Information Sharing and Coordination Between Supply Chains with Bottom-Up Negotiations^*

Abstract

This paper considers competition between two supply chains where one manufacturer has uncertain production costs and can share this private information with its rival. In contrast to existing literature, we study bottom-up negotiations in which dealers make offers to consumers before negotiating with manufacturers, as is common in many industries with complex products, such as interior design, trucks, or luxury cars. Furthermore, we allow for both quality-enhancing and cost-reducing investments and study how these variables affect the incentive to share information and the competitive effects of this conduct. We show that with bottom-up negotiations, information sharing is profitable and procompetitive. In contrast, in the classic model of vertical relations, where the manufacturer makes its choices before the retailer does, exchange of information is unprofitable. We also discuss the implementation of our mechanism by the coordinated setting of list prices.

I. INTRODUCTION

The reasons why firms competing in oligopolies exchange demand or cost information have been extensively investigated by the industrial organization literature.¹ The main message of this literature is that the exchange of information among firms depends on the nature of competition—that is, quantity vs price competition—and the type of the information being shared—that is, demand vs cost information—and can lead to various market outcomes, with significant implications for firm behavior and market performance.

These models rely on two main assumptions. First, firms that share information sell directly to final consumers. Second, information sharing has an effect on prices and quantities, but not on other variables, such as quality or service provision. However, these assumptions do not always mirror reality. First, information sharing and coordination agreements are often investigated by antitrust authorities in industries where upstream manufacturers produce goods that are distributed in the downstream market by independent dealers. Second, in many markets, firms make investments that help to increase the sales of the final product and reduce production costs.²

In these environments, information-sharing decisions appear to be more involved than in traditional models. The reason is that the effects of information sharing depend on the negotiation structure between manufacturers and their dealers, as well as the timing of pricing and investment decisions, which vary across industries. In fact, although most vertical contracting models assume that manufacturers first negotiate a wholesale price with dealers who then approach buyers, in many industries, the order of negotiations is reversed. Specifically, dealers first find an arrangement—typically including a quality level in addition to a price—with buyers, and then negotiate an internal (dealer or wholesale) price with the manufacturer, which implies that negotiations have a bottom-up structure. For instance, in industries with complex products, such as interior design, trucks, and similar products, the final offer is customer specific, with dealers and manufacturers choosing whether to include different components (bespoke or made-to-order options) and how to produce and combine these components in a cost-efficient way. Only after the offer to the specific customer is made, dealers and manufacturers negotiate an internal dealer price. We discuss examples of industries with these features after the model set-up.

These aspects of information-sharing agreements are surprisingly poorly understood. Yet, they were recently investigated in the European truck industry,³ pulpwood,⁴ and the corrugated cardboard industries.⁵ These industries feature a substantial extent of vertical separation, industry-specific negotiations, and a high degree of product customization: the three fundamental ingredients of the model that we will lay down below.

We develop a novel framework in which negotiations have a bottom-up structure and manufacturers can invest to enhance quality or service and to reduce costs. The objective is to study how the presence of investments curb manufacturers’ information sharing decisions, assess the competitive implications of such practice, and investigate the extent to which these effects rely on different negotiations protocols.

There are two competing supply chains. Each supply chain consists of a manufacturer and a dealer. We assume that one manufacturer has private information about its production cost, while the cost of the other manufacturer is commonly known. The informed manufacturer can share its private information with the rival manufacturer.⁶ After the information exchange (if any), manufacturers decide about the quality they plan to offer to the buyer as well as the cost-reducing investment, whereas the dealer decides about the price to offer to the consumer. Therefore, the offer made to the consumer consists of a price and a quality level. However, before this offer becomes valid, the dealer and the manufacturer negotiate a dealer price. Only if the dealer and the manufacturer find an agreement, the offer made to the buyer is valid; otherwise, the sale opportunity vanishes.⁷

The difference between the regimes of information sharing and no-information sharing occurs because possessing information about the costs of the rival supply chain changes the investment behavior of the manufacturer whose cost is known. Specifically, the information whether the rival has high or low costs induces this manufacturer to choose a higher or lower cost-reducing and utility-enhancing investment. If the rival has high costs, then the final price of its product will be higher. This implies that the manufacturer is in a favorable position compared with the case in which the rival’s costs are low, as it sells to the final consumer with a higher probability. Therefore, an increase in cost-reducing and utility-enhancing investment becomes more profitable. The opposite occurs if the informed manufacturer has low costs.

With information sharing, the investment levels are thus better tailored to the state of the world as the manufacturer invests more when being in a relatively advantaged position. For the manufacturer who possesses private information, this implies that its competitive position is strengthened in case of low costs but weakened in case of high costs. As the profit is larger in the former case, information sharing is always weakly profitable. Moreover, it is strictly profitable if both investment decisions matter. This is because both investments have a complementary effect on the buyer price.

As for the competitive effects, information sharing among manufacturers achieves coordination among investments and is, therefore, weakly procompetitive relative to no-information sharing, that is, it weakly increases consumer surplus compared with the case of no-information sharing. In particular, as explained above, coordination implies that investment of a manufacturer with low cost is particularly high whereas the rival invests less. This implies that the consumer buys with a higher probability from the informed manufacturer if this firm has low costs, which leads to an increase in consumer surplus.

Moreover, information sharing is strictly procompetitive if investments in cost reduction and in quality enhancement are important. The reason is that also from the perspective of the buyer, these investments exhibit complementarity. A larger investment in cost reduction coupled with a larger investment in quality implies that the consumer, when buying from the supply chain with the larger investment, benefits in both dimensions. Instead, if the consumer buys from the supply chain with the lower investments, she loses in both dimensions. Nevertheless, the gain outweighs the loss in expectation because the supply chain with the more significant investments wins the competition for the consumer at an over-proportional level. This nonlinearity implies that the consumer strictly benefits from information sharing between manufacturers.

These effects are also present in the standard model of vertical relations. In particular, also if investment decisions precede the dealers’ setting of the final good price, the uninformed manufacturer invests more in case the informed rival has high costs and less otherwise. However, in contrast to the case above, there is an additional effect of information sharing. As the dealer sets the price to the final consumer only after having negotiated with the manufacturer, it knows the investment decisions of the manufacturer. This does not make a difference in the supply chain of the informed manufacturer.⁸ However, it makes a difference in the supply chain of the uninformed manufacturer.

Specifically, if the dealer of the uninformed manufacturer observes that the investment of its manufacturer was rather small, it infers from this that the costs of the rival supply chain are relatively low. In this case, the dealer knows that it faces a relatively strong competitor and will charge a lower price. By contrast, if the uninformed manufacturer chooses rather high levels of investments, it charges a relatively high price. The reaction of the dealer, therefore, affects the profit of the competing supply chain in the opposite way than the investment decisions of the uninformed manufacturer—that is, if the reaction of the rival manufacturer is beneficial, the reaction of the rival dealer is detrimental for the manufacturer that shares information, and vice versa. On the net, the effect of the price reaction is the dominating force, as this effect directly enters the consumer’s utility and also has a negative effect on the price charged by the dealer of the informed manufacturer. Hence, information sharing is never profitable in the classic model.

Related literature: Our paper primarily relates to the literature on information exchange between firms. Several papers derived conditions for information sharing to be profitable and/or welfare enhancing, depending on whether private information is about costs or demand and whether firms compete in Cournot or Bertrand fashion. For instance, Fried (1984), Gal-Or (1985), and Shapiro (1986) show that information sharing about costs is profitable under very general conditions if firms are Cournot competitors, whereas Gal-Or (1986) and Darrough (1993) observe that effects are ambiguous if firms are Bertrand competitors. Vives (1984, 2006) finds that if firms are instead informed about demand, information sharing under Cournot competition is no longer profitable. Raith (1996) unifies these results and provides relatively general conditions for profitable and welfare-increasing information sharing. Differently from this literature, we study information sharing between supply chains that offer customized products. The message is that information exchanges may help reduce inefficiencies in the market, leading to a procompetitive market outcome.

