominantly driven by its incentive to transfer more incremental sourcing cost to the buyers. Without blockchain, the manufacturer is restricted to charge a uniform wholesale price. This means that transferring more incremental sourcing cost to the buyers entails raising the wholesale price even if the manufacturer sources from the primary (i.e., low-cost) supplier. This reduces the buyers’ willingness-to-pay, and hence, the manufacturer is forced to charge a lower wholesale price. In contrast, the dynamic wholesale price contract with blockchain enables the manufacturer to transfer the incremental sourcing cost to the buyers only when it is sourcing from the alternative (i.e., high-cost) supplier. Such contracting flexibility allows the manufacturer to transfer the incremental sourcing cost to the buyers more efficiently, and the expected wholesale price increases as a result. Correspondingly, Theorem 1(c) shows that the buyers reduce the expected order (and sales) quantities. It is important to note that, although the buyers may order less with blockchain, the equilibrium is more efficient for the supply chain because, as explained, the average per-unit sourcing cost is reduced for the supply chain and the total supply chain profit is increased.

Next, consider the situation when the manufacturer’s capacity is small (i.e., $K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$). Here, the buyers’ competition is intense, and they have a strong incentive to overorder. Thus, the impact of blockchain is primarily driven by order transparency. Moreover, the buyers’ overorder incentive is always stronger without blockchain. Because a buyer has to decide the order quantity without knowing whether the other buyer orders, it is pressured to order more aggressively for fear of a competing buyer. In contrast, blockchain enables a buyer to order different quantities contingent on the ordering status of the other buyer. In this way, the information advantage of blockchain alleviates the competitive pressure for the buyers and mitigates their overorder incentive. As a result, the total sales quantity is reduced (Theorem 1(c)). This indicates that, for a small capacity, order transparency exacerbates double marginalization and amplifies the inefficiency in the supply chain. Therefore, when the manufacturer’s capacity is insufficient, blockchain hurts the total supply chain profit (Theorem 1(a)). Because the total supply chain profit is reduced, even if the firm(s) that benefit from blockchain are willing to compensate the firm(s) that do not, blockchain cannot be initiated in the supply chain.

While blockchain always leads to a reduced expected total sales quantity, its impact on the expected wholesale price for this range of capacity is more nuanced. Theorem 1(b) shows that the expected wholesale price decreases if $K⩽\frac{3}{26}(2a-c)$ and increases if $\frac{3}{26}(2a-c)<K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$. When the manufacturer’s capacity is extremely small (i.e., $K⩽\frac{3}{26}(2a-c)$), the buyers have the strongest incentive to overorder to exhaust the manufacturer’s capacity. Thus, the strength of the buyers’ overorder incentive does not change how much the manufacturer sells, but determines the wholesale price the manufacturer can charge for each unit sold. Because the buyers’ overorder incentive is weakened with blockchain, they are willing to pay less for each unit of capacity, and hence, the manufacturer has to reduce the expected wholesale price.

However, as K increases, another consideration arises in the manufacturer’s wholesale price decision. When the manufacturer is not guaranteed to sell out its capacity, the buyers’ overorder incentive also affects how much they are willing to order. Recall that, without blockchain, a moderate overorder quantity can arise as the equilibrium (Proposition 1), in which case a higher wholesale price suppresses the buyer’s overorder incentive and reduces the manufacturer’s sales quantity disproportionately. Blockchain eliminates this moderate overorder quantity (Proposition 2). While a higher wholesale price still reduces the manufacturer’s sales quantity, the effect is less significant because it only occurs when only one buyer orders, in which case the buyers are less sensitive to the wholesale price because their order quantities are not driven by the overorder incentive. This indicates that the manufacturer is able to increase the expected wholesale price to a higher level with blockchain. When K increases sufficiently (i.e., $\frac{3}{26}(2a-c)<K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$), this additional consideration dominates in the manufacturer’s wholesale price decision, and the impact of blockchain on the expected wholesale price reverses.

