Outsourcing Competition and Information Sharing with Asymmetrically Informed Suppliers

Xia Zhao, Ling Xue Bryan School of Business and Economics, University of North Carolina at Greensboro, Bryan 479, 26170, Greensboro, North Carolina 27408, USA [email protected], [email protected]

Fuqiang Zhang Olin Business School, Washington University in St. Louis, Simon Hall 236, 1 Brookings Drive, St. Louis, Missouri 63130-4899, [email protected]

his paper studies an outsourcing problem where two service providers (suppliers) compete for the service contract T from a client. The suppliers face uncertain cost for providing the service because they do not have perfect information about the client’s type. The suppliers receive differential private signals about the client type and thus compete under asymmetric information. We first characterize the equilibrium of the supplier competition. Then we investigate two of the client’s information sharing decisions. It is shown that less information asymmetry between the suppliers may dampen their competition. Therefore, the client does not necessarily have the incentive to reduce information asymmetry between the suppliers. We characterize the conditions under which leveling the informational ground is beneficial to the client. We also find that under the presence of information asymmetry (e.g., when the suppliers have different learning abilities), sharing more information with both suppliers may enhance the advantage of one supplier over the other and at the same time increase the upper bound of the suppliers’ quotes in equilibrium. Consequently, the suppliers compete less aggressively and the client’s payoff decreases in the amount of shared information. The findings from this study provide useful managerial implications on information management for outsourcing firms.

Key words: service outsourcing; asymmetric information; information sharing; common value auction History: Received: April 2012; Accepted: April 2013 by Anil Arya, after 3 revisions.

1. Introduction caused by the cost uncertainties involved in the transaction. In most outsourcing relationships, either the The past few decades have witnessed the boom of buyer, the suppliers, or both may possess some infor- outsourcing in which firms transfer their noncore mation that is not publicly known to the other parties. business activities to third-party suppliers. Typical For instance, when a client outsources a certain task, outsourcing areas include information technology she may not know the suppliers’ exact costs for (IT) management, services, manufacturing, logistics, undertaking the task. The reason could be simply that and customer support (Goles et al. 2008, Halvey and the suppliers have private information about their Melby 2007, Kakabadse and Kakabadse 2005). The technological capabilities and operational efficiency. primary motivation for outsourcing is to maintain a We call this supplier-related cost uncertainty. As we competitive edge by reducing costs and focusing on will discuss in the literature review, this type of cost core competencies. Today outsourcing has become a uncertainty is quite intuitive and has received enor- strategic lever in the global economy (Friedman 2005), mous attention among practitioners and academics. and it is widely expected that the increasing trend of Much less attention has been paid to the so-called outsourcing will continue in the near future (Cohen client-related cost uncertainty, that is, the suppliers and Young 2006, Stevens 2009). do not have full information on certain aspects of the While the benefits of outsourcing are evident, its transaction. Consider multiple suppliers bidding for success hinges on how well the relationships between an outsourcing contract from a client. Due to the com- the outsourcing firm (client) and her suppliers are plexity of the outsourced business process, none of managed. This poses challenges for the client because the suppliers has perfect information about the actual the suppliers are usually independent entities with cost for serving the client. In addition, the suppliers different information and self-interested objectives. may have disparate information due to their different One of the difficulties in outsourcing management is backgrounds, industry experiences, and information 1 Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing 2 Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society learning abilities. This type of cost uncertainty is pre- disparate information about the client and the uncer- valent in practice and may also play an important role tain service cost. in outsourcing decision making. Similar situations may occur in other outsourcing A typical example of client-related cost uncertainty contexts as well. In the outsourcing of consulting and is IT security outsourcing. An increasing number of financial services, the output is usually determined companies rely on Managed Security Service Provid- jointly by the inputs from both the service provider ers (MSSPs) to provide cost-efficient solutions for and the client (Roels et al. 2010). Thus, the service pro- their information security management. MSSPs offer vider’s cost for achieving a certain output level a range of Managed Security Services (MSS), includ- depends on how diligent and responsible the client is, ing security monitoring, vulnerability and penetration which could be unknown to the service provider. In testing, network boundary protection, data archiving customer care outsourcing (e.g., call center outsourc- and restoration, etc. (Allen et al. 2003). The MSS mar- ing), the cost for meeting contractual performance ket has been undergoing rapid growth in recent years. depends critically on the characteristics of the service The global market of security outsourcing is fore- offered to end customers (e.g., service complexity, casted to nearly double between 2011 and 2015, when customer demographics, and demand volume). Call it will reach a total value of $16.8 billion (Infonetics center vendors may not have perfect information Research 2011). In IT security outsourcing, a MSSP’s about these characteristics. The same issue may also cost of providing MSS often depends on numerous arise in manufacturing outsourcing. For example, the factors, including the MSSP’s own capabilities, the original equipment manufacturer (outsourcer) may characteristics of the client he serves, and the match have superior information on products (e.g., the between the corporate cultures of the two firms. For design and complexity of a new product) or market instance, a client with a robust computer network, conditions (e.g., the potential market size) compared strict internal security policies, and well-trained to the contract manufacturer (supplier). This informa- employees may encounter fewer security problems tion may affect the production cost as well as the reve- (Allen et al. 2003); also a good match between the nue associated with the contract (Tan 1996). As in IT firms may foster cooperation and make it easier to security outsourcing, in the above industries the develop collaborative solutions. It is therefore less external suppliers are often uncertain and asymmetri- costly for the MSSP to meet the performance expecta- cally informed about the