The analysis also contributes to the literature on information sharing within supply chains (that is, vertical information sharing), given that supply chains compete. This literature studies the difference between linear wholesale contracts and screening contracts (Ha and Tong, 2008), the effects of diseconomies of scale on the incentives and profitability to share information (Ha et al., 2011 and 2017), and the strategic nature of contract disclosure to competing retailers serving the same manufacturer (Bisceglia, 2023).⁹ In contrast to this literature, we consider information sharing with a bottom-up negotiation protocol and note the differences to the classic model of vertical relations.

The paper is also related to a recent literature on firms exchanging information about list prices. Gill and Thanassoulis (2016) develop a model in which manufacturers use list prices as a communication device to achieve upstream cooperation (see also Raskovich, 2007, and Lester et al., 2017). Harrington and Ye (2019) study a model in which (vertically integrated) firms use list prices to signal their independent technologies and find that coordination on list prices can raise transaction prices. In their model, list prices are disclosed directly to buyers.¹⁰  Andreu et al. (2023) study list prices in supply chains. In their model, list prices provide an upper bound for the final-consumer price a dealer can set. They determine conditions so that exchanging information between manufacturers is profitable. In contrast to these papers, we focus on information sharing between manufacturers when list prices are not binding. In addition, we consider a bottom-up negotiation structure and investment incentives.

Finally, our paper contributes to the literature on supply chains and vertical relations. Since Spengler (1950), the canonical model of vertical relationships involves sequential decisions in which the manufacturer makes its decisions before the retailer does.¹¹ In a recent paper, Toxvaerd (2024) shows, in the case of bilateral monopoly, how the timing of decisions and the distribution of market power between an upstream and a downstream firm affects the efficiency of market outcomes. We add to this literature a new way of negotiations in which the wholesale price is negotiated between manufacturer and dealer only after the investment decisions and the final-consumer price are chosen.

The rest of the paper is organized as follows: Section 2 sets out the model. Section 3 presents the solution to the model. Section 4 derives the profitability and competitive effects of information sharing under bottom-up negotiations and in the classic model of vertical relations. Section 5 presents two extensions of the main model. Section 6 discusses different ways how to implement information sharing, and Section 7 concludes. The proofs of the results are in the Appendix.

II. THE MODEL

A. Environment

There are two competing supply chains. Each chain, denoted by |$i=1,2$|⁠, consists of a manufacturer (⁠|${M}_i$|⁠) and a dealer (⁠|${D}_i$|⁠) in an exclusive relationship. Each manufacturer produces a good, which is sold to the dealer who then resells it, in competition with the rival dealer, to the final consumer.

Dealers have no cost when selling the product, apart from paying a dealer price to the manufacturers. Instead, manufacturer |${M}_i$| incurs a production cost of |${c}_i$| for the product. For tractability, we assume that the production cost of |${M}_1$| is uncertain and can either be high (⁠|${c}_1={c}_H$|⁠) or low (⁠|${c}_1={c}_L<{c}_H$|⁠). The probability of low cost is denoted by |$\rho \in \left[0,1\right]$|⁠. Instead, the costs of |${M}_2$| are known and equal to |$c$|⁠, that is, |${c}_2=c$|⁠. Although simplifying the analysis, this assumption reflects the idea that manufacturers may face different costs distributions, with some manufacturers bearing more uncertainty than others—for example, because of their reliance on local raw materials whose price may vary across geographic locations, differences in supply chain complexity, and business practices. We assume that both parties in supply chain |$1$| (that is, manufacturer |${M}_1$| and dealer |${D}_1$|⁠) learn the cost realization |${c}_1$|⁠.¹²

In addition to selling the product to the dealer, the manufacturer can invest, first, to reduce its production cost and, second, to increase the consumer’s utility—for example, by offering customized products that meet the consumer’s needs. The level of cost-reducing investment by |${M}_i$| is denoted by |${k}_i$|⁠, which leads to marginal costs of |${c}_i-{k}_i$|⁠. The cost of such investment is |$\kappa \left({k}_i\right)={k}_i^2/\left(2\kappa \right)$|⁠. The manufacturer’s cost of investment |${z}_i$| to increase consumer utility is denoted by |$\beta \left({z}_i\right)={z}_i^2/\left(2\beta \right)$|⁠. The parameters |$\kappa$| and |$\beta$| represent how costly the respective investment is—for example, if |$\beta \to 0$|⁠, the manufacturer’s investment to enhance consumer utility becomes infinitely costly, which implies that the manufacturer does not invest in equilibrium. At the end of this section, we provide a discussion with several examples for these investments.

We model the demand according to the Hotelling specification. For simplicity, and for interpretation purposes, we assume that there is a single consumer. The consumer is randomly located on a line of length |$1$|⁠. Dealer |${D}_1$| is located at point |$0$| and dealer |${D}_2$| at point |$1$|⁠. The consumer’s location is uniformly distributed on the line. The utility of the consumer when located at |$y$| and buying from |${D}_i$| is the gross utility from buying the good, denoted by |$v$|⁠, plus the extra utility offered by the manufacturer (that is, |${z}_i$|⁠), minus the price denoted by |${p}_i$| and the transport cost |$t\left|y-{y}_i\right|$|⁠, where |${y}_i$| is |${D}_i$|’s location and |$t$| is the transportation cost parameter¹³; hence,

Because |${y}_1=0$| and |${y}_2=1$|⁠, and |${z}_1$| can be different from |${z}_2$|⁠, products are horizontally and vertically differentiated. Dealers do not know the position of the consumer on the line. Before purchasing, the consumer observes the offers made by both dealers, which consist of the prices set by the dealers and the utility-enhancing investment decisions made by the manufacturers. We assume that |$v$| is large enough so that the consumer always chooses to buy from one of the dealers.

We note that the model is equivalent to a standard Hotelling model with a continuum of consumers distributed on the Hotelling line. We just state the model with a single consumer to reflect that for the kind of products we are interested in, the interpretation with a single consumer is perhaps more natural because investment decisions are customer specific.

B. Information Sharing Regimes

We consider two information sharing regimes. The regime where |${M}_1$| does not share information about its costs with |${M}_2$|⁠, and the regime in which |${M}_1$| discloses its cost realization to |${M}_2$|⁠. Following the bulk of literature on information sharing, we assume that |${M}_1$| commits to share information ex ante—that is, before observing its private information.¹⁴

C. Timing of Pricing and Investment Decisions

We consider two different scenarios with respect to the timing of prices and investments. The first represents bottom-up negotiations, whereas the second is the classic model considered in vertical relations. Given its novelty, we first describe the former regime.

1. Bottom-up Negotiations

With bottom-up negotiations, every dealer |${D}_i$| first makes a plan about the consumer price |${p}_i$| to charge and every manufacturer |${M}_i$| plans its cost-reducing investment |${k}_i$| and its utility-enhancing investment |${z}_i$|⁠. After these decisions have been made, both parties in the vertical chain |$i$| (that is, |${M}_i$| and |${D}_i$|⁠) share these planned decisions. |${D}_i$| and |${M}_i$| then negotiate about the dealer price |${r}_i$|⁠, that is, the price that |${D}_i$| pays to |${M}_i$| for the product. In this negotiation, the dealer offers the price with probability |$\alpha \in \left(0,1\right)$| and the manufacturer with probability |$1-\alpha$|⁠. We consider this random-proposer take-it-or-leave-it bargaining structure (instead of, for example, Nash bargaining) to keep the model fully within noncooperative game theory.¹⁵ If the parties reach an agreement, |${D}_i$| can make an offer to the consumer consisting of the decisions |$\left\{{p}_i,{z}_i\right\}$|⁠.¹⁶ If the parties do not reach an agreement, the dealer cannot make a valid offer. The supply chain then forgoes the sales opportunity, where the reservation utilities resulting from the outside options normalized to zero. ¹⁷ Once the consumer has received the offer(s), she decides which of them to accept. The chosen manufacturer and dealer then carry out their respective plans.

The timing of the game is therefore as follows:

• Cost realization and information sharing. |${M}_1$| and |${D}_1$| learn the cost realization |${c}_1$|⁠. In the information-sharing regime, |${M}_1$| informs |${M}_2$| about |${c}_1$|⁠.

