Information exchange and strategic behavior in supply chains: application to the food sector.

Electronic commerce is altering the nature and organization of industries both in the United States and globally. The adoption of digital and Internet technology is credited for otherwise unexplained increases in U.S. productivity during the 1990s. Understanding the nature of the changes and

their impact on firm behavior and industry structure is crucial for public policy and corporate strategy. This issue is particularly important for the food industry: First, the food industry has been a leader in information technology (IT) initiatives for more than thirty years beginning with the initiative to design the scannable bar code. Second, the industry's thin profit margins could render cost-savings from the adoption of electronic commerce significant, at the margin. Third, the ever-evolving structure of this industry, with ongoing mergers and acquisitions, can be better understood in light of cost and market advantages made possible through the adoption of IT.

This article is an effort to understand the implications of the new digital economy for the informational relationship among firms along the food industry's supply chain. Based on stylized facts, information sharing and information withholding strategies are analyzed between food suppliers and retailers. Using game theory, predictions and hypotheses emerge that largely agree with anecdotal evidence. As most of the existing analytical studies in the food industry focus on the Business-to-Consumer (B2C) aspects of information strategies (e.g., Heim and Sinha 2001a, pp. 264-271; Heim and Sinha 2001b, pp. 286-299), far fewer studies exist that focus on the Business-to-Business (B2B) aspects. Yet, B2B is purported to be a more significant segment of the digital economy, using massive amounts of data to track products through the supply chain to better control quality, inventory, and costs.

A brief history of B2B e-commerce among food retailers begins with Wal-Mart's efforts that incorporated detailed daily sales data to streamline its inventory, reduce costs, and develop strategic inventory replacement plans with key suppliers. In 1992, U.S. food retailers recognized the need to adopt similar practices in order to compete effectively. The result was an initiative known as Efficient Consumer Response (ECR). The initiative faltered due either to the incompatibility of computer systems between retailers and suppliers, or to the absence of computer systems altogether. Equally important was retailers' reluctance to share sales data directly with manufacturers. Later, a similar initiative (1996) known as Collaborative Planning, Forecasting, and Replenishment (CPFR) involved a retailer sharing sales data with a manufacturer (or wholesaler) in real time, often over the Internet, and joining them in inventory replenishment agreements (Kinsey). Internet technology helps to solve the problems of incompatibility but does not resolve the "trust" issue arising from the fear of supplier opportunism. In particular, some retailers fear that suppliers who learn of their inventory, sales, and ordering practices may somehow share this information with rivals or otherwise use it in ways that would diminish retailers' profitability (Kinsey and Ashman). This reluctance is also reported in Clemons and Row, Ryan, and Nakayama.

In the food industry, Nakayama shows that information exchange plays a role in the power relationship between supermarkets and their suppliers, impacting their mutual trust and the adoption of information technology among firms. For example, when the food retailer uses electronic data interchange (EDI) for inventory coordination, the supplier's knowledge of retailer's parameters and strategies could lead to greater monitoring of retailer's sales and the timing of invoices and payments. This reduces the retailer's incentive to share its point of sale (POS) data directly with its supplier(s). This is a classic application of the asset hold-up problem: the retailer's fear of ex post supplier opportunism reduces the retailer's incentive to invest in specific information sharing assets. (1) The trade-off between the need to share information and the need to protect information is best illustrated in the following question that the retailer asks: "What is the minimum set of information to share with my supply-chain partners without risking potential exploitation?" (Lee and Whang). Gal-Or showed how information withholding may be a Nash equilibrium outcome despite its social inefficiency.

Debate in the literature on the market structure of food industry supply chains has important implications for our model. Earlier studies suggest that suppliers exercise monopoly power vis-a-vis retailers. (2) This line of analysis is supported by some recent evidence from survey data (Nakayama). Yet others, for example, Kaufman, point to the consolidation of food retailers and the rise of self-distributing retailers as an indication of a shift toward increased market power of the retailers vis-a-vis suppliers. There is some, though still scanty, evidence on this shift, and advocates of this perspective point to such trends as the increased use of long-term contracts to fix the prices charged by suppliers, the continued use of slotting fees (Patterson and Richards), the revelation of various supply discounts and incentive payments (Anders), and the growth of private labels (American Institute of Food Distribution 2000a, 2000b), as indicative of this shift. (3)

Our reading of the literature suggests that both types of market structures co-exist at present. In 2002, 46% of more than 32,000 supermarkets in the United States belonged to self-distributing chains. They captured one-third of all retail food sales. While there is a trend in the direction of increased market power of the retailers, 31% of supermarkets are still small independent retailers with less than 10 stores. Over half of independent food retailers have only a single store. Market power for such stores still resides with the supplier on the whole (King, Wolfson, and Seltzer).

This article develops a model of information sharing in the food industry that applies to both types of market structures. It begins with the independent retailer model where market power resides with the supplier, and draws out the implications of this market structure for information sharing processes. It then expands the base model by considering many suppliers serving a single retailer, applicable to a world where market power resides with the retailer. Most interestingly, the extended model is robust by being able to explain both industry trends within an integrated formulation, reducing to the base-model when the number of suppliers (n) falls to one.

One key difference between our work and that of an important paper by Rey and Tirole is that, in their work, a manufacture with monopoly power enters into a one-time contract with its retailers before demand or cost uncertainties are resolved, because the goal of that article is to devise efficient contracts, given the uncertainties. In contrast, in this article, informational exchange between the retailer(s) and the supplier is ongoing. We do not focus on the nature of the contract, because the focus here is whether, and if so, how the supplier comes to learn the retailer's information and what this implies for the information-related strategies of the retailer. Our focus is thus to understand the retailer's information strategies (technologies), rather than to explain the nature of the contracts.

Among our findings is that although information sharing reduces procurement and demand uncertainties, only large retailers are willing to share information. We explain why smaller food retailers might withhold sales data from suppliers and the conditions under which this may occur, adding to the predictive value of this study. Our findings are consistent with the summary evidence of a supermarket panel study of 866 stores by King, Wolfson, and Seltzer.

We also find that there is a revealed (or inferred) equilibrium in which suppliers learn retailers' market data even when data are withheld from suppliers. One interesting normative implication is that withholding data leads to an adverse path-dependence effect where the retailer is locked into a "bad" equilibrium.