This result indicates that the consideration of capacity rationing generates new insights for supply chain coordination. The existing literature shows that double marginalization results in an efficiency loss in an uncapacitated supply chain because of the manufacturer’s incentive to maintain a higher profit margin by charging a wholesale price that is as high as possible (e.g., Spengler 1950, Tirole 1988, Coughlan and Wernerfelt 1989, Cachon and Lariviere 2005, Cui et al. 2007). However, the insight changes in a capacitated supply chain. When the manufacturer’s capacity is insufficient, the buyers have an incentive to inflate their orders to fight for the capacity. This reduces the manufacturer’s incentive to increase the wholesale price to the highest level possible because a lower wholesale price can intensify the buyer’s overorder incentive and allow the manufacturer to sell disproportionately more. In this way, capacity rationing mitigates double marginalization and creates an efficiency gain in the supply chain, particularly when the supply chain is not transparent in the competing buyers’ ordering status. By enabling order transparency, blockchain creates a counter effect and reduces such an efficiency gain.

In sum, blockchain can be a double-edged sword for a capacitated multitier supply chain. Our results show that, while the vertical information sharing it enables improves supply chain efficiency, the horizontal information sharing it enables can amplify the inefficiency in the supply chain. This indicates that the optimal use of blockchain may not be in a way such that the entire network is made transparent. To limit the degree of transparency enabled by the blockchain, an access control layer may be needed to govern firms’ data access. We study these issues in Section 6.

5.2. Firms’ Incentives for Blockchain Adoption

In Section 5.1, we see that blockchain can be beneficial to the entire supply chain and should be adopted when the manufacturer’s capacity is sufficiently large. However, whether blockchain can be adopted depends on whether firms’ incentives are aligned. If blockchain benefits all firms at the same time, then firms’ incentives for blockchain adoption are naturally aligned. If blockchain benefits certain firms while hurting other firms, then it is important to understand who should be the initiator of blockchain and whether the initiator is able to compensate other firms sufficiently. Blockchain adoption hinges on these incentive issues; thus, we next study how blockchain affects individual firms.

To address this question, Theorem 2, (a-b), summarizes the impact of blockchain on the manufacturer and the buyers, respectively, for all values of capacity. Theorem 2(c) focuses on the case in which blockchain should be adopted (under the condition identified by Theorem 1(a), $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$) and defines whether an incentive conflict arises in this case. Figure 3 illustrates these results. We note that the threshold in Theorem 1(a) is different from those in Theorem 2, (a-b); this is so because the former result focuses on the total supply chain profit, whereas the latter results focus on the individual participants.

Theorem 2

(Firms’ Incentives for Blockchain Adoption).

1. Blockchain reduces the manufacturer’s expected profit if $K⩽\frac{1}{2}(a-c)$ and increases the manufacturer’s expected profit if $K>\frac{1}{2}(a-c)$.

2. Blockchain increases the buyers’ expected profits if $K<\frac{1}{54}(2a-c+\sqrt{112a(a-c)+55c^2})$ or $K>\frac{1}{4}\sqrt{4a^2-2c^2}$, and reduces the buyers’ expected profits if $\frac{1}{54}(2a-c+\sqrt{112a(a-c)+55c^2})⩽K⩽\frac{1}{4}\sqrt{4a^2-2c^2}$.

3. When it is beneficial for the supply chain to adopt the blockchain (i.e., $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$), we have the following:

   • c.1. If $K>\frac{1}{4}\sqrt{4a^2-2c^2}$, both the manufacturer and the buyers have the incentive to initiate the blockchain.

   • c.2. If $a-\frac{1}{4}\sqrt{4a^2+6c^2}<K⩽\frac{1}{4}\sqrt{4a^2-2c^2}$, only the manufacturer has the incentive to initiate the blockchain.