• Price and investment decisions. Each dealer |${D}_i$| chooses its planned level of |${p}_i$|⁠, and each |${M}_i$| chooses its planned levels of |${k}_i$| and |${z}_i$|⁠.

• Wholesale negotiation. |${M}_i$| and |${D}_i$| observe their respective planned decisions, but not the decisions in the rival supply chain. Each |${D}_i$| and |${M}_i$| negotiate about |${r}_i$|⁠.

• Consumer choice. The consumer receives an offer, consisting of |$\left\{{p}_i,{z}_i\right\}$|⁠, from |${D}_i$|⁠, if |${D}_i$| and |${M}_i$| reached an agreement, and decides which offer to accept. After acceptance of |${D}_i$|’s offer, |${D}_i$| and |${M}_i$| carry out their planned investment decisions.

In case of information sharing, dealer |${D}_2$| is not informed about the cost of the rival manufacturer when it decides whether to accept or reject the offer; however, because |${D}_2$| observes |${k}_2$| and |${z}_2$| before making its decision, the cost of the rival manufacturer is inferred from these choices—that is, there is no uncertainty at the acceptance stage.

This timing, where |${D}_i$| and |${M}_i$| negotiate only over |${r}_i$| but not over |${z}_i$|⁠, may reflect cases where customization options are predefined by manufacturers—for example, the available customization choices and various variants of a vehicle (like a truck or a bus) are set in advance and cannot be modified on demand. The customization demanded for these products then typically do not involve development of entirely new features but the integration of various optional components, which are usually not compatible by default. Therefore, the main challenge and associated cost arise from ensuring compatibility among these optional features.¹⁸ In the extensions (that is, Section 5.1), we consider a model in which |${D}_i$| and |${M}_i$| negotiate both |${r}_i$| and |${z}_i$|⁠, capturing scenarios where customizations can be accommodated in a short time frame, such as fashion clothing, jewelry, interior design, and so forth. Our conclusions remain the same in both models.

2. Classic Model

In the classic model of vertical relations, each manufacturer first makes investment decisions and proposes a wholesale price. The respective dealer can accept or reject this offer. In case of acceptance, it sets a price to the final consumer who then decides from which dealer to buy.¹⁹

In this scenario, the timing is therefore as follows:

• Cost realization and information sharing. Equivalent to bottom-up negotiations.

• Wholesale price and investment decisions. Each |${M}_i$| chooses |${k}_i$| and |${z}_i$| and offers a wholesale price |${r}_i$|⁠. The dealer |${D}_i$| observes the investment decisions as well as the wholesale price offer and decides whether to accept or reject the offer.

• Consumer price decisions. In case of acceptance, each |${D}_i$| sets the consumer price |${p}_i$|⁠.

• Consumer choice. The consumer receives an offer, consisting of an offer |$\left\{{p}_i,{z}_i\right\}$|⁠, from |${D}_i$| if |${D}_i$| and |${M}_i$| reached an agreement, and decides which offer to accept.

As in the case of bottom-up negotiations, |${D}_2$| observes |${k}_2$| and |${z}_2$| before negotiating the dealer price with |${M}_2$|⁠, which implies that, as above, it can infer the cost of |${M}_1$| from these choices—that is, the negotiation occurs under symmetric information.

It is important to note that there is no hold-up problem in either scenario. First, in the canonical model, the manufacturer has full bargaining power in the negotiation with the dealer. Second, in case of bottom-up negotiations, manufacturers carry out their planned investments only after they negotiated in the wholesale stage and the consumer has decided whether she buys the good from supply chain |$i$|⁠. This is a reasonable assumption for most industries with complex and customer-specific products, as the production of the good only takes place after the customer decided to buy it and an agreement between the dealer and the manufacturer is reached.

D. Solution Concept and Assumptions

Our solution concept is (weak) Perfect Bayesian Nash Equilibrium. To guarantee interior solutions, we make some assumptions on the admissible parameter space. First, we assume that |$t>\min \left\{\left(\kappa +\beta \right)/3,\sqrt{\beta \kappa}/2\right\}$|⁠, which enures that second-order conditions are satisfied. Second, we assume that the difference between manufacturers’ costs is not overly large, so that for either realization of |${c}_1$|⁠, each dealer receives demand with positive probability. The concrete assumption to ensure this is spelled out at the beginning of the Appendix. Finally, we make an assumption to ensure that production costs are (weakly) positive, that is, the cost-reducing investment does not exceed |${c}_i$|⁠. The respective assumption is also given at the beginning of the Appendix.

E. Discussion

Before describing how to solve the game for the equilibrium and present the results, it is helpful to discuss some of the main assumptions of the model.

First, we assume that manufacturers can provide service quality to increase the consumer’s utility. These services are typically customization options (add-ons). Such options have become increasingly important (for example, in the automotive industry) as customers seek to personalize their vehicles to meet their specific needs and preferences, particularly in commercial vehicle manufacturing (for example, trucks, buses, or special vehicles). As a result, automotive manufacturers have started to offer a wide range of customization options, ranging from minor cosmetic changes to major mechanical upgrades, to attract customers. For instance, many commercial vehicle manufacturers nowadays offer their customers the possibility to design their vehicles from scratch or work with a team of engineers to customize an existing model. This allows customers to project vehicles that meet their specific needs and preferences.

This dynamic is also increasingly common in industries like house-building and interior design (for example, bathrooms and kitchens). In the construction and modular housing sectors, especially for commercial or institutional projects, clients often collaborate with manufacturers on the design of prefabricated structures. After the initial design phase, clients work closely with suppliers to source specialized materials and features, with final project pricing negotiated afterward based on custom requirements. Architects and dealers frequently engage in consultations with clients to tailor spaces to their unique lifestyle, functional needs, and budget. This process is followed by negotiations with suppliers of furniture, fixtures, and raw materials to ensure that these custom choices align with cost expectations.

Customization followed by price negotiations is also a growing trend in the fashion industry, particularly among brands offering bespoke or made-to-order options. Once a garment or accessory design is customized to a customer’s preferences, brands collaborate with suppliers to source specific materials, trims, and embellishments that meet these tailored specifications. This collaboration results in a product that is both personalized and priced according to the negotiated costs with suppliers.

Second, we also assume that manufacturers can invest in cost-reducing activities. The use of new technologies, outsourcing, and lean manufacturing are just a few examples of the methods manufacturers use to reduce costs and improve efficiency. Cost-reducing activities may also favor delivery speed. Manufacturers often face the challenge of meeting customer demand for faster delivery times while maintaining profitability. To achieve this, they need to implement cost-saving strategies that help to improve efficiency. There are several strategies that manufacturers can adopt to reduce costs and speed up delivery times, including adjusting of production processes and improving logistics.

Finally, the timing with bottom-up negotiations mirrors the observation that in many industries with complex products, negotiations follow a structure in which the final product price is set before dealer and manufacturer negotiate the dealer price, as explained above. In such markets, negotiations between manufacturers, dealers, and customers are elaborate, as customers often have specific needs and requirements that may not be readily available. Dealers and manufacturers must first understand the customer’s needs to find the right product specification that meets these requirements. Only when the key aspects of the deal, such as product customization, pricing, financing, delivery, and service agreements, are settled, manufacturers and dealers can negotiate an internal price that reflects the commitments of all parties involved in the transaction.

III. EQUILIBRIUM ANALYSIS

In this section, we explain how the model works and how to characterize the equilibrium.

A. Bottom-up Negotiations

We focus on the case of bottom-up negotiations, as this structure is the novel organizational ingredient of our paper. Afterward, we briefly discuss the classic model of vertical relations.