cost for delivering the tion specified in the service level agreements (SLA). required services or goods to the client. These cost Although these factors are critical to the MSSP’s ser- uncertainties may lead to problematic outsourcing vice cost, usually the MSSP does not have perfect relationships because underestimating the service knowledge about them and therefore faces cost uncer- cost may result in the winner’s curse, where the win- tainties in serving the client. ning supplier has to incur a loss from serving the The presence of client-related cost uncertainty may client (see Kern et al. 2002 for a discussion of winner’s lead to information asymmetry among potential curse in IT outsourcing). As a result, these cost uncer- MSSPs in their competition for service contracts. Such tainties have been ranked as a primary contributing information asymmetry can be attributed to two pos- factor to contract renegotiation and termination in sible reasons. First, MSSPs may collect information outsourcing practices (Halvey and Melby 2007). and learn about service cost from different sources. The above examples demonstrate that cost uncer- For instance, some MSSPs develop better knowledge tainties and asymmetrically informed suppliers repre- of their client from prior business interactions with sent a common feature of many outsourcing settings. the client (Gefen et al. 2008), some MSSPs try to learn Obviously, when competing for the client’s out- about their clients through on-site pre-contract sourced business (e.g., a service contract), suppliers’ inspection (Allen et al. 2003), and some MSSPs obtain behaviors are influenced by their different beliefs information about their clients via third-party infor- about the service cost, which in turn determines the mation services, such as security ratings (Scalet 2008). value of the contract. Thus it is crucial for an out- Second, MSSPs may not have equal learning abilities sourcing firm to understand the impact of this infor- even when they have access to the same information mation structure when designing her outsourcing source. For instance, the insights gained from the strategy. However, there has been relatively little same factual data depend on a MSSP’s information research in the operations management literature processing capability and prior experience. It has studying the outsourcing problem when suppliers are been reported that tacit knowledge derived from not equally informed about the uncertain service cost. social interactions cannot be fully captured in formal This study attempts to shed some light on the prob- documents and reports (Gopal and Gosain 2010). lem by developing a game-theoretic model. In this Therefore, when competing for the service contract model, two suppliers compete for a service contract from a single client, potential MSSPs may have from a single client. The service cost can be either high Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 3 or low. The suppliers do not know the exact service suppliers have different learning abilities), it has been cost, but they have a prior belief about its probability found that sharing more information with both suppli- distribution. In addition, each supplier receives a sig- ers is always detrimental to the client. Although infor- nal about the service cost. The suppliers’ signals are mation sharing will improve both suppliers’ signal correlated, and one may be more accurate than the accuracies, the quality difference in the suppliers’ other. The winner of the contract is determined signals will also increase due to unequal learning through competitive bidding; specifically, the suppli- abilities. In addition, information sharing also ers simultaneously submit the price they would increases the suppliers’ expected service cost contin- charge for the service and the lower bidder wins the gent on bad signals, which is essentially the upper contract. bound of the suppliers’ quotes in equilibrium. These With this model setup, we first derive the equilib- two effects lead to less aggressive bidding behaviors rium outcome of supplier competition. The character- from the suppliers. As a result, sharing information ization of the competitive outcome has useful with both suppliers has a negative impact on the cli- implications on vendor selection and outsourcing ent’s payoff due to dampened supplier competition. strategy design for the client. Then we focus on the This finding indicates that it is not always beneficial client’s information-sharing strategies. The advances for the client to improve suppliers’ signal accuracies. in information technology have facilitated the flow of In other words, the existence of information asymme- information between trade partners. As a result, infor- try may hinder the client from improving suppliers’ mation sharing has been lauded in the literature as an information, which has important implications on the effective means to improve supply chain efficiency information management policy for outsourcing firms. (Chen 2003). In our problem setting, the client can The rest of the study is organized as follows. Sec- influence the suppliers’ information structure through tion 2 reviews the related literature. Section 3 intro- information sharing. For example, the client may help duces the model setup. Section 4 analyzes the the suppliers obtain better information about the ser- suppliers’ bidding game. Section 5 studies the client’s vice cost by disclosing internal documents and information sharing strategies and offers detailed arranging on-site visits. Therefore, we study two answers to the above questions. Finally, the study important questions related to the client’s information concludes with section 6. sharing decision as follows. First, what is the impact of supplier information 2. Literature Review asymmetry on the client’s profit? This question has practical significance because a client may wish to Internet-enabled marketplaces have gained increasing know whether she should narrow the information popularity during the past decade. In particular, the gap via information sharing with the less-informed use of auctions as a procurement tool has been widely supplier. Conventional wisdom suggests that the adopted in outsourcing practice due to the advances client should benefit from a leveled information in information technology. This study is related to the ground because it induces more supplier competition. growing literature in operations management that In contrast, we find that reducing information asym- studies outsourcing and procurement auctions where metry between the suppliers may hurt the client’s a buyer procures a certain service or product from profit under certain conditions. This is because less external suppliers with heterogeneous private costs. information asymmetry implies that the suppliers are Reviews of this literature can be found in Cachon and more likely to receive the same signals, so it may Zhang (2006), Chen (2007), Wan and Beil (2009), and either intensify or dampen the competition depend- Zhang (2010), to name a few. Our model is different ing on the received signals. In particular, when there in that the suppliers incur uncertain but homoge- is a high level of information asymmetry between the neous costs in providing