We discuss these results with reference to Theorem 2(c), which shows that an incentive conflict can exist when blockchain should be adopted in the supply chain. Recall from Theorem 1 that, in this case, the impact of blockchain is primarily driven by cost transparency so that the manufacturer can charge dynamic wholesale prices according to the sourcing cost. To see how cost transparency can lead to an incentive conflict, suppose that the manufacturer’s capacity is slightly above the level that is sufficient to eliminate the rationing game in the case without blockchain. Suppose further that blockchain is adopted. If the sourcing cost is high, the manufacturer charges a higher wholesale price, which further reduces the buyers’ order quantities; hence, the rationing game remains intact. However, if the sourcing cost is low, the manufacturer charges a lower wholesale price, which can fall below the threshold to trigger a rationing game. In fact, the manufacturer can intentionally charge a sufficiently lower wholesale price to create a rationing game. In this way, the manufacturer can take advantage of contracting flexibility to intensify the buyers’ competition and extract more surplus from them. While this clearly benefits the manufacturer, it hurts the buyers and results in conflicting incentives for blockchain adoption. Theorem 2(c) further identifies that such an incentive conflict arises if the manufacturer’s capacity is not sufficiently large (i.e., $a-\frac{1}{4}\sqrt{4a^2+6c^2}<K⩽\frac{1}{4}\sqrt{4a^2-2c^2}$, which corresponds to the dark shaded region in Figure 3). In this case, the ability of the manufacturer to trigger a rationing game leads to an incentive conflict. Thus, in order to initiate the blockchain, the manufacturer needs to compensate the buyers sufficiently so that all firms can benefit from blockchain.

When the manufacturer’s capacity is sufficiently large such that the buyers are freed from the rationing game (i.e., $K>\frac{1}{4}\sqrt{4a^2-2c^2}$, which corresponds to the light shaded region in Figure 3), the incentives of all the firms for blockchain adoption are naturally aligned. It is easy to see that the manufacturer’s benefits remain intact because it can reduce the per-unit sourcing cost and transfer its sourcing cost to the buyers more efficiently. Moreover, the buyers also benefit from contracting flexibility because, akin to the dynamic wholesale prices charged by the manufacturer, the buyers can charge dynamic retail prices in the end markets. Thus, they can sell more when facing a lower wholesale price and sell less (at higher retail prices) when facing a higher wholesale price. In this way, the buyers are willing to share the supply risk of the manufacturer. This indicates that when capacity rationing does not play a role, the value of vertical information sharing spreads to the entire supply chain without being distorted. Therefore, blockchain leads to a win–win–win; hence, it can be initiated by any firm in the supply chain, and all other firms are willing to join the blockchain without requiring any compensation scheme.

In addition, Theorem 2(b) shows another case in which the buyers benefit from blockchain: when the manufacturer’s capacity is sufficiently small (i.e., $K<\frac{1}{54}(2a-c+\sqrt{112a(a-c)+55c^2})$, order transparency can alleviate the buyers’ competitive pressure and mitigate their overorder incentive. In fact, in this case, the buyers have an incentive to form a subnetwork among themselves for horizontal information sharing. However, such horizontal information sharing hurts the manufacturer (Theorem 2(a)) as well as the entire supply chain (because the threshold of $\frac{1}{54}(2a-c+\sqrt{112a(a-c)+55c^2})$ is below the threshold for blockchain adoption, $a-\frac{1}{4}\sqrt{4a^2+6c^2}$). To prevent the supply chain from running into this situation, it is important to increase the manufacturer’s capacity level so that the supply chain falls into the region in which blockchain can create a win–win–win.

6. Implications for Blockchain Design

So far, we have considered the application of a blockchain that enables both functionalities: cost and order transparency. Such a blockchain can be implemented without an access control layer for the logistics data so that, by joining the blockchain, a firm would naturally gain access to the data records in the entire network. However, as we show, such a blockchain should not always be adopted because it may hurt the supply chain. To maximize the value of blockchain, firms can consider limiting the degree of transparency that is enabled by the blockchain. This requires that blockchain has an access control layer to restrict certain firms’ access to certain types of logistics data. In this section, we study the optimal design of blockchain and answer the question of whether a blockchain can create more value by limiting the degree of transparency. In Section 6.1, we characterize the optimal blockchain design. In Section 6.2, we investigate whether firms can reach agreement on the blockchain design that is optimal for the entire supply chain.