Consider supply chain |$i$|⁠. Let |$\left({p}_i,{z}_i,{k}_i\right)$| be the planned investment choices and pricing decisions made by |${M}_i$| and |${D}_i$|⁠. From the Hotelling formulation, it follows that, for given |$\left({p}_i,{z}_i\right)$| and |$\left({p}_{-i},{z}_{-i}\right)$|⁠, the probability with which the consumer buys from |${D}_i$| is

Therefore, conditional on its information about the rival supply chain, the (expected) profit of |${M}_i$| for given |$\left({p}_i,{z}_i,{k}_i,{r}_i\right)$| is

where |$\left({p}_{-i}^m,{z}_{-i}^m\right)$| denotes |${M}_i$|’s expectation about the rival supply chain’s choices.²⁰ As there is no uncertainty about the costs in supply chain 2, for |${M}_1$| these expectations coincide with the true choices. Instead, in the no-information-sharing regime, |${M}_2$| is not informed about |${c}_1$|⁠, which implies that |$\left({p}_1^m,{z}_1^m\right)$| is indeed an expectation.

Similarly, the (expected) profit of |${D}_i$|⁠, conditional on its information about supply chain |$-i$|⁠, for given |$\left({p}_i,{z}_i,{r}_i\right)$|⁠, is

where |$\left({p}_1^d,{z}_1^d\right)$| denotes |${D}_i$|’s expectation about the rivals’ choices. We note that in supply chain |$1$|⁠, |${M}_1$| and |${D}_1$| are both informed about |$c$|⁠, which implies that their expectation are the same and equal to the choices made in supply chain |$2$|⁠. In the regime without information sharing, the expectations of |${M}_2$| and |${D}_2$| also coincide, but are real expectations (that is, expected values based on the prior). Instead, in case of information sharing, only |${M}_2$| knows the cost of the rival manufacturer but not |${D}_2$|⁠, which implies that their expectations are different.

We now turn to the negotiation between |${D}_i$| and |${M}_i$|⁠. With probability |$\alpha$|⁠, |${D}_i$| makes an offer. To make sure that |${M}_i$| accepts this offer, |${D}_i$| must set |${r}_i$| so that its manufacturer’s participation constraint is met, that is,

At the optimal level of |${r}_i$|⁠, |$(3)$| holds with equality which implies that

This equation shows that the dealer price offered by |${D}_i$| to |${M}_i$| is increasing in |${p}_i$| because of the standard double-marginalization problem. A higher final price reduces demand, which lowers |${M}_i$|’s sales volume. Thus, to compensate the manufacturer’s loss of profit, |${D}_i$| must guarantee |${M}_i$| a higher profit margin by increasing the dealer price. Instead, the effect of |${z}_i$| and |${k}_i$| on the dealer price is not clear. Increasing these variables causes costs for the manufacturer who then needs to be compensated in form of a higher price. At the same time, an increase in |${z}_i$| rises the probability to sell and an increase in |${k}_i$| lowers production costs, which implies that the manufacturer is willing to accept a lower price for its product.

With probability |$1-\alpha$|⁠, it is |${M}_i$| who offers a dealer price to |${D}_i$|⁠. To ensure acceptance of the dealer, |${M}_i$| must set |${r}_i$| such that

which again holds with equality at the optimal offer of |${M}_i$|⁠. Therefore, the resulting dealer price is given by

As the dealer’s only costs are the dealer price, it breaks even if the manufacturer offers a dealer price equal to the planned consumer price.

We now turn to |${D}_i$|’s and |${M}_i$|’s maximization problems in the first stage of the game, starting with the former. From the discussion above, |${D}_i$| only obtains a strictly positive profit when it makes the offer to |${M}_i$|⁠, which occurs with probability |$\alpha$|⁠, as it is held down to its outside option of |$0$| in case |${M}_i$| makes the offer. The latter holds regardless of the level of |${p}_i$| chosen by |${D}_i$|⁠. Therefore, the maximization problem of |${D}_i$| with respect to |${p}_i$| is

where |${z}_i^d$| and |${k}_i^d$| are |${D}_i$|’s expectations, from the first-stage point of view, about |${M}_i$|’s choice of |${z}_i$| and |${k}_i$| (which will be correct in equilibrium) and |${\left({p}_{-i}^m\right)}^d$| and |${\left({z}_{-i}^m\right)}^d$| are |${D}_i$|’s expectations about |${M}_i$|’s expectations regarding the choices in supply chain |$-i$|⁠. Using |${q}_i^d\left(\cdotp \right)\triangleq{q}_i\left({p}_i,{z}_i^d,{p}_{-i}^d,{z}_{-i}^d\right)$|⁠, the first-order condition of |${D}_i$|’s maximization problem with respect to |${p}_i$| is²¹

This condition reflects the following trade-off. First, as is well known, for a given dealer price, by charging a higher final price, |${D}_i$| lowers the sale volume, but increases its profit margin. In addition, the dealer price that |${D}_i$| needs to offer to |${M}_i$| is increasing in |${p}_i$|⁠, which leads to a reduction in |${D}_i$|’s profit.

We next turn to the maximization problem of |${M}_i$|⁠. By the same logic as above, |${M}_i$| obtains a (strictly) positive profit only in case it makes the offer but obtains zero otherwise, regardless of its investment decisions. Therefore, |${M}_i$|’s maximization problem is

where, as before, |${p}_i^m$| is |${M}_i$|’s expectation, from the first-stage point of view, about |${D}_i$|’s choice of |${p}_i$|⁠, and |${\left({p}_{-i}^d\right)}^m$| and |${\left({z}_{-i}^d\right)}^m$| are |${M}_i$|’s expectations about |${D}_i$|’s expectations regarding the choices in the rival supply chain (which will all be correct in equilibrium). Using again the abbreviation |${q}_i^m\left(\cdotp \right)\triangleq{q}_i\left({p}_i^m,{z}_i,{p}_{-i}^m,{z}_{-i}^m\right)$|⁠, the first-order condition of |${M}_i$|’s maximization problem with respect to |${z}_i$| and |${k}_i$| are, respectively,

An increase in |${z}_i$| raises the probability of selling the product, which is represented by the first term, but also increases the investment cost for |${M}_i$|⁠, which is represented by the second term. The first-order condition with respect to |${k}_i$| involves a similar trade-off: an investment in marginal cost reduction allows |${M}_i$| to obtain a higher profit for each unit it sells but leads to higher investment costs. As for the choice of |${z}_i$|⁠, the profit increase is the smaller, the more attractive the product of the rival.

B. Classic Model

In the standard model of vertical relations, |${D}_i$| chooses |${p}_i$| in the second stage, given that is has accepted |${M}_i$|’s offer. Its maximization problem is then given by |$(2)$|⁠, leading to a standard first-order condition of

Denoting the solution to this first-order condition by |${p}_i={p}_i^{cl}$|⁠, where the superscript |$cl$| stands for classic, the maximization problem of |${M}_i$| in the first stage is

The resulting first-order conditions are

for |${r}_i$|⁠,

for |${z}_i$| and |$(9)$| for |${k}_i$|⁠.

The main difference in the conditions |$(11)$| and |$(12)$| to their respective counterparts for bottom-up negotiations is that the choices made by the manufacturer in the first stage also have an effect on the downstream price charged by the dealer, which is expressed through |$\partial{p}_i^{cl}\left(\cdotp \right)/\partial{r}_i$| and |$\partial{p}_i^{cl}\left(\cdotp \right)/\partial{z}_i$|⁠, respectively, whereas this is not possible with bottom-up negotiations, as the dealer’s and the manufacturer’s decisions are made at the same time in the latter scenario.

The above first-order conditions are helpful because they allow us to generally characterize the equilibrium in each scenario and information-sharing regime. We provide the respective solutions in the Appendix.

IV. PROFITABILITY AND COMPETITIVE EFFECTS OF INFORMATION SHARING

After having explained how to solve for the equilibrium in each scenario, we can now answer the questions whether information sharing is profitable and whether it increases or lowers consumer surplus. We start with the scenario of bottom-up negotiations.

A. Bottom-up Negotiations

The difference between the regimes of information sharing and no-information sharing occurs because possessing information about the costs in supply chain |$1$| changes the investment behavior of |${M}_2$|⁠. Specifically, the information whether the rival manufacturer has high or low costs induces |${M}_2$| to choose a higher or lower cost-reducing investment and utility-enhancing investment. If |${M}_1$| has high costs, then the price of supply chain |$1$| to the consumers will be higher. This implies that supply chain |$2$| is in a favorable position compared with the case in which the costs of |${M}_1$| are low. In particular, it sells to the final consumer with a higher probability. The consequence is that an increase in cost-reducing and utility-enhancing investment becomes more profitable. The opposite occurs if |${M}_1$|’s costs are low.

