Production, Manufacturing, Transportation and Logistics
The effect of information asymmetry on ordering and capacity decisions in supply chains

https://doi.org/10.1016/j.ejor.2020.11.004Get rights and content

Highlights

  • Asymmetric information can result in an increased capacity level in the market.

  • Asymmetric information can increase consumer welfare.

  • A retailer may prefer to conceal information by adopting a pooling equilibrium.

  • A supplier always prefers a separating equilibrium.

  • The separating quantity increases with the information gap.

Abstract

We revisit the problem of contracting under asymmetric information in a supply chain and highlight a few important properties that have not been reported previously. In our setting, a newsvendor retailer is endowed with superior information about the demand; the retailer may signal this information to the supplier by committing to purchasing a certain quantity in advance. Previous research has focused on characterizing the minimum quantity that convinces the supplier that demand is high. In this work, we claim that in some cases, the retailer prefers to order an even greater quantity than this minimum separating quantity, since committing to an advance purchase can result in incentives for the retailer to finance the entire capacity in the market—a choice that the retailer may not adopt absent information asymmetry. Such an outcome carries important implications regarding the efficiency of the supply chain and consumer welfare. In particular, our analysis shows that asymmetric information can result in a higher capacity in the market than the complete-information case; thus, asymmetric information can mitigate the double-marginalization problem and result in higher consumer welfare. We further conduct a comparison between the incentives of the retailer to signal the demand state to the supplier (resulting in a separating equilibrium) and the incentives of the retailer to withhold her private information from the supplier (resulting in a pooling equilibrium).

Introduction

The challenge of meeting supply with demand has increased significantly over recent decades (Christopher & Holweg, 2011). The increased uncertainty in the market, which is due to rapid technological changes, the frequent shift in customers' preferences, and increased competition, is considered the main reason for this challenge. One of the key tools to alleviate the problem of matching supply with demand, which is advocated by both scholars and practitioners, is information sharing among supply-chain partners. For example, firms such as Walmart and Procter & Gamble have made substantial investments in information systems and technologies to collect, analyze, and share product-sale information with their suppliers and retailers (Zhang & Chen, 2013). In addition to implementing information-exchange programs in practice, scholars working in operations management (OM) have devoted considerable effort to quantifying the value of information sharing in supply chains (Chen, 2003; Ha & Tang, 2017 and the references therein).

Although the general consensus is that information increases the overall efficiency of a centralized supply chain, the situation is different when the supply chain consists of independent profit-maximizing firms. In this case, several obstacles may prevent firms from sharing information. For example, in a decentralized supply chain, an individual firm may find concealing its private information to be beneficial when it anticipates that sharing that information would result in a disadvantageous equilibrium (Avinadav et al., 2019; Chernonog & Avinadav, 2019; Li, 2002; Li & Zhang, 2002, 2008). Furthermore, when information is unverifiable, firms may be tempted to distort the shared information in order to increase their profit at the expense of the other firms in the supply chain (see Lee, So, & Tang et al., 2000; Cohen et al., 2003; Terwiesch et al., 2005; and Ozer & Wei, 2006, who provided anecdotal evidence for cases of information manipulation with an emphasis on the semiconductor equipment industry). To remedy this problem and align the incentives of all firms within the supply chain to share information truthfully, Gan et al. (2010) proposed a menu of commitment penalty contracts that can provide greater certainty of demand as well as greater certainty of supply. Egri and Váncza (2013) pointed out that it is challenging to design applicable coordinating contracts under asymmetric information. In their paper, they designed a coordination mechanism under a vendor managed inventory (VMI) for a distributed network, whereas, in a previous paper, Egri and Váncza (2012) suggested a channel coordination protocol for the newsvendor model that provides incentives to minimize the total cost. Using a simple newsvendor framework, Sainathan and Groenevelt (2019) analyzed the ability of five popular coordinating supply-chain contracts (buyback, quantity flexibility, quantity discount, sales rebate, and revenue sharing) to coordinate the supply chain under VMI when the vendor freely decides the order quantity. Mobini et al. (2014) formulated the supplier's problem of designing optimal contracts with the assumption that the retailer's outside option depends on his private information. In a recent work, Li and Liu (2020) designed general mechanisms by directly constructing payment schemes to satisfy incentive-compatibility and individual-rationality constraints, where the retailer's private demand information is modeled as a space of either continuous or discrete states.