The next section develops the framework and includes a model of the price and quantity strategies (Stage I game), and their application to food industry. This section presents a simple model where each party is monopolistic downstream (retailer vis-a-vis consumers and supplier vis-a-vis retailer). In this framework, we find that uncertainties about the final demand and procurement errors influence the cost of goods that the supplier charges the retailer. While a retailer is a price taker in the procurement stage, it does act strategically in the information space and is thus able to manage information, deciding whether to share or to withhold market data from its supplier. The derivation of the supply-chain equilibrium under full information sharing is then followed by a model of information management strategies in general, and the possibility of information withholding (Stage II game). The final section extends the basic model to include many suppliers facing a large retailer, comparing the results with those of the base model. Drawing on summary results of the University of Minnesota's Food Industry Center's supermarket panel data by King, Wolfson, and Seltzer, the relation between market structure and IT strategies is discussed. The final section draws concluding remarks and offers possible future extensions.

The Framework

We begin with an uncertain environment in which information exchange (and the associated IT adoption game) occurs between a monopolistic retailer in the consumer product market, facing both demand and supply uncertainties, and a monopolistic supplier that is a retailer's supply source. The supplier may represent a wholesale intermediary, manufacturer, processor, or broker. As mentioned above, the assumption of a single monopolistic supplier reflects only one type of market structure. We later generalize this model to an n-supplier market structure. The assumption of a monopolistic retailer in the product market finds support in earlier studies, for example, Cotterill. More recently, it is the market power of the retailer vis-a-vis suppliers that is at issue. Supporting this assumption is the view that the food industry has been fundamentally transformed from a supply-push to a demand-pull model as developments of scanning technology permit information transmission from final demand, up through the supply chain (Chase, Kinsey 2001). This allows a more complete extraction of consumer surplus by allowing greater product differentiation and price discrimination. To take into account the recent shifts of market power from supplier to the retailer, we extend our basic model in a later section.

The game involves two stages. The first stage is a contemporaneous game in which the retailer is engaged in price and quantity decisions. The second stage involves a sequential game in which the retailer must make long-term decisions on costly investments in information technology, based on possible responses from the supplier. This stage is represented in an extensive game form in which we look for subgame perfect equilibrium outcomes.

Stage I Game: Quantity and Pricing Decisions

Retailer. The retailer maximizes expected profits by choosing the size of orders forwarded to the supplier. Profits are subject to two independent sources of uncertainty: demand uncertainty and supply uncertainty. Of importance is the fact that the effect of demand uncertainty on profits is asymmetric with respect to overestimation or underestimation of the demand. Demand uncertainty arises because final realized demand [q.sub.d] is subject to random stochastic shocks, [delta], in addition to its dependence on the price level, P. This can be written as:

(1a) [q.sub.d] ([delta], P) = a(1 + [delta]) - P /b with

[delta] ~ f(0, [[sigma].sup.2.sub.[delta]] and [delta] [member of] (-1, 1)

where a and b are the parameters of linear demand. (4) In equation (1a) random shocks appear in a relative form. Also, we assume that 8 is symmetrically distributed with a known distribution [delta] and with mean zero and variance [[sigma].sup.2.sub.[delta]]. With a > P, positive realized demand requires that [delta] > -1. Thus, [delta] must have a truncated distribution which is also symmetric (such as truncated normal) so that [delta] [member of] (-1, 1).

The retailer must choose the size of orders, which we call [q.sub.o] to be placed with the supplier. Orders will have to be decided based on the retailer's expectation of demand, given the price level, that is

(1b) [q.sub.o] = E([q.sub.d]) = [[integral].sup.1.sub.-1][q.sub.d]([delta], P)f([delta])d[delta]

= a-P/b.

Equation (1b) thus identifies a relation between orders and the price. This relationship will aid with the retailer's choice of optimum size orders. (More will be said about the order and pricing decision later.) A final relationship that will also be needed is the relation between [q.sub.d] and [q.sub.o] which we get by subtracting equation (1b) from equation (1a):

(1c) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Before we discuss these issues further, a second source of uncertainty must be identified. This is supply uncertainty and occurs due to random procurement errors around [q.sub.o] (see below), which we denote by u:

(2) [q.sub.s] = (1 + u) [q.sub.o] with u ~ g (0, [[sigma].sup.2.sub.[delta]])

and u [member of] (-1,1)

where g is also a symmetric truncated distribution as was the case with f.

Demand and supply shocks arise due to two different, and statistically independent, sources of error: Demand shocks are due to forecasting errors, while over-supply and under-supply shocks reflect coordination difficulties between orders and deliveries due to communication, administrative, or human errors. For example, even companies, such as Campbell Soup, characterized by predictable and stable demand, have observed that resource planning for production, distribution, transportation, and warehousing can be unpredictable, causing supply-chain-wide inefficiencies, which lead to both stock-outs and stockpiles (Fisher). Proctor and Gamble has observed a similar problem in its diaper supply chain (Rai). Moreover, such procurement errors seem to decline with the application of supply-chain Information Technologies. For example, in the nonfood sector, Dell reported a drop in procurement errors from 200 to 10 per million after it implemented its new procurement technology (Perman).

The sequence of retailer's decisions is as follows: (a) Orders [q.sub.o] are placed knowing only the distribution of demand and supply shocks but not the actual shocks. (b) Demand shocks, g, are realized. (c) Price is decided based on the realized demand equation P([q.sub.d]) = (1 + [delta])a - b[q.sub.d] (from equation (1a)) which is the original demand, shifted by an amount [delta]a. This shift in demand is consistent with the excess or shortfall of demand relative to orders seen in equation (1c). To clear the market, the price, say [p.sub.o], is set such that consumer willingness to pay occurs where the quantity demanded equals [q.sub.o] along the new demand schedule. For example, suppose qh is a specific realization of demand. Then, [p.sub.o] [equivalent to] P([q'.sub.d] | [q'.sub.d] = [q.sub.o]) = (1 + [delta])a - [q.sub.o]. Thus, [p.sub.o] depends only on [q.sub.o] and the demand shock, that is, [p.sub.o] = P([q.sub.o], [delta]). (5) (d) Supply shocks, u, are now realized. (e) Since the pricing decision accounts for demand shocks but not supply shocks, any supply shortage vis-a-vis orders ([q.sub.s] < [q.sub.o]) leads to "stock-outs" while any excess ([q.sub.s] < [q.sub.o]) leads to "stockpiles" which are later sold at a reduced price, s (see below for more details).