As we show in the proof of Proposition 1, in expectation, the investment of |${M}_2$| is the same as in the case of no-information sharing.²² However, the investment levels are better tailored to the state of the world as |${M}_2$| invests more when being in a relatively advantaged position. For |${M}_1$|⁠, this implies that its rival invests the same amount in expectation. However, without information sharing, the investment levels are the same regardless of whether |${M}_1$| has high or low costs. Instead, with information sharing, |${M}_1$|’s competitive position is strengthened in case of low costs but weakened in case of high costs.

The previous argument implies that |${M}_1$| benefits from information sharing if it turns out to have low costs, but looses if it has high costs. As the profit is larger in the former case compared with the latter, it follows that:

Proposition 1.  Under bottom-up negotiations, information sharing is always weakly profitable for  |${M}_1$|  and it is strictly profitable if both investment decision matter, that is, if both  |$\beta$|  and  |$\kappa$|  do not go to zero.

The intuition is as follows: Both the quality-enhancing and the cost-reducing investment have an effect on the buyer price. The quality-enhancing investment allows the dealer to charge a higher price, whereas the cost-reducing investment lowers production cost directly, which leads to a lower buyer price. Although the expected cost-reducing investment is the same in the two regimes, the fact that the cost-reducing investment is better tailored to the state of the world in the regime with information sharing affects both a supply chain’s profit margin and the probability that the consumer buys from the supply chain. The manufacturer can couple this effect with an adjustment of the utility-enhancing investment to increase its profits.

Specifically, |${M}_i$| benefits most from a reduction in the rival’s investment if it has low costs, as the mark-up in the supply chain and the probability to win the consumer is then particularly large. This implies that the profit to be shared between |${M}_i$| and |${D}_i$| is also relatively high. To the contrary, |${M}_i$| is hurt by an increase in the rival’s investment to a relatively small extent if it has high costs, as the mark-up and the probability to win the consumer is then relatively small. As a consequence, the two opposing effects enter |${M}_i$|’s expected profit nonlinearly, with the benefit outweighing the costs. As a consequence, there is a complementarity between the two investment decisions when it comes to information sharing, and this complementarity implies that sharing information is strictly profitable.

We next turn to the competitive effects. As information sharing among manufacturers achieves coordination among investments, the following holds:

Proposition 2.  Under bottom-up negotiations, information sharing is always weakly procompetitive relative to no-information sharing and it strictly benefits the consumer if investment in cost reduction and in quality enhancement are important.

As explained above, coordination implies that the investments of a manufacturer with low cost are particularly high, whereas the rival invests less then. This implies that the consumer buys with a higher probability from |${M}_1$| in case |${M}_1$| has low costs, which can lead to an increase in consumer surplus.

However, because the expected equilibrium price and investments are the same in both regimes, it is not clear whether information sharing among manufacturers strictly improves consumer surplus. We again obtain the result that information sharing is strictly procompetitive if investments in cost reduction and in quality enhancement are important. The reason is that, also from the perspective of the buyer, these investments exhibit a complementarity. A larger investment in cost reduction coupled with a larger investment in quality implies that the consumer, when buying from the supply chain with the larger investment, benefits in both dimensions. Instead, if the consumer buys from the supply chain with the lower investments, she loses in both dimensions. Nevertheless, the gain outweighs the loss in expectation because the supply chain with the more significant investments wins the competition for the consumer at an over-proportional level. In particular, as the winning supply chain is the one that lower costs with a high probability, the consumer faces a lower price and a higher quality when buying from this chain. The consumer buys from the other chain only if her preference for that product is particularly high (that is, if her location on the Hotelling line is very close to this product).²³ Therefore, in case of information sharing, the consumer buys more often from the firm that offers the lower price and that has invested more in cost reduction and quality improvements. This complementarity of investments implies that the consumer strictly benefits from information sharing between manufacturers.

B. Classic Model

The effects of information sharing on investments described with bottom-up negotiations are also present in the standard model of vertical relations. In particular, also if investment decisions precede the dealers’ setting of the final good price, |${M}_2$| will invest more if |${M}_1$| has high costs and less if |${M}_1$| has low costs.

However, in contrast to the case above, there is an additional effect of information sharing in the classic model. As the dealer sets the price to the final consumer only after having negotiated with the manufacturer, it knows the investment decisions of the manufacturer. This does not make a difference in supply chain 1. As |${D}_1$| knows |${M}_1$|’s costs, it anticipates |${M}_1$| investment decisions correctly. However, it makes a difference in supply chain 2. In case of information sharing, |${M}_2$| tailors its investments to the state of the world, and because |${D}_2$| can observe |${M}_2$|’s investment, it will also react with a different consumer price.

Specifically, if |${D}_2$| observes that |${M}_2$|’s investment was rather small, it infers from this that the cost of the rival supply chain is relatively low. In this case, |${D}_2$| knows that it faces a relatively strong competitor. As prices are strategic complements, |${D}_2$| is therefore inclined to charge a lower price. By contrast, if |${M}_2$| chooses rather high levels of investments, |${D}_2$| knows that it faces a weaker competitor and charges a relatively high price.

The reaction of |${D}_2$| therefore affects the profit of supply chain 1 in the opposite way than the investment decisions of |${M}_2$|⁠. In particular, if |${M}_1$|’s cost are low and profits in supply chain 1 are therefore rather high, information sharing amplifies this higher profit through the choices of |${M}_2$|—that is, |${M}_2$| chooses smaller levels of investment—but diminishes this higher profit through the price decision taken by |${D}_2$|—that is, |${D}_2$| sets a lower price. The opposite result occurs if |${M}_1$|’s cost are high and information is shared.

From the discussion above, the reaction of |${M}_2$| to information sharing is therefore beneficial for |${M}_1$|⁠, whereas the reaction of |${D}_2$| is detrimental for |${M}_1$|⁠. As we show in the Appendix, the effect of the price reaction is dominating, as this effect directly enters the consumer’s utility and also has a negative effect on the price charged by |${D}_1$|⁠. We therefore obtain the following:

Proposition 3.  In the classic model of vertical relations, information sharing is not profitable.

Notice that this does also not depend on the importance of the investments, as the price effect is stronger.

V. EXTENSIONS

A. Negotiation over Quality Investment

In the main model, we consider the case in which the negotiation between manufacturer and dealer only occurs over the wholesale price. Instead, the planned quality-enhancing and cost-reducing investment decisions of the manufacturer and the planned consumer price decision of the dealer are made upfront. As mentioned above, this structure reflects the idea that potential product components are already developed, which implies that the manufacturer’s cost arise from combining the different features.

However, another reasonable structure is one in which the quality of the product is also negotiated between the dealer and the manufacturer, in addition to the wholesale price. This scenario reflects a structure where new product features can be accommodated in a short time frame and can therefore be negotiated by the firms. In such a scenario, the first offer of the dealer to the consumer consists only of the price. Afterward, the dealer verifies this offer in the negotiation with the manufacturer and then informs the consumer about the quality it can offer. This implies that the manufacturer only makes the cost-reducing investment upfront.

In the latter scenario, the timing of the game is as follows:

• Cost realization and information sharing. Equivalent to main model.

• Price and investment decisions. Each dealer |${D}_i$| chooses its planned price level of |${p}_i$|⁠, and each |${M}_i$| chooses its planned level of |${k}_i$|⁠.

• Wholesale negotiation. |${M}_i$| and |${D}_i$| observe their respective planned decisions, but not the decisions in the rival supply chain. Each |${D}_i$| and |${M}_i$| negotiate about |${r}_i$| and |${z}_i$|⁠.

• Consumer choice. Equivalent to main model.