A different approach to align the incentives of firms in a supply chain to share information truthfully is via signaling mechanisms (Cachon & Lariviere, 2001; Ozer & Wei, 2006), in which the party with the superior information takes a costly action in order to demonstrate its accountability regarding the shared information. In a supply chain consisting of a retailer who sources from a single supplier, one of the main signaling mechanisms that has been suggested is advance purchase. According to this mechanism, a retailer who possesses superior information about future market demand commits in advance to purchasing a certain quantity. The supplier, upon observing the early commitment of the retailer, updates his belief about the future market demand and secures capacity based on this updated information.

Although this mechanism has been studied extensively in the OM literature (e.g., Cachon & Lariviere, 2001; Ozer & Wei, 2006), we re-visit this problem, and study a situation in which the retailer, due to their proximity to the market, has superior information about the consumer demand. The supplier needs to secure the capacity prior to the selling season, and the advance purchase of the retailer can influence the former's belief regarding the market demand, and, consequently, the capacity level.

In particular, we explore the following research questions:

  • How can the retailer convey the market state to the supplier in a credible manner?

  • What are the economic conditions that will induce the retailer to finance the entire capacity in the market?

  • What is the effect of asymmetric information on the efficiency of the supply chain and on the payoffs of the retailer and the supplier?

  • What is the effect of asymmetric information on consumer welfare?

  • Which type of equilibrium – separating or pooling – is better for the retailer and the supplier?

  • What is the effect of the gap between the possible market conditions on the ability of the retailer to signal the true market state?

In this work, we demonstrate a number of important properties that, to our best knowledge, have not previously been reported. Under situations of asymmetric information, when the retailer is endowed with superior information, the advance-purchase mechanisms previously studied ensure that a retailer who observes a favorable market condition commits to a quantity that a retailer who observes a less favorable market condition cannot imitate. In particular, we show that three scenarios can arise as an equilibrium outcome, one of which has not been previously reported.

Under the settings of asymmetric information and the ability of the retailer to order in advance, two main factors affect the order quantity of the retailer. First, the retailer evaluates the market attractiveness based on her economic factors (measured by the retailer's critical fractile) against the supplier's market attractiveness (measured by the latter's critical fractile). These economic factors are not influenced by the market uncertainty, but are derived based on the overage and underage costs of each party. If the market attractiveness of the retailer is better than that of the supplier, in some cases, the retailer will prefer financing the entire capacity over benefiting from the free capacity that the supplier would have secured even under the complete information setting. An example of such a case is when the supplier, based on his evaluation of the market attractiveness, is interested in securing a limited capacity that is considerably lower than the preferred capacity of the retailer. The latter understands that in order to induce the supplier to build additional units, she will need to commit to financing the entire capacity that she wishes the supplier to secure. We show that when such a case occurs under the complete-information setting, the same outcome would also arise under the asymmetric-information setting. This implies that when the economic factors of the retailer are much better than those of the supplier, switching from complete information to asymmetric information has no influence on the equilibrium outcome because the retailer chooses to finance her optimal capacity level in both settings.

The value of the advance purchase as a signaling tool comes into play when the retailer is satisfied with the capacity level that the supplier chooses to secure under complete information, and orders zero units in advance. Under asymmetric information, to credibly convey the market state, a high-type retailer (i.e., a retailer who observes a high market demand) needs to commit to purchasing a certain quantity that a low-type retailer (i.e., a retailer who observes a low market demand) cannot mimic. Most of the research that has analyzed settings similar to ours has concentrated on this problem—finding an advance-order quantity that ensures that a low-type retailer will be indifferent between revealing the true market condition and attempting to mislead the supplier to secure a high capacity level by committing in advance to purchasing a large quantity.