the products/services. In suppliers, the dampening effect dominates the inten- particular, the suppliers face uncertainties about the sifying effect and the client’s profit may decrease as cost for serving the same buyer, which is a common the information gap diminishes. This result cautions value for different suppliers. outsourcing managers about their information shar- Our study involves information sharing, so it is ing strategy and provides insights into the circum- related to papers that study the impact of information stances under which a client should strive to level the sharing/information leakage in supply chains. Repre- informational ground for competing suppliers. sentative studies include Li (2002), Li and Zhang Second, how much information should the client (2008), and Anand and Goyal (2009). Chen (2003) share with the suppliers? By disclosing more informa- reviews the supply chain management literature on tion, the client may improve the accuracy of the sig- information sharing. A common assumption in this nals observed by both suppliers. Interestingly, in our literature is that the supply chain structure is exoge- setting with information asymmetry (e.g., when the nously given. In contrast, the buyer in our model uses Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing 4 Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society an auction for vendor selection, and we study how to honestly publicize all information she has. This is improve the effectiveness of the auction through because honest reporting can reduce the bidders’ pri- information sharing. vate information and thus lower their information In our model, the suppliers receive different but rent. However, in another Milgrom and Weber correlated signals about a common contract value, so (1982b) study, they show that the seller may lower their competition represents a common-value auction her expected profit by disclosing her own information (CVA). Several studies in the CVA literature study when the seller’s information is complementary to the asymmetrically informed bidders (i.e., the auctioned better-informed bidder. In that study, complementar- object is of identical value to the bidders but the bid- ity essentially implies that the disclosure of the sell- ders possess different amounts of information about er’s private information increases the information such a value), and therefore are most relevant to our asymmetry between the bidders, which dampens the work. These CVA studies diverge in characterizing competition in the auction. In our study, we find that the bidders’ profitability in competition. Some studies when the client’s information is complementary to suggest that only the better-informed bidder can both suppliers’ information but the suppliers are make positive expected profit (e.g., Engelbrecht- equipped with different learning abilities, the client Wiggans et al. 1983, Hauswald and Marquez 2006), will not share her information with the suppliers while other studies find that both the better-informed either. Such a finding, though based on a different bidder and the less-informed bidder can make posi- problem setting, is consistent with the insight from tive expected profits (e.g., Banerjee 2005, Hausch Milgrom and Weber (1982b). 1987). Our study bridges the gap between these two groups by using a unified model to capture both cases 3. Model Setup and characterizing the conditions for each case to arise. A firm (client) needs to outsource her service process A few CVA studies look into the issue of informa- to an outside service provider (supplier). For ease of tion sharing, that is, whether the seller has incentives exposition, we consider the example of IT security to help improve the less-informed bidder’s informa- outsourcing. The service has a value V for the client tion. Wilson (1975) suggests that decreasing informa- and there are two pre-qualified suppliers from whom tion asymmetry between the bidders would intensify the client can choose. The suppliers face uncertain their competition. Milgrom and Weber (1982b) also cost for serving the client due to the reasons discussed find that if the seller has access to some of the better- in the Introduction. To focus on the information informed bidder’s information, he can increase its asymmetry issue, we assume that the suppliers are profit by publicizing that information. Hausch (1987) identical (e.g., they have the same technology and are and Banerjee (2005), however, find that decreasing the equally efficient in delivering the required service) information asymmetry level may soften bidder com- except that they may be asymmetrically informed petition and hence lead to lower seller revenue. Such about the client’s service cost. There are two possible a finding, though interesting, is based on some restric- service costs, cl and ch (cl < ch < V). The low cost cl is tive conditions. Hausch (1987) assumes that the associated with situations where the client would be better-informed bidder’s estimate of the object value less costly to serve (e.g., it is equipped with a suffi- is negatively affected by the improved precision of ciently robust IT system) while ch is associated with the less-informed bidder’s information. Due to the the opposite situations. For easy reference, call the cli- lack of tractability, Hausch (1987) relies on a numeri- ent a good (G) type if her service cost is cl, and a bad cal example to illustrate the finding. To simplify anal- (B) type if her cost is ch. We use T to denote the client ysis, Banerjee (2005) assumes that the bidders never type and assume that T = G with probability Pr(G) = c bid when receiving a bad signal. These approaches (0 < c < 1) and T = B with probability Pr(B) = 1c. undermine the robustness of the results because they One may view c as the fraction of low-cost clients in are based on either numerical analysis or constrained the market, which is public information. bidding behavior. In view of these limitations, we The suppliers possess asymmetric information develop an analytical model that is not subject to about the client and the associated service cost. As these restrictions. By solving the suppliers’ equilib- mentioned earlier, such information asymmetry may rium bidding strategies, we analytically characterize be due to the differences in the suppliers’ information the conditions under which information asymmetry sources and their learning abilities. Without loss of may either intensify or dampen bidder competition. generality, suppose supplier 1 is better informed In addition to information asymmetry between the about the client than supplier 2. We model informa- suppliers, we also study the sharing of information tion asymmetry between the two suppliers as follows. between the client and the suppliers. Milgrom and Supplier 1 receives a signal S about the client type. Weber (1982a) suggest that the seller should always The signal can be either good (g) or bad (b). Let Pr(g|T) Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 5 and Pr(b|T) denote the probabilities of S = g and vice cost with a signal S. It can be readily shown S = b, respectively, conditional on T 2 {G,B}. Define that

PrðgjGÞ¼; PrðbjGÞ¼1 ; c c ; ð1Þ E½C¼PrðGÞcl þð1 PrðGÞÞch ¼ cl þð1 Þch ð4Þ PrðgjBÞ¼0; and PrðbjBÞ¼1: \ ; E½Cjg¼PrðGjgÞcl þ PrðBjgÞch ¼ cl E½C