Orders [q.sub.o] are decided by maximizing expected profits as expected revenue less expected cost. Expected revenue streams differ in different circumstances. Specifically,

(3a) revenue = P([q.sub.o], [delta]) [q.sub.o] if [delta] [less than or equal to] 0

= P([q.sub.o], [delta]) [q.sub.o] if [delta] [greater than or equal to] 0 and u [less than or equal to] 0

= P([q.sub.o], [delta]) [q.sub.o] if [delta] [greater than or equal to] 0 and u [less than or equal to] 0.

Note that in all three cases, P ([q.sub.o], [delta]) reflects consumer's willingness to pay. Also note that in the second term where u [less than or equal to] 0, supply, and not orders, is the binding contraint. (6)

Equation (3a) does not account for ex post overstocks, associated with [q.sub.s] > [q.sub.0]. The possibility of overstock remains because, even with a flexible pricing mechanism that adjusts to realized demand, supply shocks still remain unaccounted for. Unlike stock-outs, overstocks involve accumulation of inventories, leading to a market clearing problem. Since our model is a one-period model and thus no inventories are carried over to the next period, the excess supply must be disposed of, in the same period. We therefore assume an ex post "Sale" model to rapidly eliminate the excess using significant price mark-downs, as is often observed. This requires a second pricing decision within the same (single) purchasing period based on ex post outcomes. The prospect of a "stock-pile effect" can be taken into account a priori. Let s be the revenue loss per unit, due to "below-cost pricing" if [q.sub.o] < [q.sub.s] (or u > 0). For example, if [p.sub.s] is the sale price and [c.sub.T] is total procurement unit cost, then [p.sub.s] < [c.sub.T], and s = [c.sub.T] - [p.sub.s]. Total loss is then S([q.sub.s] < [q.sub.o]). The loss, s, is then sufficient to absorb excess inventories. With this in mind, ex post overstock costs become:

(3b) overstock costs = s([q.sub.s] < [q.sub.o]) if [q.sub.s] > [q.sub.o] (i.e., u > 0).

Later, we decompose [c.sub.T] into the cost of obtaining the product from the supplier, and the operational cost of bringing the product to the market, such as documentation, invoicing, advertisement, etc. Procurement costs are independent of whether orders are too little or too much, compared to the demand. They are, therefore, symmetric with respect to oversupply or stock-outs that stem from demand shocks and can be written unconditionally as [c.sub.T] x [q.sub.o].

We now combine equations (3a) and (3b), and [c.sub.T] to find expected profits. This requires attaching the relevant probabilities to the conditional terms in equations (3a) and (3b):

(4) E([[pi].sub.r]) = P([q.sub.o], [delta])[q.sub.s] x prob([delta] [greater than or equal to] 0, u [less than or equal to] 0)

+ P([q.sub.o], [delta])[q.sub.o] x prob([delta] [greater than or equal to] 0, u [less than or equal to] 0)

+ P([q.sub.o], [delta])[q.sub.o] x prob([delta] [less than or equal to] 0, u [less than or equal to] 0)

- s([q.sub.s], [q.sub.o]) x prob (u > 0) - [c.sub.T][q.sub.o].

We can then use P([q.sub.o], [delta]) = (1 + [delta])a - [q.sub.o] and [q.sub.s] = (1 + u)[q.sub.o] to express equation (4) in terms of [q.sub.o]. Evaluating the density functions over the relevant intervals then yields:

(5) E([[pi].sub.r]) = [1 - 1/2 [[OMEGA].sub.u<0] - [[OMEGA].sub.[delta]<0]

+ (1 - [[OMEGA].sub.u<0])[[OMEGA].sub.[delta]<0]]a[q.sub.o]

- b[1 - 1/2 [[OMEGA].sub.u]<0)[[OMEGA].sub.[delta]>0]][q.sup.2.sub.o]

- 1/2 s[q.sub.o][[OMEGA].sub.u>0] - [c.sub.T][q.sub.o].

In equation (5),

(5a) [[OMEGA].sub.[delta]<0] [equivalent to][absolute value of [[integral].sup.0.sub.[delta]=-1][delta]f([delta])d[delta]]

[[OMEGA].sub.[delta]<0] [equivalent to] [[integral].sup.1.sub.[delta]=0][delta]f([delta])d[delta]]

[[OMEGA].sub.u<0] [equivalent to] [absolute value of [[integral].sup.0.sub.u=-1]ug(u)du]

[[OMEGA].sub.u>0] [equivalent to] [absolute value of [[integral].sup.0.sub.u=-1]ug(u)du].

These terms represent the conditional means of [delta] and u. Although they are pair-wise equal in size ([[OMEGA].sub.[delta]<0] = [[OMEGA].sub.[delta]>0] and [[OMEGA].sub.u>0] = [[OMEGA].sub.u<0]) due to the symmetry of their underlying density functions, they carry different meaning. For example [[OMEGA].sub.[delta]<0] and [[OMEGA].sub.[delta]>0] represent the average size of unanticipated negative and positive demand shocks and [[OMEGA].sub.u<0] and [[OMEGA].sub.u>0] represent the average size of unanticipated negative and positive supply shocks. The latter two are also responsible for supply driven stock-outs and stock-piles, respectively. (Note also that 0 < [[OMEGA].sub.[delta]], [[OMEGA].sub.u] < 1, since [delta] and u are [member of] (- 1, 1).)

Equation (5) shows that adverse demand and under-supply shocks ([[OMEGA].sub.[delta]]<0 and [[OMEGA]u<0) entail a negative scale effect via the first term in equation (5), indicating smaller sales than otherwise possible, but a positive slope effect via the second term. This issue is tied to the market power of the retailer via-a-vis the consumers: For a competitive firm demand is perfectly elastic and b = 0. Then, [[OMEGA].sub.[delta]]<0 and [[OMEGA].sub.u<0 reduce expected profits unambiguously. In contrast, a firm with market power vis-a-vis consumers can adjust prices, moderating the adverse effects of such shocks on profits. In summary:

PROPOSITION 1. Retailers with market power vis-a-vis consumers can better absorb the adverse effects of demand and supply shocks due their price setting ability in coping with unexpected shocks.