Interestingly, we show there are cases where a high-type retailer may choose to order in advance a quantity that even exceeds the minimum separating quantity. The high-type retailer faces two options: in the first option, the retailer orders the minimum separating quantity that convinces the supplier that demand is high; consequently, the supplier secures the appropriate capacity level for this market condition, based on his own economic factors. In the second option, the retailer decides to finance the entire capacity level according to her view of the market attractiveness—a quantity that exceeds the optimal capacity level of the supplier. The high cost of the advance purchase induces the high-type retailer to place an order in advance that is even higher than the separating quantity. Thus, an interesting situation arises—in this signaling game, all the incentive-compatibility constraints are not binding. This outcome differs from that of previous research on this problem, which showed that a separating equilibrium is achieved when the low-type retailer's incentive-compatibility constraint is binding.

Our finding that in some cases, the need to order in advance induces the high-type retailer to order a quantity that exceeds the required level to convince the supplier that demand is high, has important implications regarding the efficiency of the supply chain and the consumers’ welfare. Usually, asymmetric information leads to market failures and inefficiency (Spence, 1973). In contrast to this view, we show that asymmetric information can actually improve the efficiency of the supply chain. In our model, three cases arise, depending on the values of the retailer's and the supplier's critical fractiles. In the first case, the retailer orders the same quantity as in the case of complete information. In the second case, the retailer orders a higher quantity than the one the supplier would have secured under complete information. Consequently, in this case, the supply chain benefits from the increased capacity level, and the performance of the supply chain is better than that under complete information. Finally, in the third case, the high-type retailer orders the minimum separating quantity, and the supplier, based on his updated belief, builds the same capacity level as in the complete-information case. Therefore, in two cases, the secured capacity is the same in the complete- and asymmetric-information cases, while in the third case, the supply chain benefits from a higher capacity under asymmetric information than under complete information. The increased capacity level discussed above also has important consequences for the consumers. In our model, since the retail price is exogenous, consumer welfare is determined by the probability of purchasing the product, and an increased capacity results in a higher purchasing probability. Therefore, since asymmetric information may result in higher market capacity, it may also result in higher consumer welfare.

We complement our study by analyzing another option that is available to the retailer: ordering in advance a quantity that does not affect the prior belief of the supplier—a pooling equilibrium. We characterize the conditions that ensure the existence of such an equilibrium, and we further compare the payoff of the retailer under the two possible types of equilibrium—the separating equilibrium and the pooling equilibrium. We demonstrate that there are cases in which the retailer will prefer the pooling equilibrium, which implies that no information is revealed in the supply chain, over incurring the signaling cost required to convey the market condition to the supplier in a truthful manner. While there are cases in which the retailer prefers the pooling equilibrium, we prove that the supplier is always better off when the separating equilibrium is played.

To summarize, in this paper, we revisit the canonical problem of using the advance-purchase mechanism to signal the market demand in a vertical supply chain contracting over one selling season. We highlight a few important properties that, to our knowledge, have not been previously reported for this setting:

  • 1.

    The need to signal the market condition by ordering in advance may result in ordering a quantity that is even higher than the minimum separating quantity—i.e., the quantity that convinces the supplier that demand is high. In this case, under asymmetric information and when demand is high, the retailer finances the entire capacity, and this capacity is even higher than the capacity in the market under complete information.

  • 2.

    When the retailer finances the entire capacity, this results in a separating equilibrium in which all incentive-compatibility constraints are non-binding. This situation differs from a standard signaling game. Usually, in a signaling game, the party that attempts to convey information chooses the minimum quantity that conveys this information, such that the incentive-compatibility constraint of the low type would be binding. In our setting, there are cases in which the retailer chooses to order in advance a quantity that exceeds the minimum separating quantity.