We can analyze this scenario in a similar way as in Section 3. In the negotiation stage, if |${D}_i$| makes an offer, it still offers a wholesale price as in |$(4)$| to ensure that |${M}_i$| accepts its offer. In contrast to the main model, however, |${z}_i$| is not decided before the negotiation. Instead, |${D}_i$| includes |${z}_i$| in its negotiation and chooses it to maximize

In the first stage, |${D}_i$| then maximizes its profit over |${p}_i$| as in |$(6)$|⁠. In case |${M}_i$| makes the offer in the negotiation stage, the timing is adjusted accordingly.

Solving this model, we obtain that the resulting decisions are nevertheless the same as in the main model, which leads to the following result:

Proposition 4.  If the investment in product quality is included in the negotiation between  |${M}_i$|  and  |${D}_i$|, the same results as in Propositions 1 and 2 occur, that is, information sharing is always weakly profitable for  |${M}_1$|  and procompetitive, and strictly so if investment in cost reduction and in quality enhancement are important.

The intuition behind this result is as follows: If |${M}_i$| is the proposer in the negotiation, it chooses an investment in product quality to maximize its profit, given that |${D}_i$| accepts the offer. As it ensures acceptance of |${D}_i$| through the appropriate wholesale price offer, as in the main model, its maximization problem with respect to |${z}_i$| is the same as in the main model. The only difference is that in the main model, |${M}_i$| chooses |${z}_i$| before the negotiation whereas in the extension, it does so in the negotiation. However, because this does not change the maximization problem, the outcomes are the same.

Instead, if |${D}_i$| is the proposer in the negotiation, it now also makes an offer about |${z}_i$|⁠. To ensure acceptance of |${M}_i$|⁠, it chooses its offer about the wholesale price accordingly, that is, |${r}_i$| is set so that |${M}_i$| breaks even. However, when maximizing about |${z}_i$|⁠, |${D}_i$| takes into account that it needs to adjust |${r}_i$| as well to induce |${M}_i$| to accept. The optimal adjustment follows the same objective as that of |${M}_i$| when maximizing over |${z}_i$|⁠. Therefore, at the optimal offer, the incentives of |${M}_i$| and |${D}_i$| in their choice about |${z}_i$| are aligned, which implies that they choose the same |${z}_i$|⁠.

As a consequence, the outcome with respect to |${z}_i$| is the same regardless whether |${M}_i$| or |${D}_i$| makes the offer and equal to the one of the main model. Therefore, also the result with respect to information sharing is the same.

B. Reverse Bargaining Structure of the Classic Model

In our main model, we denoted the bargaining structure in which the dealer first plans a price for the final consumer and afterward negotiates the dealer price with the manufacturer as bottom-up negotiations. It involves simultaneous (planned) choices of the consumer price and the investment levels of the manufacturer. Instead, in the classic model in which the manufacturer proposes a dealer price, the investment levels and the dealer price are chosen before the dealer sets a final-consumer price.

In this section, we now consider a different move order that can be seen as the natural counterpart to the classic framework where the dealer has the bargaining power at the wholesale stage and chooses the consumer price and the dealer price before the manufacturer makes investment decisions.

Specifically, we consider the following timing:

• Cost realization and information sharing. Equivalent to the main model.

• Consumer price and wholesale price decisions. Each |${D}_i$| sets the consumer price |${p}_i$| and offers a wholesale price |${r}_i$|⁠. The manufacturer |${M}_i$| observes the consumer price as well as the wholesale price offer and decides whether to accept or reject the offer.

• Investment decisions. Each |${M}_i$| chooses |${k}_i$| and |${z}_i$|⁠.

• Consumer choice. The consumer receives an offer|$\left\{{p}_i,{z}_i\right\}$| if |${D}_i$| and |${M}_i$| reached an agreement and decides which offer to accept.

In contrast to the classic model in which upstream firms have bargaining power at the wholesale stage, in this timing the bargaining power is in the hand of the dealer. In addition, this firm acts as a first mover in setting the consumer price and the manufacturer decides about its investments only later on. With this timing, we obtain the following result:

Proposition 5.  If the dealer chooses consumer and wholesale prices before the manufacturer makes investment decisions, information sharing is neutral.

The proposition states that the outcome and the profits in this scenario are the same regardless of whether information sharing takes place or not. In fact, as we show in the Appendix, if the dealer makes the pricing decisions before the manufacturer makes investment decisions, the optimal prices set by the dealer are such that there is no margin left for the manufacturer, regardless of whether the manufacturer knows the cost of the rival supply chain or not. This implies that the manufacturer will not invest in cost reduction or quality improvements. Therefore, information sharing has no effect.

The intuition behind the pricing decision of the dealer is as follows: To induce the manufacturer to invest, the dealer needs to offer a wholesale price that is above the manufacturer’s marginal costs. As the dealer also needs to set the consumer price above the wholesale price to obtain positive profits, this involves double marginalization. Therefore, when raising the wholesale price, the dealer faces the trade-off of reducing its own margin and increasing demand through the increased quality investment of the manufacturer.

However, the margin of the dealer is the consumer price minus the wholesale price. If the dealer lowers both prices by one unit, its margin is unchanged, but its demand raises as the final-consumer price is lower. As an increase in product quality raises demand by the same amount as a reduction in the consumer price, the dealer is strictly better off by lowering both prices by the same amount as compared with inducing investment of the manufacturer. Therefore, the optimal pricing policy of the dealer always involves a wholesale price equal to the level of the manufacturer’s marginal costs, which implies that the manufacturer makes no investment.

C. Practical Relevance

In light of the above results, in this section, we discuss informally how supply chains can achieve information exchange with the help of list prices and how the information sharing regime studied above can be interpreted in such an environment.

On a general level, to be effective, information-sharing agreements require some degree of coordination between their members (see, for example, Ziv, 1993). Most of the existing models assume that firms can commit to reveal their private information to rivals. The implicit hypothesis is that these agreements are organized by certification intermediaries—for example, auditors, data analytic companies, marketing information services firms, trade associations, and so forth—who own the technology to discover the private information of the participants to the agreement and can commit to disclosure rules that disseminate this knowledge among them (see, for example, also Lizzeri, 1999). Manufacturers can then freely exchange their cost information without specifying the communication protocol or the “language” through which this information is shared.

In the real world, however, firms do not communicate through a vague “word of mouth” process, but signal their private information to rivals through other variables that de facto form the language through which firms communicate. List prices often play this information role because dealers can set buyer prices that are different from the list prices, which implies that the latter do not matter for the buyers’ decisions—that is, the effective prices paid by the buyers are usually substantially lower than the list prices. Hence, list prices are nondistortionary and manufacturers can share their cost information by announcing list prices tailored to their private information. In this respect, list prices can serve the role of variables for information exchange between manufacturers. In the case of complex and highly personalized products, for example, list prices may, indeed, mirror information about the costs of each add-on or product characteristic and, therefore, their exchange allows competing supply chains to anticipate rival prices and investments in a better way.

If manufacturers have a good estimate about their own cost,²⁴ as is the case in our model, list price setting occurs individually. A manufacturer then informs the dealer of its own brand about the cost realization through the list price and also has the possibility to share the independently set list price with the other manufacturer.

However, if manufacturers’ costs have a common element and a manufacturer may lack a good estimate about these elements, setting the list price individually would miss out some information. The list price can then be improved by setting it jointly (that is, at an industry meeting). This ensures that the information of all manufacturers is taken into account. By a similar mechanism as in our model, the investment decisions of manufacturers are then coordinated in a better way, which can have a profitable and procompetitive effect.

We finally note that the procompetitive effect of information sharing that we identified in the paper is not only present in a one-period model of competition between supply chains but also with repeated interaction. However, in an infinitely repeated game, additional effects may arise. For instance, information sharing might facilitate collusion between firms.²⁵ However, this is not a necessary outcome and depends on the specific situation, particularly on whether the mechanism by which information is shared has a binding element for final prices.

First of all, it is ex ante not clear why an exchange of information would foster collusion as firms may also achieve collusion without sharing information if they are patient enough (for example, Tirole, 1988). Recently, some ideas were developed why the setting of list prices to achieve information sharing can make it easier for firms to achieve a collusive outcome.