Note also that unanticipated excess demand [[OMEGA].sub.[delta]]>0 in equation (5) enters positively via the scale effect a[q.sub.o] but its effect is adjusted downward by the term (1 - [[OMEGA].sub.u<0). The positive effect obtains because excess demand triggers price increases that benefit the firm. But, this benefit is dampened by the stock-out effect from unanticipated supply shortfalls. Finally, the third term, S[q.sub.o][[OMEGA]u>0 is the cost associated with eliminating the stock-pile and equilibrating the market, for example, by price markdowns, as we discussed.

We can simplify equation (5) by taking advantage of the symmetry [[OMEGA].sub.[delta]<0 = [[OMEGA].sub.[delta]>0 to get:

(5') E([[pi].sub.r]) = (1 - [[OMEGA].sub.u<0]/2 - [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0])a[q.sub.o] - b(1 - (1 - [[OMEGA].sub.u<0]/2 - [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0])[q.sup.2sub.o] - s[q.sub.o][[OMEGA].sub.>0]/2 - [c.sub.T][q.sub.o].

The surviving terms, [[OMEGA].sub.>0] and [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0] in equation (5') are worth analyzing. Although the term [[OMEGA].sub.[delta]>0], which represents a positive surprise should, by itself, benefit the retailer, by the latter raising its price, the combined term [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0] represents a stock-out effect and thus a lost opportunity. This is why the term [[OMEGA].sub.[delta]>0] shows up in equation (5) with a positive sign but the term [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0] shows up in equation (5') with a negative sign.

To simplify the presentation from this point on, we define,

(6) [PSI] [equivalent to] 1 - 1/2[[OMEGA].sub.u>0] - [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0]

so that expected profits from equation (5') become:

(5") E([[pi].sub.r]) = [PSI]a[q.sub.o] - [PSI]b[q.sup.2.sub.o] - 1/2s[q.sub.o][OMEGA].sub.u>0] - [c.sub.T][q.sub.o].

Optimizing decision. As mentioned, the firm chooses the order size, [q.sub.o], to maximize expected profits. The first order condition, dE([[pi].sub.r])/d[q.sub.o] = 0, yields,

(7) [q.sup.*.sub.o] = 1/2b a[PSI] - 1/2s[[OMEGA].sub.u>0] - [c.sub.T]/[PSI].

Concavity of expected profits in [q.sub.o] together with [q.sup.*.sub.o] > 0 imply a[PSI] - 1/2s[[OMEGA].sub.u>0] - [c.sub.T] > 0 and [PSI] > 0. From the definition of [PSI] in equation (6), this implies 1/2[[OMEGA].sub.u<0] + [[OMEGA].sub.u<0][[OMEGA].sub.[delta]>0] < 1, imposing a limit on the size of stock-out. Substituting equation (7) into equation (5"), a retailer's best profit level is:

(8) Max{E([[pi].sub.r])} [equivalent to] [[pi].sup.e*.sub.r] = 1/4b[PSI][(a[PSI] - 1/2s[[OMEGA].sub.u>0] - [c.sub.T]).sup.2] = b[q.sup.*2.sub.o][PSI]

where the second form of [[pi].sup.*2.sub.r] in equation (8) comes from equation (7). Note that [[pi].sup.e*.sub.r] > 0 since [PSI] > 0.

Effects of supply and demand shocks. We have seen that unanticipated supply and demand shocks affect expected profits in opposite ways; negatively via scale effect of demand (a) and positively via its slope effect (b). This is the case whether profits are expressed by equation (5) or by equation (5'). This dual effect also shows up in equation (8). However, simple algebra shows that, in all the cases, the scale effect dominates and thus the effect of the shocks is always negative. (7) In short, we have:

(9) [differential][[pi].sup.e*.sub.r]/[differential][[OMEGA].sub.[delta]>0], [differential][[pi].sup.e*.sub.r]/[differential][[OMEGA].sub.u<0], [differential][[pi].sup.e*.sub.r]/[differential][[OMEGA].sub.u>0] < 0, [differential][q.sup.*.sub.o]/[differential][[OMEGA].sub.[delta]>0], [differential][q.sup.*.sub.o]/[differential][[OMEGA].sub.u<0], [differential][q.sup.*.sub.o]/[differential][[OMEGA].sub.u>0] < 0.

PROPOSITION 2 .Retailers' expected profits and orders are adversely affected by unanticipated supply and demand shocks.

Supplier. We assume that the supplier is monopolistic vis-a-vis the retailer. This condition will be relaxed later when we consider many suppliers facing a single retailer. To analyze supplier behavior, we need to first decompose the unit cost [c.sub.T]. Let:

(10) [c.sub.T] = c + [c.sub.o]

where c is the unit cost that the supplier charges the retailer, and [c.sub.o] is the operational costs within the retail firm once the products are received, for example, documentation, advertisement, etc. Then, the supplier profits are given by:

(11) E([[pi].sub.s]) = (c - v)E([q.sub.s]([c.sub.T]))

where v is unit production costs and [q.sub.s]([c.sub.T]) = (1 + u)[q.sup.*.sub.o]([c.sub.T]) by equation (2). In turn, [q.sup.*.sub.o]([c.sub.T]) is given by equation (7), that is, the supplier observes the retailer's downward sloping demand as a function of cost of goods [c.sub.T]. Supplier's expected profits become:

(12) E([[pi].sub.s]) = [[integral].sup.1.sub.-1](c - v)[q.sup.*.sub.o](c + [c.sub.o])

x(1 + u)g(u) du

=(c - v)[q.sup.*.sub.o](c + [c.sub.o]).

Equation (12) shows that a larger c benefits the supplier, to the extent it is passed onto the retailer via the (c - v) term, but also adversely affects the supplier, to the extent that higher product cost dampens retailer's orders (as [differential][q.sup.*.sub.o]/ [differential]c < 0). The supplier balances these trade-offs by optimizing over the choice of c. Substituting for [q.sup.*.sub.o] from equation (7) yields:

(13) dE([[pi].sub.s])/dc = 0 [right arrow] [c.sup.*]

= 1/2 (a[psi] - 1/2 s[[OMEGA].sub.u>0] - [c.sub.o] + v).

From the definition of [psi] in equation (6), notice the following:

(14) [differential][c.sup.*]/[differential][[OMEGA].sub.[delta]>0] < 0.