  • 3.

    Asymmetric information can result in improved efficiency of the supply chain and increased consumer welfare. While other scholars have obtained similar results regarding the welfare-enhancing effect of asymmetric information (e.g., Li & Zhang, 2008), to the best of our knowledge, the underlying reason for this finding (which is discussed in the present paper) has not been previously presented. In our setting, the need to signal the market condition results in the decision of the high-type retailer to finance a higher capacity level than that under complete information. Consequently, it alleviates the problem of double-marginalization (Spengler, 1950), thus, improving both the efficiency of the supply chain and consumer welfare.

  • 4.

    The retailer may prefer to hide her private information, by adopting a pooling equilibrium, rather than to signal her private information by adopting a costly separating equilibrium. This preference depends on the prior probability that the market condition is high. While the retailer may prefer the pooling equilibrium, the supplier always prefers the separating equilibrium.

  • 5.

    When the separating equilibrium is played, it does not hurt the supplier to be the uninformed party in the supply chain. On the contrary, the supplier may actually benefit from the need of the retailer to signal the market condition in a credible manner.

The main managerial insights that stem from this research are as follows. The supplier benefits from information asymmetry; information asymmetry forces the retailer to signal the state of the demand and this signaling benefits the supplier. In a similar manner, the consumers also benefit from information asymmetry due to the fact that information asymmetry can result in increased capacity in the market. In contrast, the retailer suffers from information asymmetry due to the signaling costs. Therefore, there are cases in which the retailer prefers the pooling equilibrium (i.e., not to reveal any information) over signaling information to the supplier.

The remainder of the paper is organized in the following way. Section 2 outlines the existing research relevant to our work. Section 3 describes the main model analyzed in this study. Sections 4 and 5 provide the equilibrium analysis for the complete-information benchmark and for the asymmetric-information case, respectively. In Section 6, we analyze the effects of asymmetric information on the consumers, the firms in the supply chain, and the overall efficiency of the supply chain. In Section 7, we propose an alternative equilibrium in which no information is revealed—the pooling equilibrium. We discuss the properties of this equilibrium and compare it with the separating equilibrium. In Section 8, we study an in-depth example that is based on a general uniform distribution, and we conclude in Section 9.

Section snippets

Literature review

This work is mainly relevant to the stream of research that studies information exchange among supply-chain partners under asymmetric information in one selling season. In addition, it contributes to the study of supply-chain coordination.

The management of information in supply chains has received considerable attention in OM literature. Scholars have evaluated the effect of information on issues such as the ability to better match supply with demand, set the capacity level in an efficient

3.1 The general market

We study a supply chain consisting of a single retailer (referred to as ‘she’/‘her’) who sources a product from a single supplier (‘he’/‘him’). Due to the lengthy process of building capacity, prior to the selling season, the supplier must decide on the capacity level, which is denoted by K. We assume that the marginal cost of securing capacity is constant, and we denote it by c0. We further assume that the capacity investment of the supplier can be observed by the retailer, and that the cost c0

Capacity financing under complete information

To better understand the effect of asymmetric information on the decisions of the supplier and the retailer, we start by providing a benchmark in which both parties observe the market condition. Under complete information, if the retailer does not commit to purchasing any units in advance (i.e., qadv=0), the supplier will invest in the capacity level Ki0=argmaxK{πs(K|μi,0)}.

According to the cost structure used in our model, we define zs1c0/w and zr1w/r as the critical ratios (i.e., the

Asymmetric information

We now analyze the asymmetric situation. In this case, the retailer observes the market condition, and the supplier can establish a posterior belief about the market condition based on the advance purchase of the retailer. We are interested in characterizing a separating equilibrium in which the ordered quantity allows the supplier to correctly infer the market condition.