6.1. Optimal Blockchain Design

To derive the optimal blockchain design, we evaluate two alternative blockchain cases: (1) the case with only cost transparency, in which the manufacturer charges different wholesale prices contingent on the supplier used, but the buyers place orders without knowing the number of buyers who order, and (2) the case with only order transparency, in which the buyers place orders contingent on the number of buyers who order but the manufacturer charges a uniform wholesale price. These alternative blockchain designs can be achieved by creating an access control layer. For example, limiting the blockchain functionality to cost transparency could be feasible if the blockchain does not grant the buyers permission to access either the content of the data recorded by other buyers (e.g., a buyer’s logistics data that can verify it is ordering or not from the manufacturer) or the existence of the record of such data but grants the buyers permission to access the data recorded by the manufacturer (e.g., manufacturer’s logistics data that can verify from which supplier it is currently sourcing). The consideration of these two blockchain cases expands our model to a 2 × 2 framework in which firms can choose whether to include each type of transparency in the blockchain design.¹³ The model formulation and equilibrium analyses for these alternative blockchain cases are provided in Online Appendix C. The following theorem summarizes the optimal blockchain design by comparing the supply chain profit under the four cases in the 2 × 2 framework. Figure 4 illustrates the optimal blockchain design for the supply chain.

Theorem 3

(Supply Chain Optimal Blockchain Design).

1. If $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$, a blockchain design that enables both cost and order transparency is optimal.

2. If $K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$, there exist thresholds ${\overline{K}}_1$ and ${\overline{K}}_2$ (where ${\overline{K}}_1<{\overline{K}}_2<a-\frac{1}{4}\sqrt{4a^2+6c^2}$) such that the optimal blockchain design is to only enable cost transparency if ${\overline{K}}_1<K<{\overline{K}}_2$, and blockchain should not be adopted otherwise. Moreover,

   $$\begin{array}{ll}{\overline{K}}_1\hfill & \equiv \frac{1}{22}(14a-\sqrt{64a^2+66c^2}),\hfill \\ {\overline{K}}_2\hfill & \equiv \{\begin{array}{ll}\frac{1}{39}(51a-32c-2\sqrt{270a^2-348ac+22c^2})\hfill & if \hspace{0.17em}a⩽7c,\hfill \\ \frac{1}{2}(a-c)\hfill & if \hspace{0.17em}a>7c.\hfill \end{array}\hfill \end{array}$$

Recall from Theorem 1 that, when blockchain enables both cost and order transparency, it should be adopted in the supply chain only when the manufacturer’s capacity is large (i.e., $K>a-\frac{1}{4}\sqrt{4a^2+6c^2}$, which corresponds to the light shaded region in Figure 4). Theorem 3(a) refines this result by showing that limiting the blockchain functionality to only one type of transparency cannot further benefit the supply chain in this case.

Theorem 3(b) presents an additional result that limiting the blockchain functionality to cost transparency can benefit the supply chain when the manufacturer’s capacity is small. Specifically, when $K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$, even though blockchain should not be adopted in its original form of enabling both types of transparency, there exists a region in which the manufacturer’s capacity is moderately small (i.e., ${\overline{K}}_1<K<{\overline{K}}_2$, which corresponds to the dark shaded region in Figure 4) and a blockchain that only enables cost transparency should be adopted. These two thresholds define three cases within $K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$, which we discuss as follows.

Compared with the case with sufficient capacity, the impact of cost transparency is more nuanced when capacity is insufficient as the manufacturer’s dynamic wholesale prices interact with the rationing game. Depending on the capacity level, the manufacturer utilizes the flexibility stemming from cost transparency in different ways. When the manufacturer’s capacity is moderately small (i.e., ${\overline{K}}_1<K<{\overline{K}}_2$), the buyers may choose a moderate overorder quantity that falls between $\frac{1}{2}K$ and K in the case without blockchain. Correspondingly, the manufacturer’s wholesale price is not capacity-constrained, and it can use the uniform wholesale price to transfer part of the incremental sourcing cost to the buyers (recall from Proposition 1 that $w^{\mathcal{N}}$ is increasing in c in this case). However, as the manufacturer transfers more incremental sourcing cost to the buyers by increasing its wholesale price, it loses the ability to induce the overordering of buyers at the same time. Thus, the restriction to charge a uniform wholesale price causes a dilemma for the manufacturer and limits its ability to take advantage of the buyers’ overorder incentive. Such a dilemma can be overcome if the manufacturer can charge dynamic wholesale prices. With blockchain, the manufacturer only needs to transfer the incremental sourcing cost to the buyers when the sourcing cost is high, whereas when the sourcing cost is low, it is freed from the need to transfer any sourcing cost and instead focuses on inducing the overordering of buyers by charging a significantly lower wholesale price. In this way, the manufacturer can take more advantage of the buyer’s overorder incentive, and as a result, the buyers order more and double marginalization is alleviated. Therefore, a blockchain that only enables cost transparency improves the total supply chain profit in this case, and this alternative form of blockchain design should be adopted.