This inequality is of key significance and worth summarizing:

PROPOSITION 3. A monopolistic supplier acts opportunistically by increasing the supply price it charges the retailer ([c.sup.*]), when it has more information on the final demand facing the retailer.

The intuition behind this proposition is as follows: higher uncertainty implies higher [[OMEGA].sub.[delta]>0]. This increases the retailer's stockouts, reducing expected marginal benefits of sales and, with that, derived demand/orders (see inequality (9)). Reductions in uncertainty reduce [[OMEGA].sub.[delta]>0], shifting up derived demand and with that, the optimal supply price, [c.sup.*]. This proposition suggests that the retail firm might have an incentive to withhold information from the supplier, in order to keep the supplier's estimate of [[OMEGA].sub.[delta]>0] large and thus [c.sup.*] small. This would be especially beneficial if the retailer could itself take advantage of such information without sharing it with the supplier. We will discuss this point more fully in relation to IT adoption strategies of supply chains.

Before we turn to these issues, supplier profits need to be derived. First, output is found by substituting for [c.sup.*], as a component of overall costs [c.sub.T], from equation (13) into equation (7). Supplier profits are then found by substituting for output and [c.sup.*] into equation (12), yielding:

(15) Max{E([[pi].sub.s])}

[equivalent to] [[pi].sup.e*.sub.s] = ([c.sup.*] - v)[q.sup.*.sub.o]

= 1/8b[psi][[a[psi] - 1/2 s[[OMEGA].sub.u>0] - [c.sub.o] - v].sup.2].

Note that the effect of a demand shock [[OMEGA].sub.[delta]>0] on supplier profits is negative (as it was on the retailer's). We can see this for example by totally differentiating equation (12) in [[OMEGA].sub.[delta]>0] so that

[differential][[pi].sup.e*.sub.s]/[differential][[OMEGA].sub.[delta]>0] = [differential] [c.sup.*]/[differential][[OMEGA].sub.[delta]>0] [q.sup.*.sub.o]([c.sup.*]) + ([c.sup.*] - v)[differential][q.sup.*.sub.o]([c.sup.*])/[differential] [[OMEGA].sub.[delta]>0].

Since a[c.sup.*]/[differential][differential][[OMEGA].sub.[delta]>0] < 0 (by equation (14)) and [differential][q.sup.*.sub.o]/[differential][[OMEGA].sub.[delta]>0] < 0 (by equation (9)), then [differential][[pi].sup.e*.sub.s]/[differential][[OMEGA].sub.[delta]]<0 < 0. Similar results are found in the case of supply shocks. In sum,

(16) [differential][[pi].sup.e*.sub.s]/[differential] [[OMEGA].sub.[delta]>0], [differential][[pi].sup.e*.sub.s]/[differential] [[OMEGA].sub.u>0], [differential][[pi].sup.e*.sub.s]/[differential] [[OMEGA].sub.u<0] < 0.

These results are summarized as follows.

PROPOSITION 4. Supplier profits are adversely affected by unanticipated demand and supply shocks. A reduction in these improves both retailer and supplier profits.

Application to the Food Industry

Suppose that the retail firm adopts a strategy (technology) to predict, analyze, and forecast final demand. In the food industry, for example, the retailer could adopt Product Movement Analysis as seen in table 1. These practices make use of POS data that are obtained from scanner technology to better gauge and forecast final demand. In our model, this means [[OMEGA].sub.[delta]<0] would fall. The retailer's adoption of such technologies would also raise supplier profits (first inequality in equation (16)). This gives a supplier the incentive to learn the retailer's information. A supplier could do so by adopting a data sharing technology such as some variant of the well-known CPFR.

However, sharing market data with a monopoly supplier raises a retailer's unit cost as seen by inequality (14). In fact, Nakayama finds that a food retailer's upstream adoption of EDI for order (and inventory) coordination, approximating the concept of CPFR here, results in a tighter control of the retailer's markup by the supplier, in effect raising the retailer's costs. This would reduce the retailer's incentive to share the POS data with the supplier. Faced with this reticence, a supplier may provide the retailer with additional incentives to join the CPFR exercise. One such incentive, as Nakayama finds, is the suppliers' provision of "incremental value added services," for example, analysis and assistance in sales and marketing, providing product information, coordination in shipping and delivery, etc., thereby reducing supply uncertainties. In our model, such data sharing reduce [[OMEGA].sub.[delta]<0] and [[OMEGA].sub.[delta]>0], increasing retailer profits by the second and third inequalities in equation (9).

Yet, a retailer may choose to act strategically vis-a-vis the supplier in information space. Such a retailer observes the dependence of costs on [[OMEGA].sub.[delta]>0], giving it the incentive to use POS data for its own use in order to increase profits (see the first inequality in equation (9)), but to withhold the data from the supplier in order to keep down that part of the product's costs attributable to the supplier, c. Interestingly, we find that the incentive to do so exists, even when this means less order coordination (higher values of [[OMEGA].sub.[delta]<0]), providing an explanation for a retailers' fear of supplier opportunism, for example, retailers' lack of "trust," so often reported in the food industry.

It turns out that even under theses conditions, the supplier can extract some information from the retailer, based on the latter's order history. This theoretical result is supported by evidence in the food industry. Thus Nakayama (p. 198) states, "...suppliers obtain more accurate and timely information on product sales and on their partner's operational status through such EDI transaction sets as purchase orders and product activity." However, we shall see that in some cases, it is possible for the supplier to only partially learn information about the retailer's market. This finding has interesting industry-wide implications. For example, it provides the incentive to the supplier to downwardly integrate as is the case with wholesalers SuperValu and Nash Finch who have acquired a number of retail food stores. The supplier quest to access retailer's valuable POS data, via retailer's internal use of EDI, may be equally matched by the retailer's efforts to protect such information. One way to achieve this is for the retailer to vertically integrate upward, developing its own supplies sources. Evidence on the emergence of both large retailers, for example, Wal-Mart, and self-distributing retailers with their own warehousing capabilities, for example, Krogers, is consistent with this pattern. Such upward integration allows the retailer to internalize "excess" costs (c - v here), as per Williamson.

While we do not consider vertical integration in this paper, we do consider a case where retailers choose more than one supplier, thereby creating competitive pressure on suppliers. This approach is also consistent with the available evidence on the shift of market power to the retailers. In a subsequent section, we show that the supplier's ability to act opportunistically falls along with its market power (reflected in reduced mark-up, c - v), as the number of suppliers, n, increases. However, for now we focus on the small "independent retailer" model. The next section analyzes supply-chain equilibrium with information sharing schemes, using this as a benchmark against the signaling games and the asymmetric information schemes discussed later.