That is, for a good type, the signal is g with proba- E½Cjb¼PrðGjbÞcl þ PrðBjbÞch k ≤ k ≤ k bility (0 1) and b with probability 1 ; how- ð1 Þcc ð1 cÞc E½Ccc ¼ l þ h ¼ l [ E½C: ever, the signal from a bad type is always b. For 1 c 1 c 1 c instance, the bad client does not have the necessary infrastructure and managerial capability to provide a That is, a good (bad) signal g (b) implies a lower friendly task environment, so the better-informed (higher) expected cost. Note that the signal is unbi- supplier seldom receives a good signal based on the ased since E[C] = E[C|g]Pr(g) + E[C|b]Pr(b). client’s reputation in the industry. Supplier 2 cannot observe the signal S. For instance, The assumption in Equation (1) is used to improve supplier 2 is a new entrant and does not have much the transparency of the analysis, and it can be general- information about the client’s type. We assume he ~ ized without affecting our main results. For instance, receives a garbling of supplier 1’s signal, denoted S. ~ ~ we have also analyzed a more general model where The value of S can be either good (g~)orbad(b). Let ~ ~ the signal from a bad-type client is g with probability Prðg~ j SÞ and Prðb j SÞ be the probabilities of S ¼ g~ and b ≤ b ≤ k b ~ ~ (0 ) and b with probability 1 . Our main S ¼ b, respectively, conditional on S. Deﬁne model corresponds to the special case with b = 0. Another special case is when k = 1 b = (1 + w)/2, ~ 1 þ q ð~j Þ¼ ð j Þ¼ ; where supplier 1 receives symmetric signals from the Pr g g Pr b b 2 ð5Þ two types of clients, that is, the signal from a good- ~ 1 q + w and PrðbjgÞ¼Prðg~jbÞ¼ ; type (bad-type) client is g(b) with probability (1 )/2 2 (0 ≤ w ≤ 1) and b(g) with probability (1 w)/2. It has ≤ q ≤ been found that the qualitative insights remain where 0 1 captures the extent of the garbling. q = ~ unchanged in these more general models. When 0, the signal S is useless for supplier 2 ~ ~ ~ ~ We may view k as the quality of the signal. When because for a given S, he receives S ¼ b or S ¼ g k = with equal probability. However, as q increases, it 1, the signal provides perfect information about ~ the client’s type; when k = 0, the signal is useless becomes more likely that S represents the same sig- because it is always bad regardless of the client nal as S; that is, the information asymmetry between q = type. Throughout the study we focus on k > 0to the suppliers diminishes. When 1, the suppliers avoid the trivial case. Let Pr(g) and Pr(b) denote the are equally informed, and there is no information q probabilities of S = g and S = b, respectively. Then asymmetry anymore. Hence we may use as a con- we have Pr(g) = cPr(g|G) + (1 c)Pr(g|B) = ck, trol of asymmetric supplier information. Note that q = Pr(b) = 1 Pr(g) = 1 ck. We emphasize that the with 1, the suppliers are identical ex ante and the game reduces to Bertrand competition. signal S is informative in the sense that the supplier ~ will be more certain about the client’s true type To examine the quality of the signal S, we derive after observing S. To see this, let Pr(T | S) represent the posterior probabilities of the client type condi- the posterior probability that the cost type is tional on supplier 2’s noisy signal: T 2 {G,B}, given the signal S 2 {g,b}. Based on PrðGjg~Þ¼PrðGjgÞPrðgjg~ÞþPrðGjbÞPrðbjg~Þ Bayes’ rule, we may calculate cð2q þ 1 qÞ ¼ ; ð6Þ PrðgjGÞPrðGÞ 1 q þ 2qc PrðGjgÞ¼ ¼ 1 c; ð2Þ PrðgjGÞPrðGÞþPrðgjBÞPrðBÞ ~ ~ ~ PrðBjbÞ¼PrðBjgÞPrðgjbÞþPrðBjbÞPrðbjbÞ PrðbjBÞPrðBÞ ð1 cÞð1 þ qÞ PrðBjbÞ¼ ¼ : ð7Þ PrðbjGÞPrðGÞþPrðbjBÞPrðBÞ 1 þ q 2qc c ð3Þ 1 c: ¼ c 1 It can be readily shown that PrðG j g~Þ PrðG j gÞ 1 ~ and PrðB j bÞ PrðB j bÞ, where the equality holds Thus a good signal S = g indicates that the client only when q = 1. This means that S is indeed a more ~ has a low cost for sure, while a bad signal suggests accurate indicator of the client’s type than S. A couple that the client is more likely to have a high cost. of points are worth noting here. First, due to the sto- Let E[C] be the supplier’s expected service cost chastic nature of the signals, S does not necessarily ~ without any signal and E[C|S] be the expected ser- dominate S for all possible realizations; for example, Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing 6 Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society supplier 1 may receive a bad signal S = b while sup- practice. In fact, it has been commonly used in service ~ plier 2 may receive a good signal S ¼ g~ from a good outsourcing: The client announces a service contract type client. Second, although a bad type client always to outsource (the contract may provide details about sends a bad signal S = b to supplier 1, supplier 2 may the outsourced service and specify the required ser- ~ still receive a good signal S ¼ g~. This is again because vice levels); then the suppliers bid for the contract on supplier 2’s signal is more noisy than supplier 1’s. price. We assume that both the client and the suppli- ~ Given the signal S, the expected service cost per- ers are risk neutral and aim to maximize their ~ ~ ceived by supplier 2 is E½CjS¼Prðg j SÞE½C j gþ expected payoffs. In addition, everything is common ~ ~ ~ PrðbjSÞE½C j b, where Prðg j SÞ and Prðb j SÞ are the knowledge except the cost type T and the two signals ~ posterior probabilities of S = g and S = b respectively, S and S. ~ ~ conditional on S 2fg~; bg. Based on the Bayes’ rule, Deﬁne social surplus as the sum of the payoffs of there are all parties in the system. In our setting, it is V E[C], = c + c p p where E[C] cl (1 )ch. Let 1 and 2 denote the ~ ~ PrðSjgÞPrðgÞ two suppliers’ expected payoffs, respectively. Then PrðgjSÞ¼ ~ ~ and PrðSjgÞPrðgÞþPrðSjbÞPrðbÞ the client’s expected payoff is equal to the difference ~ ð8Þ between the social surplus and the sum of the suppli- ~ PrðSjbÞPrðbÞ : ers’ payoffs, that is, Π = V E[C] p p . PrðbjSÞ¼ ~ ~ 1 2 PrðSjgÞPrðgÞþPrðSjbÞPrðbÞ

Then we can show the following relationship 4. Supplier Competition among the expected service costs (all proofs are pre- This section studies the equilibrium outcome of the sented in Appendix S1). Bayesian game played by the suppliers. In our model ~ setting, the suppliers’ game can be characterized by a LEMMA 1. c ¼ E½CjgE½Cjg~E½CE½CjbE½Cjb l common-value auction. In this auction, supplier i c : h (i = 1,2) chooses a quote p to maximize his expected i ~ payoff p . When q = 1, the signals S and S are identi- The client knows that supplier 1 has superior infor- i cal, that is, the suppliers always obtain the same mation about the service cost compared to supplier 2. information. They engage in Bertrand competition, However, like the suppliers, the client does not have and the equilibrium strategy is to quote E[C | g] when perfect information about the service cost. Recall that receiving signal g and E[C | b] when receiving signal the service cost depends on numerous factors, many of b. Information asymmetry is present when 0 ≤ q < 1. which are random and not perfectly known to the client The following proposition states that there is no (e.g., service complexity, suppliers’ capabilities, match pure-strategy equilibrium in the game in the presence between the firms, and demand uncertainties). There- of information asymmetry between the suppliers. fore, we assume that the client knows the probability distribution (i.e., c) but not her exact type. This is a stan- PROPOSITION 1. No pure-strategy equilibrium exists in dard treatment in the common-value auction literature the suppliers’ quoting game when q < 1. that assumes the seller does not know the exact value of the auctioned object. We have also examined the other Next we derive the mixed-strategy equilibrium extreme case where the client has perfect information for such a game. Let G ðp j SÞ¼Prðp p j SÞ about her own type. The qualitative insights from the 1 1 denote supplier 1’s mixed strategy in equilibrium, main model are quite robust in both extreme cases. where G ðp j SÞ is a cumulative distribution function The sequence of events in our model is as follows. 