However, the same insight does not carry through when the manufacturer’s capacity is outside this moderate interval. When the manufacturer’s capacity is too small (i.e., $K⩽{\overline{K}}_1$), the buyers overorder to the maximum level K in the case without blockchain, and the manufacturer’s uniform wholesale price is capacity-constrained. This indicates that the manufacturer loses the ability to transfer its incremental sourcing cost to the buyers (recall from Proposition 1 that $w^{\mathcal{N}}$ is independent of c in this case). However, with cost transparency, the manufacturer can gain the ability to transfer its incremental sourcing cost to the buyers when the sourcing cost is high. Because the manufacturer charges a higher wholesale price in this scenario, the buyers may order less than K as a result, and double marginalization is exacerbated. Similarly, when the manufacturer’s capacity is too large (i.e., ${\overline{K}}_2⩽K⩽a-\frac{1}{4}\sqrt{4a^2+6c^2}$), the manufacturer’s uniform wholesale price is also capacity-constrained in the case without blockchain as the buyers overorder to the minimum level $\frac{1}{2}K$. Correspondingly, cost transparency can enable the manufacturer to transfer its incremental sourcing cost to the buyers, leading to a worsening of double marginalization. Therefore, in both these cases, blockchain hurts the supply chain profit even though its functionality is limited to cost transparency, and there is no form of blockchain design that benefits the supply chain.

6.2. Firms’ Incentives for Blockchain Design

After uncovering the optimal design of blockchain from the supply chain’s perspective, we now study whether individual firms have the incentives to adopt such a blockchain design. For this, we compare the manufacturer’s and the buyers’ profits in the extended 2 × 2 framework in which firms are allowed to choose the optimal blockchain design and obtain the following theorem.

Theorem 4

(Firms’ Incentives for Blockchain Design). Consider the case in which it is optimal to use blockchain to only enable cost transparency (i.e., ${\overline{K}}_1<K<{\overline{K}}_2$). The manufacturer always has the incentive to choose the optimal blockchain design. However, there exist thresholds ${\overline{K}}_3$ and ${\overline{K}}_4$ (where ${\overline{K}}_1<{\overline{K}}_3<{\overline{K}}_4⩽{\overline{K}}_2$) such that the buyers have the incentive to choose the optimal blockchain design if and only if ${\overline{K}}_3<K<{\overline{K}}_4$. Moreover,

$$\begin{array}{ll}{\overline{K}}_3\hfill & \equiv \frac{3}{638}(18a+\sqrt{1600a^2-638c^2}),\hfill \\ {\overline{K}}_4\hfill & \equiv \{\begin{array}{ll}\frac{1}{271}[27a+2\sqrt{6(403a^2-542ac+271c^2)}]\hfill & if \hspace{0.17em}a⩽7c,\hfill \\ \frac{1}{2}(a-c)\hfill & if \hspace{0.17em}a>7c.\hfill \end{array}\hfill \end{array}$$

Theorem 4 shows that, when it is optimal to use blockchain to only enable cost transparency (i.e., ${\overline{K}}_1<K<{\overline{K}}_2$), the manufacturer always has the incentive to choose such an optimal blockchain design. This is because the contracting flexibility stemming from cost transparency enables the manufacturer to achieve both of its needs to induce more overordering from the buyers when the sourcing cost is low and to transfer more incremental sourcing cost to the buyers when the sourcing cost is high. This helps the manufacturer overcome the dilemma that it faces in the case without blockchain, that is, if it raises the uniform wholesale price to transfer more sourcing cost to the buyers, its ability to induce the buyers to overorder is compromised at the same time.