Equilibrium under Information Sharing

Equilibrium in the supply-chain model just described arises from substituting the cost function (13) into the retailer's expected profits (8). Since a component of costs is set by the supplier, the underlying assumption here is that the parameter [[OMEGA].sub.[delta]>0] implicit in equation (8) (via [psi]), is observed by both the supplier and the retailer. In this sense, we have full information equilibrium. Let [[PI].sup.E.sub.r] denote retailer's expected profits under this information sharing equilibrium. Then,

(17) [[PI].sup.E.sub.r] = [[pi].sup.e*.sub.r]([c.sup.*] = b[psi] [q.sup.*2.sub.o]([c.sup.*])

= 1/16b[psi] (a[psi] - 1/2 s [[[OMEGA].sub.u>0] - [c.sub.o] - v).sup.2]

where the second form is found by substituting for [c.sup.*] from equation (13). Equation (17) prepares the groundwork for a retailer who wishes to act strategically in information space based on the realization that the supplier price c depends on its knowledge of the final demand, via [[OMEGA].sub.[delta]>0]. For now, however, we treat equation (17) as the aggregate equilibrium solution with full information and establish some key properties of equation (17). First, the effect of a demand shock, [[OMEGA].sub.[delta]>0], needs to be reexamined. Here, a rise in [[OMEGA].sub.[delta]>0] causes countervailing tendencies: it lowers profits for a given cost (first inequality in equation (9)) but it also reduces optimum costs [c.sup.*] per (13). It is this latter possibility that will be the basis for possible information withholding strategies that might be exercised by the retailer. However, with information sharing strategies, the overall effect of an adverse demand shock is to lower retailer profits. To see this, we first re-express equilibrium profits in equation (17) in terms of optimum profits to find, [[PI].sup.E.sub.r] = 1/4 [[pi].sup.e*.sub.r]|c=v. Differentiating this in [[OMEGA].sub.[delta]>0] yields, [differential][[PI].sup.E.sub.r]/ [differential][[OMEGA].sub.[delta]>0] = (1/4)[differential] [[pi].sup.e*.sub.r]/[differential][[OMEGA].sub.[delta]>0|c=v]. But the latter is negative by equation (9). Thus, by analogy with equation

(9) [differential][[PI].sup.E.sub.r]/[differential] [[OMEGA].sub.[delta]<0] < 0.

Stage II Game: Information Management Strategies

Information sharing strategies between parties in a supply chain are aimed at inventory management and minimization of supply disruptions. Yet, information is often the retailer's strategic asset and the concern that information may be used against him/her may temper the desire to adopt IT. This issue is clear in Nakayama's study of the food industry in which the retailer-supplier power relationship is at the core of the retailer's decision to adopt EDI. Thus, based on his survey of grocery stores, he finds that "there is evidence that power shifts toward suppliers with EDI links" (Nakayama, p. 208). Yet, as related earlier, an alternative perspective points to the rise of an opposite trend, that is, a shift of market power to the retailer. Since independent retailers and large retail giants both seem to co-exist, both perspectives may be valid. We shall pursue the independent retail model in this section and analyze the behavior of a large monopsonistic retailer, facing many suppliers in a subsequent section.

Formal game theoretic approaches have been utilized to study the IT adoption strategies by firms, for example, Dewan, Jing, and Seidman. We carry this analysis further by viewing the retailer's strategy choices as the outcome of a sequential game between the retailer and the supplier. The underlying assumption is that quantity-pricing decisions have a shorter time horizon than IT decisions, allowing for the sequential dimension.

Stylized facts will be used to model our information game. These facts are based on the results from the annual report from The 2002 Supermarket Panel study of 866 supermarket stores (King, Wolfson, and Seltzer). This is shown in table 1. We assume that the food retailer already has scanner technology. Table 1 shows that most food retailers have also adopted the next two tiers of IT, indicated by the first two rows. The first row, Electronic Transmission of Orders to Vendors and Suppliers, which is a proxy for basic EDI technology has the effect of increasing efficiency. This can be captured by a drop in unit operation cost [c.sub.o]. The second row, Product Movement Analysis (PMA), enables the retailer to better estimate, analyze, and forecast market demand. In our model, this means a reduction in [[OMEGA].sub.[delta]>0]. This information is of critical value to the retailer and to its upstream supplier (the wholesaler, distributor, manufacturer, processor, or broker) who could use it to better streamline and manage its inventories. Since this means better alignment of retailer orders with supplier deliveries, that is, a smaller [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in our model, both the retailer and the supplier benefit. This leads to the question of whether a retailer is willing to share this information with the upstream supplier. In table 1 (third and fourth rows), two other technologies, Electronic Transmission of Movement Data to Headquarters (ETMD) and Scanning Data for Automatic Inventory Refill (SDAIR), are grouped under the general title "Data Sharing Technologies" and capture this information-sharing mode. The fact that among the smaller stores (first two columns), a much smaller fraction subscribes to these information sharing technologies than to the technologies of the first two rows, suggests that smaller stores may be the most reluctant group to share information with their suppliers. In the remainder of the article, we will shed light on this finding and discuss the circumstances of information sharing and information withholding modes.

We model the subgame perfect equilibria from the retailer's choice of the most profitable strategy, given the supplier's response to each strategy. These strategies are presented in figure 1, based on the stylized facts just described.