1 ~ conditional on the signal S. Similarly, let G ðp j SÞ¼ First, the client announces the request for quote ~ 2 Prðp p j SÞ denote supplier 2’s mixed strategy in (RFQ); second, both suppliers receive their private 2 equilibrium. Then supplier 1’s expected payoff func- signals about the client’s type (i.e., supplier 1 observes ~ tion can be written as S and supplier 2 observes S); third, both suppliers simultaneously send their quotes to the client, each p ðp jSÞ¼Prðg~jSÞðp E½CjSÞð1 G ðp jg~ÞÞ specifying a fixed fee (price) p (i = 1,2) that the sup- 1 1 1 2 1 i ~ ~ : plier would like to charge for the service; next, the þ PrðbjSÞðp1 E½CjSÞð1 G2ðp1jbÞÞ ð9Þ client awards the service contract to the supplier with the lower quote (in case of a tie, the client awards the The first term on the right-hand side of Equation (9) contract by flipping a fair coin); lastly, the winning is supplier 1’s expected payoff when supplier 2 ~ supplier delivers the service as required to the client. receives a signal S ¼ g~, and the second term is the ~ ~ We focus on the fixed-fee contract because it is expected payoff when supplier 2 receives S ¼ b. Sup- quite simple and relatively easy to implement in plier 2’s expected payoff function is given by Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 7

p ~ ~ 2ðp2jSÞ¼PrðgjSÞðp2 E½CjgÞð1 G1ðp2jgÞÞ depends on the relationship between Pr(g) and Pr(b). ~ Proposition 3 presents the firms’ equilibrium strate- þ PrðbjSÞðp2 E½CjbÞð1 G1ðp2jbÞÞ: ð10Þ gies for the case Pr(g) ≤ Pr(b) (or equivalently, c 1 The first term on the right-hand side of Equation (10) 2), that is, supplier 1 is more likely to receive a is supplier 2’s expected payoff when supplier 1 receives bad signal. asignalS = g, and the second term is the expected payoff when supplier 1 receives S = b. Equation (10) PROPOSITION 3. Suppose 0 < q < 1 and Pr(g) ≤ Pr(b). differs from Equation (9) in that the expected service The suppliers’ equilibrium strategies can be characterized cost changes with supplier 1’s signal. This is because as follows: (i) supplier 1 quotes p1 ¼ E½C j b when observ- = supplier 1’s signal is more accurate than supplier 2’s. ing S b, and quotes according to G1ðpjgÞ¼1 þ ~ ~ We first characterize the equilibrium of the supplier ðPrðbjgÞðp E½CjbÞÞ=ðPrðgjgÞðp E½Cj gÞÞ; where p 2 q = q = ½E½C j g~; E½C j b when observing S = g. (ii) Supplier 2 game for 0. When 0, supplier 2 does not ~ ~ obtain any meaningful information from the signal. quotes p2 ¼ E½C j b when observing S ¼ b, and ~ ~ The distribution of supplier 2’s signal reduces to quotes according to G2ðpjgÞ¼1 ððE½CjgE½CjgÞ ~ ~ ~ ~ Prðg~jgÞ¼PrðbjgÞ¼Prðg~ j bÞ¼PrðbjbÞ¼1. Supplier PrðbjgÞðp E½CjgÞÞ=ðPrðgj gÞðp E½CjgÞÞ; where p 2 2 ~ ~ ~ 2’s posterior beliefs are the same as his prior beliefs. ½E½C j g; E½C j b when observing S ¼ g. ~ In particular, Prðg j g~Þ¼PrðgjbÞ¼PrðgÞ; Prðbjg~Þ¼ ~ ~ PrðbjbÞ¼PrðbÞ and E½C j g~¼E½Cjb¼E½C. The It is worth mentioning that for Pr(g) ≤ Pr(b), sup- competition is essentially between a privately plier 2’s expected payoff is always zero regardless of informed supplier and an uninformed supplier. The his signal. However, supplier 1’s expected payoff is ~ next proposition presents the suppliers’equilibrium E½C j gE½Cjg0 when he receives a good signal quoting strategies. and 0 when he receives a bad signal. That is, less accurate information about the client type puts supplier 2 PROPOSITION 2. Suppose q = 0. The suppliers’ equilib- in a disadvantageous position. To help understand rium strategies can be characterized as follows: (i) supplier Proposition 3, Figure 1(a) depicts the support of the = 1 quotes p1 ¼ E½C j b when observing S b and quotes suppliers’ quotes. = according to G1ðpjgÞ¼ 1 þðPrðbÞðp E½CjbÞÞ ðPrðgÞ Proposition 4 characterizes the suppliers’ equilib- ðp E½CjgÞÞ; p 2½E½C; E½Cjb when observing S = g. rium strategies for the case Pr(g) > Pr(b) (or equiva- ~ c [ 1 (ii) Supplier 2 ignores the signal S and quotes according to lently, 2), that is, supplier 1 is more likely to G2ðpÞ¼1 ðE½CE½CjgÞ=ðp E½C j gÞ; p 2½E½C; receive a good signal. E½C j b: PROPOSITION 4. Suppose 0 < q < 1 and Pr(g) > Pr(b). We next consider 0 < q < 1. It turns out that for any The suppliers’ equilibrium strategies can be characterized given pair of probabilities Pr(g) and Pr(b), a unique as follows: (i) Supplier 1 quotes p1 ¼ E½C j b when equilibrium exists and the equilibrium structure observing S =b, and quotes according to

Figure 1 An Illustration of the Suppliers’ Equilibrium Quoting Strategies

(a) (b) Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing 8 Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 8 ~ ~ < ðpE½CjgÞPrðbjgÞðpE½CjbÞ; ;^ the more informed supplier has a single-side informa- 1 Prðgjg~ÞðpE½CjgÞ p2½p pÞ G ðpjgÞ¼ ~ : tion advantage (SIA) as observed in the auction litera- 1 : PrðbjbÞðpE½CjbÞ 1þ ~ ; p2½p^;E½Cjb ture (e.g., Engelbrecht-Wiggans et al. 1983, Hauswald PrðgjbÞðpE½CjgÞ and Marquez 2006). When Pr(g) > Pr(b), both suppliers can enjoy positive expected payoffs. This is the when observing S = g, where the cutoff levels p^ case with double-side information advantages (DIA). and p(p^ [ p) are defined in the proof. (ii) Supplier 2 The fact that supplier 1 does not observe supplier 2’s ~ ðpE½CjgÞ private signal enables supplier 2 to also earn an infor- quotes according to G ðp j bÞ¼1 ~ ; p 2 2 PrðbjgÞðpE½CjgÞ mation rent, even though supplier 2’s signal is not as ~ ~ ½p^; E½C j b when observing S ¼ b, and quotes according good as supplier 1’s. ~ ðpE½C j gÞ Prðb j gÞðp E½C j gÞ The above result reveals that the client has to leave to G ðp j g~Þ¼1 ; p 2½p; p^; 2 Prðg~ j gÞðpE½CjgÞ a positive information rent to the suppliers as long as ~ when observing S ¼ g,~ where the cutoff levels p^ and q < 1 (i.e., the suppliers have asymmetric information p ðp^ [ pÞ are defined in the proof. about the service cost). Nevertheless, having two suppliers is always better than having just a single Figure 1(b) illustrates the support of the suppliers’ supplier from the client’s perspective. When there is quotes for Pr(g) > Pr(b). Similar to the previous case ≤ | no supplier competition, a single supplier with strong with Pr(g) Pr(b), supplier 1 will quote E[C b]when bargaining power will quote V and extract all the sur- observing a signal S = b. However, when supplier 1 = plus. However, when there are two suppliers compet- observes a signal S g, he will randomize his quote ing against each other, they will bid down to