For instance, Boshoff and Paha (2021) argue that list prices can serve as a focal or reference point from which firms find it more difficult to deviate. Harrington (2024) analyzes a model in which he explicitly considers the different hierarchy levels in a firm. He shows that upper-level executives prefer collusion through price setting of lower-level employees to preserve the advantages of price discrimination rather than setting prices themselves. List prices might be a way to achieve this by providing lower-level employees with the right information.²⁶

However, there is considerable evidence, both from laboratory experiments as well as from field experiments, that the argument that list price setting and information sharing facilitates collusion does not hold. For instance, Davis and Holt (1988) consider a laboratory experiment in which subjects can set list prices and exchange information. In the first treatment, the set list prices are binding, whereas in the second treatment, they are not. They find that prices are at supracompetitive levels only in the first treatment but are down to competitive levels very soon on the second treatment. List and Price (2005) also find strong support for this effect in a field experiment. Therefore, the argument that information sharing can facilitate collusion should be taken with care. In particular, it only holds under the condition that list prices are binding to a sufficiently large extent, which is usually not fulfilled.

VI. CONCLUSION

This paper studies a model of supply chain competition in which one manufacturer’s costs are uncertain and private information within the supply chains. In contrast to previous literature, we study bottom-up negotiations, where each supply chain—through the dealer—first makes an offer consisting of a price and a quality level to the consumer, and dealer and manufacturer negotiate the dealer price only thereafter. This model fits well with several markets in which complex and customer-specific products are offered, and bargaining between the involved parties works in a different way than often assumed in the literature on vertical market relations.

We use the model to study the profitability and the competitive effects of information sharing between manufacturers. In our framework, we identify a novel effect of such information sharing. The exchange of cost information allows manufacturers to tailor investment decisions to the state of the world, which renders these decisions more efficient.

We show that with bottom-up negotiations, information sharing is profitable and procompetitive. In particular, a complementarity between cost-reducing and quality-enhancing investment exists, which implies that information sharing enhances efficiency and is beneficial for all parties.

In contrast, in the classic model of vertical relations, an exchange of information is unprofitable. This result occurs because not only the rival manufacturer reacts to the information but also the dealer, which changes the competitive conditions between supply chains. As the dealer behaves more aggressively if costs are low but less aggressively if costs are high, it counters the behavior of the manufacturer. We show that this effect dominates and renders information sharing unprofitable.

Footnotes

References

APPENDIX

Before showing our results, we spell out the assumptions on costs under which our analysis is valid. First, to ensure that differences between costs are sufficiently small, so that each dealer receives demand with positive probability in all regimes, we assume

and

with |$E\left[c\right]=\rho{c}_L+\left(1-\rho \right){c}_H$|⁠. Second, the cost-reducing investment does not exceed |${c}_i$|⁠, which implies that production costs are positive, if

Proof of Proposition 1. 

We start with the scenario without information sharing. The first-order condition of |${D}_1$| with respect to |${p}_1$| is given by |$(7)$| and can be written as

Similarly, the first-order conditions for |${M}_1$| with respect to |${z}_1$| and |${k}_1$| are given by |$(8)$| and |$(9)$|⁠, respectively, and can be written as

and

For supply chain 2, the first-order condition of |${D}_2$| with respect to |${p}_2$| is

and the first-order conditions of |${M}_2$| with respect to |${z}_2$| and |${k}_2$| are

and

Determining the second-order conditions, we obtain that all maximization problems are strictly concave if |$2t>\sqrt{\kappa \beta}$|⁠, which is fulfilled by our assumptions.

Solving the three first-order conditions for supply chain 1 for |${p}_1\left({c}_1\right)$|⁠, |${z}_1\left({c}_1\right)$|⁠, and |${k}_1\left({c}_1\right)$|⁠, we obtain

and

where we dropped the argument |$c$| in the variables |${p}_2$|⁠, |${z}_2$|⁠, and |${k}_2$|⁠. Similarly, solving the three first-order conditions for supply chain 2, we obtain

and

where, as in equilibrium expectations are correct, |${p}_1^e=\rho p\left({c}_L\right)+\left(1-\rho \right)p\left({c}_H\right)$|⁠, |${z}_1^e=\rho z\left({c}_L\right)+\left(1-\rho \right)z\left({c}_H\right)$|⁠, and |${k}_1^e=\rho k\left({c}_L\right)+\left(1-\rho \right)k\left({c}_H\right)$|⁠. Equations |$(16)$|–|$(21)$| provide us with a system of nine equations for nine unknowns—that is, |${p}_1\left({c}_L\right)$|⁠, |${z}_1\left({c}_L\right)$|⁠, |${k}_1\left({c}_L\right)$|⁠, |${p}_1\left({c}_H\right)$|⁠, |${z}_1\left({c}_H\right)$|⁠, |${k}_1\left({c}_H\right)$|⁠, |${p}_2(c)$|⁠, |${z}_2(c)$|⁠, and |${k}_2(L)$|—which can be solved to get the equilibrium values. They are given by

and

for the two prices set by |${D}_1$| in the two states of the world, by

and

for the different investment levels of |${M}_1$| in case |${c}_1={c}_L$|⁠, by

and

for the different investment levels if |${c}_1={c}_H$|⁠,²⁷ and by

by the respective variables for |${D}_2$| and |${M}_2$|⁠.

From these variables, we can determine the expected profit of |${M}_1$|⁠. Given that |${M}_1$|’s cost is |${c}_1\in \left\{{c}_L,{c}_H\right\}$|⁠, its profit is given by

where |${r}_i^m$| is given by |$(5)$|⁠.²⁸ Inserting the respective values and noting that the expected profit is |$\rho{\varPi}_1\left({c}_L\right)+\left(1-\rho \right){\varPi}_1\left({c}_H\right)$|⁠, we obtain, after simplifying, that the expected profit of |${M}_1$| in case of no-information sharing is

We next turn to the regime with information sharing. This does not affect the first-order conditions of |${M}_1$| and |${D}_1$|—that is, they have the same structure as above. Instead, this is different for |${D}_2$| and |${M}_2$|⁠. Particularly, for |${D}_2$|⁠, the first-order condition can now be written as

because |${D}_2$| is not informed about the cost of |${M}_1$| when setting |${p}_2$|⁠. Instead, |${M}_2$| is informed about |${M}_1$|’s cost realization. In addition, at the negotiation stage (that is, |$t=2$|⁠), |${D}_2$| and |${M}_2$| are informed about the intended decisions. This implies that there is no uncertainty left in the maximization of |${M}_2$|⁠. The first-order conditions |$(8)$| and |$(9)$| can then be written as

and

for |${c}_1\in \left\{{c}_L,{c}_H\right\}$|⁠. Overall, these first-order conditions constitute a system of eleven equations for eleven unknowns. Specifically, |${M}_1$| and |${M}_2$| each make two investment decisions and condition them in the state of the world, which are overall eight investment variables. In addition, |${D}_1$| sets its price also conditional on the state of the world, whereas |${D}_2$| only chooses one price. Therefore, there are in sum three decisions of the dealers. Solving this system, we obtain that the prices of |${D}_1$| are given by

and

and the price of |${D}_2$| by

The different investment levels of |${M}_1$| in case |${c}_1={c}_L$| are²⁹

and

and those in case |${c}_1={c}_H$| are

and

The investment levels of |${M}_2$| are

and

in case |${c}_1={c}_L$|⁠, and

and

in case |${c}_1={c}_H$|⁠. Using |$\alpha{c}_L+\left(1-\alpha \right){c}_H=E\left[{c}_1\right]$|⁠, it is easy to check that |$\alpha{z}_2^I\left({c}_L\right)+\left(1-\alpha \right){z}_2^I\left({c}_H\right)={z}_2^N$| and |$\alpha{k}_2^I\left({c}_L\right)+\left(1-\alpha \right){k}_2^I\left({c}_H\right)={k}_2^N$|⁠, that is, the average investment of |${M}_2$| in case of information sharing is the same as |${M}_2$|’s investment without information sharing.