Strategy 1. EDI plus Product Movement Analysis

This is path 1 in figure 1. When the food retailer adopts EDI strategies (table 1, row 1) for order transmission, its cost of handling the product declines. We show this by replacing [c.sub.o] with [c'.sub.o] (with [c'.sub.o] < [c.sub.o]). Adopting PMA (table 1, row 2) facilitates retailer's demand forecasts, reducing demand uncertainties. Thus, [[OMEGA].sub.[delta]>0] falls, for simplicity, we assume it falls to zero. This increases retailer profits (first inequality in equation (9)). But, if this information was also shared with the supplier, supplier profits also increases (first inequality in equation (16)). Thus, the supplier has reasons to provide an incentive to the retailer to share this information. Evidence suggests that in the food industry one such incentive is the supplier's subsidizing of the retailer's use of IT. For our model, we assume that this technology is provided to the retailer at no cost. In addition, the data sharing strategies of ETMD and SDAIR (table 1, rows 3 and 4) entail the added incentive to the retailer that the supplier shares its forecast of the retailers needs. This has the effect of better procurement coordination so that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] falls (we assume again that it falls to zero). Evidence for this behavior in the food sector is also found in Nakayama. Despite these incentives, however, the retailer's adoption of data-sharing strategies may cause an increase in its costs of procuring the goods, because of the supplier's increased opportunism. This is seen from inequality (14), [differential][c.sup.*]/ [differential][[OMEGA].sub.[delta]>0] < 0. In the food industry, evidence supports this finding as suppliers exercise greater control over the independent retailers' mark-ups and promotions, in effect raising their costs. For this reason, the retailer may accept or reject the supplier's initiative. We first consider the supplier's net gains from the retailer's accepting supplier's offer.

Retailer Response 1: Share Information (Full Information Game)

This is shown as the Response Path 1 in figure 1. Sharing POS data means that for both parties, the unexpected shocks in supply and the demand are eliminated ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [[OMEGA].sub.[delta]>0] = 0). Retailer's net gains from this strategy are its equilibrium profits in equation (17), adjusted for the (flow) cost r([F.sub.1] + [F.sub.2]) of financing the two technologies with fixed costs, [F.sub.1] and [F.sub.2], where r is the rate of interest. Also, as mentioned, costs of operation fall from [c.sub.o] to [c'.sub.o] due to the efficiencies introduced by EDI. The result is:

(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

To predict a retailer's behavior, we need to compare [[GAMMA].sub.1] in equation (18) with the net gains from the alternative strategy of withholding information. Thus, we first turn to the case where the retail firm might reject the supplier's offer of sharing information.

Retailer Response 2: Withhold Information (Asymmetric Information Game)

This case, described by the Response Path 2 in figure 1, is the most interesting case to analyze, because it explains why retailers may withhold valuable sales data from suppliers. Consider inequality (14) which says that the supplier increases its unit cost ([c.sup.*]) to the retailer, when it has more information on the retailer's final demand. A retailer acting strategically in the information space observes this dependence of costs on the information available to the supplier. Analytically, this means that although information sharing lowers costs via better supply-chain coordination (thus lowering [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), there may also be a downside, as the supplier can use its market power over the retailer to raise [c.sup.*]. The retailer may then choose to withhold sales information from the supplier. By doing so, it keeps procurement costs [c.sup.*] low and estimate its own final demand.

The IT strategy of the retailer would, in this case, be to reject the suppliers' offer of information sharing technologies (labeled SDAIR and ETMD in table 1), foregoing the benefits of procurement coordination and leaving [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] positive. The fact that the retailer's information is now distinct from the supplier's information points to an information wedge between the two. Thus, we evaluate equilibrium profits (equation (8)) by distinguishing the information available to the retailer ([[OMEGA].sup.r.sub.[delta] > 0), from supplier's information ([OMEGA].sup.s.[delta] > 0). In equation (8), the "own-information" effect enters directly, but the information effect from the supplier operates via costs (equation (13)). From the definition of [PSI] in equation (6) optimal unit cost in this scheme is:

(19) [c.sup.*'] = (1/2) [a (1 - 1/2 [[OMEGA].sub.u<0] - [[OMEGA].sub.u<0] [[OMEGA].sup.s.sub.[delta]<0]) -1/2 s [[OMEGA].sub.u>0] - [c.sub.o] + v].

This yields:

Net Gain of Strategy [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(20) = 1/16b [[a(1 - 1/2 [[OMEGA].sub.u < 0]) - ([c.sup.'.sub.o]) - s/2 [[OMEGA].sub.u > 0] + a[[OMEGA].sub.u < 0 [[OMEGA].sup.s.sub.[delta] > 0]].sup.2]/ (1 - 1/2 [[OMEGA].sub.u < 0]) - r([F.sub.1] + [F.sub.2]).

In equation (20), as in equation (18), operation costs fall from Co to Co. Also, note that [[OMEGA].sup.r.sub.[delta]] = 0 denotes the information gain to the retailer but not the supplier. The latter continues to perceive that [[OMEGA].sup.s.sub.[delta] < 0] > 0. Since [differential] [[GAMMA].sub.2]/[differential][[OMEGA].sup.s.sub.[delta] > 0] > 0, we have the following important result.

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

PROPOSITION 5. The effect of a retailer withholding sensitive market data from its supplier is to increase the retailer's profits, all else equal.

But all else is not equal. Compared to the information sharing scheme (equation (18)), the retailer's information withholding now leads to poor procurement coordination, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. We now determine the equilibrium value of [[OMEGA].sup.s.sub.[delta] > 0] and examine this trade-off.

Multiple Equilibrium and Information Withholding

A key and surprising finding in this case is that despite the retailer's withholding demand data from the supplier, the latter can in fact extract some information, by observing the retailer's order behavior. To establish this, let [q.sup.*r(e).sub.o] be the size of orders expected by the supplier, and [q.sup.*r.sub.o] be the retailer's actual orders. In equilibrium, expectations are realized, implying that [q.sup.*r(e).sub.o] = [q.sup.*r.sub.o], or

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In equation (21), the procurement component of the unit cost, c, is expressed as a function of [[OMEGA].sup.s.sub.[delta] > 0] as per equation (13). The fact that c([[OMEGA].sup.s.sub.[delta] > 0]) shows up to both parties identically in equation (21) is because the retailer is now aware that the supplier perceives [[OMEGA].sup.s.sub.[delta] > 0]. It can therefore manipulate the supplier's information flow. This implies that while the supplier acts strategically in the quantity space, the retailer can act strategically in information space. Beyond that, the retailer operates on its own information set, given by [[OMEGA].sup.r.sub.[delta] > 0]. Setting [[OMEGA].sup.r.sub.[delta] > 0] = 0, as before, and using the optimum quantity equation (7), we get:

In equation (22), [differential][q.sup.*r(e).sub.o]/[differential] [[OMEGA].sup.s.sub.[delta] > 0] < 0 and [differential][q.sup.*r.sub.o]/ [differential][[OMEGA].sup.s.sub.[delta] > 0] > 0 so that, in [q.sub.o] - [[OMEGA].sup.s.sub.[delta] > 0] space, [q.sup.*r(e).sub.o] is downward and [q.sup.*r.sub.o] is upward sloping. Equation (22) then yields two solutions:

(23) [[OMEGA].sup.*1.sub.[delta] > 0] = 0,

[[OMEGA].sup.*2.sub.[delta] > 0] = a (1 - 1/2 [[OMEGA].sub. < 0]) + 1/2 s[[OMEGA].sub.u > 0] + [c.sup.'.sub.o] + [upsilon]/a [[OMEGA].sub.u < 0] > 0.