E[C | b] over [p,E[C | b]], whose lower bound p is higher than ~ ≤ or lower. That is, supplier competition ensures that its counterpart E½C j g under Pr(g) Pr(b). This sug- the client makes a positive profit, even if the suppliers gests that supplier 1 competes less aggressively than are asymmetrically informed. in the previous case. To see what causes this difference, we may examine the condition Pr(g) > Pr(b). This condition can be rewritten as 5. Information Sharing ~ The preceding section characterizes the equilibrium PrðbjgÞðE½CjbE½CjgÞ [ E½Cjg~E½Cjg: ð11Þ outcome of supplier competition. It has been shown Note that the left-hand side of Equation (11) is sup- that the outcome of the bidding game hinges upon plier 1’s expected payoff if he undercuts the quote the suppliers’ information structure. In most practical E[C | b] and only wins when supplier 2 receives situations, the client can influence the suppliers’ infor- ~ ~ S ¼ b. The right-hand side is supplier 1’s payoff if he mation structure through information sharing. For ~ example, the client may help the suppliers obtain quotes p1 ¼ E½Cjg and wins for sure regardless of supplier 2’s signal. The inequality in Equation (11) better information about the service cost by disclosing indicates that unlike in the case Pr(g) ≤ Pr(b), now it is internal documents and arranging on-site visits. This not optimal for supplier 1 to always beat supplier 2. section proceeds to study the client’s information Instead, supplier 1 would rather bet on the chance sharing strategies. Specifically, we are interested in ~ ~ that supplier 2 receives S ¼ b and only win in that the two questions raised in the introduction: First, case. Therefore, supplier 1 competes less aggressively what is the impact of information asymmetry between when he receives S = g. the suppliers on the client’s profit? Second, how much Given the above equilibrium outcomes, Proposition information should the client share with both suppli- 5 characterizes the suppliers’ expected payoffs in ers? The following two subsections analyze these two equilibrium. questions and derive some useful managerial insights. For simplicity, we assume that the cost of PROPOSITION 5. (i) Suppose q = 1. Both suppliers’ pay- information sharing is negligible for the client. offs are zero in the equilibrium. (ii) Suppose 0 < q < 1. q In the equilibrium, supplier 1’s expected payoff is always 5.1. Changing via Information Sharing positive, while supplier 2’s expected payoff is positive if In our model, information asymmetry exists because Pr(g) > Pr(b), and is zero otherwise. Supplier 1’s supplier 2’s information is not as accurate as supplier expected payoff is always higher than that of supplier 2. 1’s. The difference between the suppliers’ signals S ~ q (iii) Suppose q = 0. Supplier 1’s payoff is positive while and S is defined by the parameter as in Equation (5). q supplier 2’s payoff is zero in the equilibrium. When is larger (smaller), the two signals are more (less) similar or the degree of information asymmetry Consider the general situation 0 < q < 1. When between the suppliers is lower (higher). Thus, we use Pr(g) ≤ Pr(b), only supplier 1 (i.e., the more informed q 2 [0,1] to measure the similarity between the sup- supplier) earns a positive rent. This is the case where pliers’ signals. This subsection examines the impact of Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 9 this information asymmetry on the client’s profit. supplier 2 (and supplier 1) will always quote the high- Clearly, if less information asymmetry leads to higher est possible bid E[C|b] when receiving a bad signal. profit, then the client would have incentives to reduce Due to the intensifying effect, an increase in q always information asymmetry between suppliers (increase leads to more intense supplier competition and drives q) via information sharing. For instance, if the client down supplier 1’s profit. When Pr(g) > Pr(b), both the has access to some of supplier 1’s information, then dampening effect and the intensifying effect exist. In the client may increase q by sharing that information this case, supplier 1 is likely to receive a good signal. with supplier 2. We next analyze the client’s optimal When q is large, supplier 2 is also more likely to information sharing strategy on q. receive a good signal due to the low level of informa- A natural conjecture would be that decreasing infor- tion asymmetry. Consequently, the intensifying effect mation asymmetry will intensify competition because dominates the damping effect and an increase in q it levels the ground for the suppliers. For example, the intensifies the supplier competition, whereas, when q suppliers’ bidding game boils down to Bertrand com- is small, supplier 2 is more likely to receive a bad sig- petition when q = 1, which erodes the suppliers’ pay- nal due to the high level of information asymmetry offs. As a result, the client may always want to reduce between the suppliers. As a result, the dampening information asymmetry between the suppliers, for effect dominates the intensifying effect and an example, by sharing supplier 1’s information that is increase in q softens the supplier competition. Over- available to her with the less-informed supplier. The all, the suppliers’ payoffs are quasi-concave in q in intuition is consistent with the findings in the auction this case; that is, they first increase and then decrease literature (e.g., Milgrom and Weber 1982b, Wilson to zero at q = 1. 1975) and appears to be a prevalent view among An interesting implication of Proposition 6 is that practitioners as well. The IT outsourcing case study by under Pr(g) > Pr(b), it might be in the suppliers’ best Kern et al. (2002) links weak competition to ex ante interest to bilaterally share their information. When q q supplier asymmetries and recommends that the client the level of information asymmetry is high (i.e., < 1), should assist the disadvantageous supplier with infor- both suppliers will benefit if the better-informed sup- mation gathering. However, we find that this intuitive plier reveals his information to the less-informed q = q idea is not always valid in our model setting. Proposi- party (until 1 is achieved). Further, when the q q tions 6 and 7 illustrate how the suppliers’ and the cli- level of information asymmetry is low (i.e., > 2), ent’s expected payoffs vary with q. the less-informed supplier prefers to ignore some of the available information and doing this also benefits PROPOSITION 6. (i) When Pr(g) ≤ Pr(b), supplier 1’s the better-informed supplier as well. expected payoff is decreasing in q, and supplier 2’s expected payoff is always zero (independent of q). (ii) PROPOSITION 7. (i) When Pr(g) ≤ Pr(b), the client’s ex- > q q ≤ q q > When Pr(g) Pr(b), there exist 1 and 2 (0 1 < pected payoff is increasing in . (ii) When Pr(g) Pr(b), q q ≤ q ≤ q q q q 2 <1)such that supplier 1’s expected payoff is increas- there exists 0 (0 1 0 < 2 < 1), where 1 and 2 q q q q q ing in for 2 [0, 1] and decreasing in for 2 are given in Proposition 6 such that the client’s payoff is q q q q q q ( 1,1], and supplier 2’s expected payoff is increasing in decreasing in for 2 [0, 0] and increasing in for q q q q q q q for 2 [0, 2] and decreasing in for 2 ( 2,1]. 2 ( 0,1].