Following the same procedure as in the case of no-information sharing, we can determine the expected profit of |${M}_1$| to get

where |$\mu \equiv \left(3t-\beta -\kappa \right){\left(\left(2t-\beta \right)\left(2t-\kappa \right)+4{t}^2\right)}^2$|⁠.

Comparing the expected profits with each other by subtracting the profit without information sharing from the profit with information sharing between manufacturers yields

which—due to the fact that all terms in parentheses are strictly positive for |$3t-\psi -\beta -\kappa >0$|—is strictly positive if |$\beta >0$| and |$\kappa >0$|⁠. |$\blacksquare$|

Proof of Proposition 2 

We start again with the regime of no-information sharing. Suppose first that |${M}_1$| who has low costs. Then, |${D}_1$| and |${M}_1$| set |${p}_1^N\left({c}_L\right)$| and |${z}_1^N\left({c}_L\right)$|⁠, whereas |${D}_2$| and |${M}_2$| set |${p}_2^N$| and |${z}_2^N$|⁠, as determined above. The marginal consumer is located at |${x}_m=1/2+\left({p}_2^N-{p}_1^N\left({c}_L\right)-{z}_2^N+{z}_1^N\left({c}_L\right)\right)/2$|⁠. Inserting the respective values, we obtain

If the location of the consumer is between 0 and |${x}_m$|⁠, she buys from |${D}_1$|⁠, whereas she buys from |${D}_2$| if her location is between |${x}_m$| and 1. The consumer surplus is then given by

where |${x}_m\left({c}_L\right)$| is given by |$(25)$| and the respective prices and investment values are stated above.

In case |${c}_1={c}_H$|⁠, the relevant prices and investment values to determine the consumer surplus are |${p}_1^N\left({c}_H\right)$|⁠, |${z}_1^N\left({c}_H\right)$|⁠, |${p}_2^N$|⁠, and |${z}_2^N$|⁠, where these values are again shown above. The resulting consumer surplus is

where |${x}_m\left({c}_H\right)$| is given by

The expected consumer surplus in case of no-information sharing is then |$\rho C{S}_{c_L}^N+\left(1-\rho \right)C{S}_{c_H}^N$|⁠.

We can proceed in the same for the case of information sharing. If |${c}_1={c}_L$|⁠, then consumer surplus is given

with

where the respective price and investment choices (that is, |${p}_1^I\left({c}_L\right)$|⁠, |${p}_2^I$|⁠, |${z}_1^I\left({c}_L\right)$|⁠, and |${z}_2^I\left({c}_L\right)$|⁠) are given above. Similarly, for |${c}_1={c}_H$|⁠, consumer surplus is

with

The expected consumer surplus is |$\rho C{S}_{c_L}^I+\left(1-\rho \right)C{S}_{c_H}^I$|⁠.

Subtracting the expected consumer surplus without information sharing from that with information sharing, that is, |$\left(\rho C{S}_{c_L}^I+\left(1-\rho \right)C{S}_{c_H}^I\right)-\left(\rho C{S}_{c_L}^N+\left(1-\rho \right)C{S}_{c_H}^N\right)$|⁠, we obtain

which is strictly positive for all |$\beta >0$|⁠, |$\kappa >0$|⁠, and |$3t-\beta -\kappa >0$|⁠. |$\blacksquare$|

Proof of Proposition 3 

We can proceed in the same way as in the case of bottom-up negotiations, that is, using the first-order conditions explained in Section 3 to determine the equilibrium dealer and wholesale price as well as the investment decisions, and then insert them into the expected profit of the manufacturer. Doing so, we obtain that the difference between the expected profit with information to that without information sharing is given by

where the inequality is again due to the assumption that |$3t-\beta -\kappa >0$|⁠. |$\blacksquare$|

Proof of Proposition 4 

In the timing in which |${z}_i$| is part of the negotiation, the final-consumer price |${p}_i$| is still chosen by |${D}_i$| and the cost-reducing investment |${k}_i$| is still chosen by |${M}_i$|⁠, regardless of which firm makes the offer in the negotiation. Therefore, these variables are still chosen as in |$(7)$| and |$(9)$|⁠.

Suppose that |${M}_i$| proposes the contract (which consists of |${r}_i$| and |${z}_i$|⁠). In the same way as in the main model, |${M}_i$| will set |${r}_i^m={p}_i$| to obtain the entire surplus in the negotiation. As |${M}_i$| maximizes its profit and |${p}_i$| and |${k}_i$| are already decided, the first-order condition is still given by |$(8)$|⁠, which implies that the choice of |${M}_i$| with respect to |${z}_i$| is the same as in the main model.

If |${D}_i$| proposes the contract, it will set |${r}_i^d$| as in the main model to ensure that |${M}_i$| accepts the offer. It then maximizes |$(6)$| with respect to |${z}_i$|⁠. This yields a first-order condition of

Inserting

into |$(26)$| and simplifying, we obtain

Using |$(9)$| and inserting |${r}_i^m={p}_i$|⁠, |$\partial{q}_i^m\left(\cdotp \right)/\partial{z}_i=1/(2t)$|⁠, and |${\beta}^{\prime}\left({z}_i\right)={z}_i/\beta$| also yields |$(27)$|⁠. Therefore, the optimal choice of |${z}_i$| is the same, regardless of whether |${D}_i$| and |${M}_i$| makes the offer of the wholesale contract. As this holds independent of the information-sharing regime and because all other variables are then also chosen in the same way as in the main model, the profits are the same as in the main model. Therefore, the result with respect to information sharing is also the same as in the main model. |$\blacksquare$|

Proof of Proposition 5 

Using backward induction, we start in the second stage by determining the optimal investment of |${M}_i$|⁠. Because the demand function is |$\left({z}_i-{p}_i-E\left[{z}_{-i}\right]+E\left[{p}_{-i}\right]\right)/(2t)$|⁠, the profit of |${M}_i$| is, following the discussion in Section 3,

Maximizing |$(28)$| with respect to |${z}_i$| and |${k}_i$| and checking whether the profit function is concave, we obtain |${\partial}^2{\varPi}_i/\partial{\left({z}_i\right)}^2=-1/\beta$|⁠, |${\partial}^2{\varPi}_i/\partial{\left({k}_i\right)}^2=-1/\kappa$|⁠, and

Therefore, the latter is strictly positive if |$t>\sqrt{\beta \kappa}/2$|⁠, which is fulfilled by assumption. It follows that the Hessian is negative definite, which implies that the profit function is concave. Solving the first-order conditions, we obtain

Tuning to the first stage, from Section 3, the profit function of the dealer is

We can insert |${z}_i\left({c}_i\right)$| from |$(29)$| and then check whether the right-hand side of |$(30)$| is concave in |${p}_i$| and |${r}_i$|⁠. This yields |${\partial}^2{\pi}_i/\partial{\left({p}_i\right)}^2=-4t/\left(4{t}^2-\beta \kappa \right)<0$|⁠, |${\partial}^2{\pi}_i/\partial{\left({r}_i\right)}^2=-2\beta /\left(4{t}^2-\beta \kappa \right)<0$|⁠, and

Therefore, the Hessian is indefinite and the two first-order conditions describe a saddle point. The maximum is therefore at an extremal value. Setting |${p}_i$| and/or |${r}_i$| at very high levels can never be optimal for |${D}_i$| as it would lead to zero profits due to the fact that that either demand or the margin becomes zero (the latter, if |${r}_i$| equals |${p}_i$|⁠). Instead, setting |${r}_i$| at the lowest possible level to still guarantee supply from the manufacturer, that is, |${r}_i={c}_i$|⁠, whereby |${c}_i\in \left\{{c}_L,{c}_H\right\}$|⁠, and setting |${p}_i$| according to the resulting first-order condition—that is, |${p}_i=\left({c}_i+t+E\left[{p}_{-i}\right]-E\left[{z}_{-i}\right]\right)/2$|—give the highest profit for |${D}_i$|⁠. As this result does not depend on the information-sharing regime, it holds regardless of whether |${M}_i$| is informed about |${c}_{-i}$| or not. Because |${M}_i$| does not invest in |${z}_i$| and |${k}_i$| in equilibrium in either regime, information sharing is neutral.

Author notes