In contrast, the buyers do not always have the incentive to choose such an optimal blockchain design. Cost transparency leads to a trade-off for the buyers. On the one hand, with cost transparency, the manufacturer charges a lower wholesale price to induce more overordering from the buyers, which reduces the overall ordering costs for the buyers. On the other hand, the increased overorder incentive intensifies the buyers’ competition. We further find that, if ${\overline{K}}_3<K<{\overline{K}}_4$, the former effect dominates, and the buyers are better off with cost transparency, whereas if ${\overline{K}}_1<K⩽{\overline{K}}_3$ or ${\overline{K}}_4⩽K<{\overline{K}}_2$, the latter effect dominates, and the buyers are worse off with cost transparency. Therefore, we see that the range of manufacturer’s capacity in which the optimal blockchain design only enables cost transparency consists of two parts: the range $({\overline{K}}_3,{\overline{K}}_4)$ in which both the manufacturer and the buyers can naturally benefit from a blockchain that only enables cost transparency, and the range $({\overline{K}}_1,{\overline{K}}_3]\cup [{\overline{K}}_4,{\overline{K}}_2)$ in which the manufacturer needs to compensate the buyers sufficiently to implement such a blockchain so that all firms can benefit from it.

In practice, when blockchain is adopted in a supply chain, firms may have a tendency to restrict data sharing only to participants with whom they transact directly (Vitasek et al. 2022), particularly when they are uncertain about the impact of sharing data beyond immediate supply chain partners or with a potential competitor. While this may be a path of least resistance to experiment with blockchain in its early stage, our findings indicate that to fully unlock the value of blockchain, firms should go beyond one-to-one information sharing. In particular, for both types of transparency that we study in this paper, the blockchain implementation requires the two firms who transact directly to share transaction records with a third firm. For example, cost transparency requires the manufacturer to share its raw material origin information, generated in its transaction with the upstream suppliers, with the downstream buyers. Similarly, order transparency requires the buyers to observe the data records (not necessarily the data content) of other buyers within the same tier. As such, our paper highlights that the correct design of an access control layer is one that facilitates network information sharing in the blockchain rather than one-to-one information sharing and it is important for firms to design more flexible forms of contracts according to the expanded information scope to reap more benefits from blockchain.

7. Conclusion

Blockchain technology, together with IoT and smart contracts, can have a transformative impact on supply chains and substantially change the way that firms cooperate and compete. This paper makes four main contributions by enhancing the understanding of blockchain-enabled transparency in supply chains. First, it develops a unified framework to study both vertical (i.e., cost transparency) and horizontal (i.e., order transparency) information sharing in a supply chain. This unified framework provides a comprehensive view of how the two types of blockchain-enabled transparency interact with each other and jointly impact the supply chain. Second, our results highlight upstream production capacity as an important mediator in governing the value of supply chain transparency. As the capacity increases, the dominating effect of blockchain changes from order transparency to cost transparency, and the impact of blockchain reverses as a result. Third, this paper shows that blockchain should be adopted to enable the maximum degree of transparency only when the upstream is not too capacitated. However, the supply chain may need to overcome an incentive misalignment issue, and the upstream manufacturer may need to be the initiator of blockchain and to properly compensate the downstream buyers if the manufacturer’s capacity is not sufficiently large. Fourth, this paper demonstrates that it may not be optimal to utilize the blockchain’s functionality of increasing transparency to its full potential. Firms should be cautious about horizontal order transparency because it can exacerbate double marginalization and hurt the supply chain. Meanwhile, a blockchain that only enables vertical cost transparency can benefit not only the entire supply chain, but also all individual firms, the implementation of which requires an access control layer for logistics data. To conclude, our work provides industry practitioners with a better understanding of where the costs and benefits of blockchain fall and makes prescriptions regarding how blockchain collaboration can be achieved between supply chain partners and how they should choose the optimal blockchain design.