The above result indicates that the supplier compe- Proposition 7 shows that the client’s payoff is not tition is not necessarily more intense when there is always monotonically increasing in q. In other words, less information asymmetry. The explanation for this reducing information asymmetry between the suppli- result is as follows. As q increases, there is less infor- ers may hurt the client’s payoff. This yields useful mation asymmetry between the two suppliers, so they insight on how the client should manage supplier are more likely to receive the same signal. Conse- information asymmetry. In an ideal situation where quently, supplier 2 will quote more aggressively the client can fully control the parameter q, she when receiving a good signal, because he is more con- should remove supplier information asymmetry com- ﬁdent that supplier 1 also receives a good signal. On pletely by setting q = 1. That is, the client can help the the other hand, supplier 2 will compete less aggres- less-informed supplier achieve a signal that is as accu- sively when receiving a bad signal, because it is more rate as the better-informed supplier’s. The suppliers’ likely that supplier 1 also receives a bad signal. There- payoffs are squeezed to zero, and the client extracts fore, an increase in q generates two countervailing all the surplus from the system. However, a more effects on the supplier competition: an intensifying realistic assumption is that the client only has limited effect and a dampening effect. control of information asymmetry. In many practical When Pr(g) ≤ Pr(b), the dampening effect does not situations, it might be hard to completely eliminate exist. This is because Proposition 3 shows that information asymmetry between the suppliers. Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing 10 Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society

Consider the example where one of the suppliers is asymmetry between the suppliers. This is essentially an incumbent with prior business experience with the about information sharing with the less-informed client. There are many factors that prevent an entrant supplier. In this subsection, we continue to address supplier from gaining exactly the same client infor- the second question, that is, whether the client wants mation as the incumbent. For instance, the client may to disclose information to both suppliers. By disclosing not have access to all of the incumbent supplier’s more information, the client may improve the accu- information; it is very likely that the information racy of the signals observed by both suppliers. This acquired from third-party information sources is not can be done through various means, such as clarifying as accurate as the information inferred from the first- the service requirements and disclosing more internal hand data. In addition, even if the entrant supplier documents to the suppliers. However, as discussed can use pre-contract on-site investigation to learn earlier, the suppliers may have different learning abil- about the client, it is still unable to obtain certain tacit ities; that is, they may not generate the same under- knowledge, for example, the employee conduct and standing of the service cost from the disclosed organizational culture at the client firm. The incum- information. For example, a supplier who has more bent supplier, however, may have a better under- industry experience or is located closer to the client standing of these intricacies through his past can better interpret the data shared by the client. interactions with the client. Under these circum- Hence, under the presence of information asymmetry stances where the client can only slightly reduce between the suppliers (e.g., when the suppliers have information asymmetry (e.g., q is always smaller than different learning abilities), it is not clear whether q 0), it might be optimal for the client to maintain a sharing more information is always beneficial to the high level of information asymmetry between the client. suppliers, especially when Pr(g) > Pr(b). Such infor- This question can be addressed by examining the mation asymmetry can intensify the supplier compe- impact of k on the client’s profit. Notice that in our tition. Our result cautions the client about her model, k is a proxy for the quality of the suppliers’ information disclosure strategy under these situa- signals. When k = 0, supplier 1 always receives bad tions. Interestingly, reducing information asymmetry signals, and his posterior beliefs about a client’s type between the suppliers may make the client worse off after receiving a signal, S, are the same as the prior if the current level of information asymmetry is rela- beliefs. That is, Pr(G|g) = c and Pr(B|b) = 1 c for tively high (q < q ). In other words, helping the less- k = 0. Similarly, from Equations (6) and (7) we know 0 ~ informed supplier is beneficial to the client only when PrðG j g~Þ¼c and PrðB j bÞ¼1 c for k = 0. When the supplier’s information disadvantage is not very 0 < k < 1, with a bad type, supplier 1 always significant. receives a bad signal, but for a good type, he The above result also illustrates how the client’s receives a good signal with probability k < 1. So a information disclosure strategy depends on the distri- good signal (S = g) confirms a good-type client, bution of the client type (measured by c) and the whereas a bad signal (S = b) indicates a bad-type k 1c signal quality (measured by ). The above counterin- client with a probability of 1c (see Equations (2) > c [ 1 c ck tuitive result holds only for Pr(g) Pr(b)or 2. and (3)). This probability (1 )/(1 ) increases So if there is a large proportion of high-cost clients or with k; that is, a higher k leads to a more accurate the signal quality is sufficiently low (i.e., Pr(g) ≤ Pr(b) signal for supplier 1. To illustrate the effect of k on because ck is small), then the client always has incen- supplier 2’s signal quality, we may examine the pos- tives to help the less-informed supplier achieve a terior probabilities of the client type given in Equa- more accurate signal. This can level the competition tions (6) and (7). It can be verified that both PrðG j g~Þ ~ ground and thus induce more aggressive quoting and PrðB j bÞ are increasing in k. That is, a higher k from the suppliers. Otherwise (i.e., Pr(g) > Pr(b) also leads to a more accurate signal for supplier 2. because ck is large) the client’s payoff does not neces- When k = 1, supplier 1’s signals are perfect and sup- sarily increase as the level of information asymmetry plier 2’s signals are least noisy. between suppliers decreases. A useful implication is From the above discussion, we may use k as the that if the client could make investments to either extent to which the client shares information with become a better type (increase c) or improve the sig- both suppliers. Sharing more information improves k, nal quality (increase k), her information disclosure which implies that the quality of both suppliers’ sig- strategy may change accordingly as ck passes the nals improves. Generally speaking, q may also change 1 threshold value 2. as the client shares more information; however, allowing a variable q introduces significant difficul- 5.2. Changing k via Information Sharing ties into the analysis. So, for the analysis below, we The above subsection studies the first question, that focus on the benchmark case where q is fixed. In fact, is, whether the client wants to reduce information now we may view q as a measure of the difference in Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 11 the suppliers’ learning capabilities, which are exoge- We emphasize that even though q is fixed, chang- nously determined. ing k will affect the quality difference between the suppliers’ signals. When q < 1, the suppliers do not PROPOSITION 8. Consider a fixed q < 1, that is, there is benefit symmetrically from the increase in k (i.e., more information asymmetry between the suppliers. (i) When accurate signals). When k increases, both suppliers’ Pr(g) ≤ Pr(b), supplier 1’s payoff is increasing in k, and information quality improves, but the improvement supplier 2’s payoff is always zero. (ii) When Pr(g) > Pr(b), for supplier 2 has to be discounted by q. Therefore, both suppliers’ payoffs are increasing in k. (iii) The the quality difference between the suppliers’ signals client’s expected payoff is always decreasing in k. There- becomes greater as k increases. fore, the client’s optimal decision is to choose the lowest However, notice that the change in quality differ- possible k. ence caused by k and that caused by q have different implications on supplier competition and the client’s Proposition 8 presents a surprising result: improv- payoff. While increasing the quality difference by ing the suppliers’ information always negatively decreasing q is good for the client in certain cases (i.e., q q > impacts the client’s payoff. Why does the client suffer when < 0 and Pr(g) Pr(b)), increasing the quality from more accurate supplier signals? Intuitively, the difference by raising k is always bad for the client. client should be willing to send more accurate signals. Such a distinction can be explained as follows. Recall This will motivate the suppliers to quote more aggres- that changing q only affects the signal quality of the sively because a good signal is associated with a low less-informed party; in contrast, changing k will service cost. However, we find that the opposite is improve both firms’ signals. In