Before analyzing the separating equilibrium, we provide the following observation regarding the inability of the supply-chain

Asymmetric information and supply-chain performance

Asymmetric information is usually viewed as a market failure (Akerlof, 1970). The classic results in economics and the OM literature suggest that to mitigate the issue of asymmetric information and achieve a separating equilibrium, some efficiency loss is required due to the cost of signaling (e.g., Spence, 1973). In this section, we explore the effect of asymmetric information on the efficiency of the supply chain and the welfare of the consumers. Surprisingly, we show that asymmetric

The pooling equilibrium

So far, we have concentrated on analyzing the separating equilibrium. Another possible equilibrium is when the retailer does not signal her private information, but rather chooses the same order quantity regardless of the market condition. In this case, the supplier cannot gain new information about the market condition based on the retailer's advance order, and, thus, he makes his capacity decision according to the prior belief regarding the market condition (see Eq. (2)). This type of

Numerical example and sensitivity analysis

To illustrate the main findings of this research, we use an example in which the random element of the demand, ε, follows a uniform distribution. The mathematical developments are provided in the supplementary file. First, we prove that in this case, the threshold above which the retailer always prefers to finance the entire capacity under complete information is zr̲=1(1zs)2, which is in line with Corollary 1. An interesting property of zr̲, which characterizes the uniform distribution case,

Summary

Information sharing is considered one of the main strategies, advocated by both researchers and practitioners, to increase the efficiency of vertical supply chains. Consequently, special effort has been devoted to understanding the ways in which firms can share information under settings of information asymmetry. In the canonical problem of a single supplier that sells to a single retailer, the retailer, due to her proximity to the market, is endowed with better forecasting capabilities, and

Acknowledgments

The authors thank two anonymous referees for suggestions that improved this paper, and Isaac Meilijson for assisting with the task of extending the proof of Proposition 4(ii) to a general demand distribution.

References (52)

  • J. Zhang et al.

    Coordination of information sharing in a supply chain

    International Journal of Production Economics

    (2013)
  • G. Akerlof

    The market for ‘Lemons’: Quality uncertainty and the market mechanism

    Quarterly Journal of Economics

    (1970)
  • K.S. Anand et al.

    Strategic information management under leakage in a supply chain

    Management Science

    (2009)
  • T. Avinadav et al.

    Revenue-sharing between developers of virtual products and platform distributors

    European Journal of Operational Research

    (2020)
  • Y. Aviv et al.

    Financial cross ownership and information dissemination in a supply chain

    Manufacturing and Service Operations Management

    (2020)
  • P. Bajari et al.

    Incentives versus transaction costs: A theory of procurement contracts

    Rand Journal of Economics

    (2001)
  • O. Besbes et al.

    Intertemporal price discrimination: Structure and computation of optimal policies

    Management Science

    (2015)
  • G.P. Cachon et al.

    Contracting to assure supply: How to share demand forecasts in a supply chain

    Management Science

    (2001)
  • F. Chen

    Information sharing and supply chain coordination. Handbooks in operation and managements science

    (2003)
  • I.K. Cho et al.

    Signaling games and stable equilibria

    The Quarterly Journal of Economics

    (1987)
  • M. Christopher et al.

    “Supply Chain 2.0”: Managing supply chains in the era of turbulence

    International Journal of Physical Distribution & Logistics Management

    (2011)
  • M.A. Cohen et al.

    Measuring imputed cost in the semiconductor equipment supply chain

    Management Science

    (2003)
  • C.J. Corbett et al.

    A supplier's optimal quantity discount policy under asymmetric information

    Management Science

    (2000)
  • V.P. Crawford et al.

    Strategic information transmission

    Econometrica

    (1982)
  • D. Fudenberg et al.

    Game theory

    (1991)
  • X. Guo et al.

    Signaling through price and quality to consumers with fairness concerns

    Journal of Marketing Research

    (2016)
  • Cited by (0)

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