particular, it can be true in our model setting. The competitive intensity shown that the suppliers’ expected service cost, between suppliers is lower given more accurate E[C | b], is constant in q but convexly increasing in k. signals. Since E[C | b] is the upper bound of the suppliers’ We next take a closer look at how the suppliers’ quotes, a higher E[C | b] implies less aggressive bids quoting strategies vary with k.Ask increases, sup- from the suppliers. Therefore, while the client may plier 1 is more likely to receive a good signal given a benefit from a greater quality difference caused by good type client. Supplier 1 is more confident that a varying q, a greater quality difference caused by bad signal indicates a bad type client, which suggests increasing k hurts the client. a higher E[C | b]. Proposition 3 shows that the suppli- This study presents an interesting case in which the ers randomize their quotes over ½E½C j g~; E½Cjb when client does not strive to improve suppliers’ informa- Pr(g) ≤ Pr(b). The more accurate signals enable sup- tion in service outsourcing. This complements the plier 1 to better estimate E[C | b] and quote more con- findings in the literature. Milgrom and Weber (1982b) servatively to avoid losses. This will in turn make show that the seller may not share information with supplier 2 compete more cautiously. On the other all bidders when the seller’s information is comple- hand, as k increases, supplier 2 also receives more mentary to only the better informed bidder’s informa- accurate signals. Supplier 2 is more confident that a tion. The complementary information will enhance ~ good signal S ¼ g~ indicates a good type client and is the better informed bidder’s information advantage ~ willing to lower his quote when S ¼ g~. This forces the and thereby hurt the seller’s profit. We find that when suppliers to compete more aggressively. The aggres- the client’s information is complementary to both siveness of the suppliers is determined by the trade- suppliers’ information and the suppliers have distinct off between these two effects. The overall expected abilities to learn from the released information, infor- prices quoted by the suppliers are monotonically mation disclosure may widen the information gap increasing when Pr(g) ≤ Pr(b). This suggests that the between the suppliers and thus dampen the competi- suppliers will compete less aggressively when they tion. As a result, the client has no incentive to disclose are given more accurate signals. any information to the suppliers. When Pr(g) > Pr(b), the suppliers randomize their | quotes over [p,E[C b]] as shown in Proposition 4. 6. Conclusion Increasing k results in a higher E[C | b] and a lower E½C j g~, suggesting that condition (11) is more likely The practice of outsourcing has been increasingly to be met and the suppliers are less willing to lower used in the industry as a competitive strategy in the their prices. Therefore, the lower bound of the sup- fast-changing, global market environment. Under- pliers’ quotes, p, is also increasing. The overall standing how firms should design their outsourcing expected prices quoted by the suppliers are mono- strategies and manage the relationships with the sup- tonically increasing in k when Pr(g) > Pr(b), which pliers is critical to the success of outsourcing. This again suggests less intense competition between the study is motivated by the phenomenon that in many suppliers. outsourcing contexts, the suppliers’ cost for serving a Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing 12 Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society client is dependent on various factors including, the when there is a sufficiently large proportion of high- characteristics of the client. Since the suppliers do not cost clients in the market, the suppliers compete have perfect knowledge about these factors, they do more aggressively when there is a low level of infor- not know the exact cost for serving the client either. mation asymmetry; on the other hand, when the pro- This in turn leads to asymmetrically informed suppli- portion of low-cost clients is large, the supplier ers because they learn about the client through competition could be more intense when the sup- different information sources with diverse informa- plier information asymmetry is either very high or tion accuracy. In this study, we study a client’s out- very low. In IT security outsourcing, for example, sourcing problem where two suppliers compete for this implies that when the client companies generally the client’s service contract under asymmetric beliefs have a robust IT infrastructure, they need to be care- about the service cost. The main findings and insights ful when sharing information because their profit from this study can be summarized as follows. may not monotonically change with the level of We first identify the Bayesian Nash equilibrium of information asymmetry. the suppliers’ game for any given information struc- In this paper, we also study a common situation ture. A pure-strategy equilibrium generally does not where the client can improve the quality of the suppli- exist in the presence of information asymmetry; how- ers’ signals by disclosing more data to both suppliers. ever, we are able to derive the unique mix-strategy Under the presence of information asymmetry equilibrium. It has been shown that in the equilib- between the suppliers (e.g., when the suppliers have rium, the better-informed supplier always enjoys a different learning abilities), we address the question positive (expected) payoff, and it is higher than that of whether sharing more information is beneficial to of the less-informed supplier. The less-informed sup- the client. Interestingly, we find that the client has no plier’s payoff can be either zero or positive, depend- incentive to share any information with the suppliers. ing on the parameter values. This means that in our The reason is that the suppliers will not benefit model framework, both SIA (where only the better- equally from the shared data; in addition, the suppli- informed supplier earns an information rent) and ers’ expected service costs contingent on bad signals DIAs (where both suppliers have positive expected will be higher, which leads to less aggressive quotes. rents) may arise. Therefore, sharing more information with both sup- Then we examine how information asymmetry pliers is detrimental to the client. This suggests that between the suppliers affects the client’s performance. the existence of supplier information asymmetry may It has been found that reducing information asymme- hinder the client’s information sharing effort in out- try between the suppliers does not necessarily improve sourcing. Thus, understanding the information struc- the client’s payoff. In particular, helping the less- ture between suppliers is critical for a client when informed supplier obtain more accurate information devising her information management strategies. about the service cost may hurt the client’s payoff. This is because the bidding behavior of the less-informed supplier depends on his signal: he would compete References more aggressively when the signal indicates a low ser- Allen, J., D. Gabbard, M. Christopher. 2003. Outsourcing Managed vice cost, but less aggressively when the signal indi- Security Services. Carnegie Mellon Software Engineering Institute, Carnegie Mellon University, Pittsburgh, PA. cates a high cost. As improving the signal accuracy Anand, K. S., M. Goyal. 2009. Strategic information management will make the less-informed supplier more confident under leakage in a supply chain. Manage. Sci. 55(3): 438–452. about the true cost, it may induce either more or less Banerjee, P. 2005. Common value auctions with asymmetric bid- competition depending on the realization of the signal. der information. Econ. Lett. 88:47–53. Either of these two effects may be dominant under dif- Cachon, G. P., F. Zhang. 2006. Procuring fast delivery: Sole ferent circumstances. Therefore, the client does not sourcing with information asymmetry. Manage. Sci. 52(6): – always benefit from reducing information asymmetry 881 896. between the suppliers. Chen, F. 2003. Information sharing and supply chain coordination. Handbooks Oper. Res. Manag. Sci. 11: 341–421. The above finding on the impact of information Chen, F. 2007. Auctioning supply contracts. Manage. Sci. 53(10): asymmetry provides useful insight into the client’s 1562–1576. information management strategy. Conventional wis- Cohen, L., A. Young. 2006. Multisourcing: Moving Beyond Outsourc- dom suggests that the client should assist the suppli- ing to Achieve Growth and Agility. Harvard Business School ers with more information gathering in order to level Press, Boston, MA. the playground of competition (see, e.g., Kern et al. Engelbrecht-Wiggans, R., P. R. Milgrom, R. J. Weber. 1983. Com- petitive bidding and proprietary information. J. Math. Econ. 2002). In contrast, we have demonstrated in a reason- 11: 161–169. able setting that sharing information to reduce Friedman, T. L. 2005. The World Is Flat: A Brief History of the supplier information asymmetry may dampen com- Twenty-First Century. Farrar, Straus and Giroux, New York, petition and lower the client’s payoff. To be specific, NY. Zhao, Xue, and Zhang: Outsourcing Competition and Information Sharing Production and Operations Management 0(0), pp. 1–13, © 2013 Production and Operations Management Society 13

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