An important feature of the function [q.sup.*r(e).sub.o] that we will exploit later is that it is discontinuous at [[OMEGA].sup.s.[delta] > 0] = 1/[[OMEGA].sub.u < 0] (1 - 1/2 [[OMEGA].sub.u < 0]) which we define as [[OMEGA].sub.[delta] > 0]. It is seen that,

(24) [[OMEGA].sup.*1.sub.[delta] > 0] < [[OMEGA].sub.[delta] > 0] < [[OMEGA].sup.*2.sub.[delta] > 0].

This means that information converges toward either equilibria, depending on the initial uncertainty about demand. For example, if initial uncertainty is high, so that the demand shock exceeds [[OMEGA].sub.[delta] > 0], then the relevant equilibrium is [[OMEGA].sup.*2.sub.[delta] > 0], while for low levels of initial uncertainty, the demand shock is less than [[OMEGA].sub.[delta] > 0] and the full information equilibrium, [[OMEGA].sup.*1.sub.[delta] > 0] = 0, is achieved. In the latter case, the retailer's attempt to withhold information in fact fails, as the supplier fully infers the retailer's private information. Thus, we can write:

PROPOSITION 6. Depending on the initial level of market uncertainty, supplier inference of the retailer's order behavior leads to information convergence to one of two distinct equilibria: full information equilibrium if initial market uncertainty is low, or incomplete (partial) information equilibrium if initial market uncertainty is high.

The existence of a revealed equilibrium emerging from supplier inference based on retailer's orders is consistent with the food industry evidence (Nakayama, p. 198).

Comparing Strategies 1 and 2

Let [[OMEGA].sup.o.sub.[delta]] > 0] denote some initial mean value of demand shock that is associated with an initial market uncertainty in the absence of any IT strategy. This is shown in figure 2 (Case 1-Case 4). If the retailer adopts the IT strategy 1, the information sharing strategy, it will eliminate this demand uncertainty to itself and to the supplier regardless of the size of uncertainty. Its net gain under this strategy is shown by the flat line in any of the figure 2 (Case 1-Case 4), representing curve [[GAMMA].sub.1] as per equation (18). A retailer gains under the alternative strategy 2, the information withholding strategy, as shown by the Net Gain curve F2 per equation (20). This curve rises in the amount of information that is withheld from the supplier, [[OMEGA]..sup.s.sub.[delta] > 0], which is the horizontal axis. The intersection of the two curves defines a threshold value of say, [[OMEGA].sub.[delta] > 0], between the two strategies, given by equating equations (18) and (20). The figures point to several possibilities, depending on a comparison of the three parameters, [[OMEGA].sub.[delta] > 0], [[OMEGA].sup.*2.sub.[delta] > 0], and [[OMEGA].sup.o.sub.[delta] > 0]. An interesting possibility is that even if information-withholding is a dominant strategy initially, the profit advantage associated with this strategy may not persist. Cases 1-4 below illustrate several of these possibilities corresponding to figure 2 (Case 1-Case 4), respectively. The first three cases all have a high initial uncertainty, so that [[OMEGA].sup.o.sub.[delta] > 0] > [[OMEGA].sub.[delta] > 0], and therefore the retailer finds it profitable to withhold information from the supplier initially (i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).

[FIGURE 2 OMITTED]

Case 1. In this case, the threshold level [[OMEGA].sub.[delta] > 0] exceeds the equilibrium [[OMEGA].sup.*2.sub.[delta] > 0]. Recalling that [[OMEGA].sub.[delta] > 0] corresponds to the discontinuity, then, figure 2 (Case 1) shows that [[OMEGA].sup.*1.sub.[delta] > 0] = 0 < [[OMEGA].sub.[delta] > 0] < [[OMEGA].sup.*2.sub.[delta] > 0] < [[OMEGA].sub.[delta] > 0] <[[OMEGA].sup.o.sub.[delta] > 0]. In this case, even though information withholding initially pays, as the supplier extracts the information content of final demand from retailer orders, the value of [[OMEGA].sup.s.sub.[delta] > 0] falls along the horizontal axis, converging to the equilibrium value of [[OMEGA].sup.*2.sub.[delta] > 0] where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], that is, the profitability condition reverses. (Note that [[OMEGA].sup.*1.sub.[delta] > 0] = 0, cannot be reached due to the dis8>0 continuity at [[OMEGA].sub.[delta] > 0].)

Case 2. Here, the threshold value of [[OMEGA].sub.[delta] > 0] is less than the root value [[OMEGA].sup.*2.sub.[delta] > 0] so that [[OMEGA].sup.*1.sub.[delta] > 0] = 0 < [[OMEGA].sub.[delta] > 0] < [[OMEGA].sub.[delta] > 0] < [[OMEGA].sup.*2.sub.[delta] < 0] < [[OMEGA].sup.o.sub.[delta] < 0](figure 2 .(Case 2)). Information withholding then remains profitable both initially and after convergence to [[OMEGA].sup.*2.sub.[delta] > 0, that is, [[GAMMA].sub.1] > [[GAMMA].sub.2] remains.

Case 3. Here, [[OMEGA].sup.*1.sub.[delta] > 0] = 0 < [[OMEGA].sub.[delta] > 0] < [[OMEGA].sup.o.sub.[delta] < 0] < [[OMEGA].sub.[delta] > 0] < [[OMEGA].sup.*2.[delta] < 0] (figure 2 (Case 3)). The thresh-old value [[OMEGA].sub.[delta] > 0] is less than the discontinuity [[OMEGA].sub.[delta] > 0]. Also, average unanticipated demand shock at the initial state [[OMEGA].sup.o.sub.[delta] > 0] is small enough to be less than [[OMEGA].sub.[delta] > 0], reflecting a stable final demand, but large enough to make information withholding initially profitable (by exceeding [[OMEGA].sub.[delta] > 0]. As is seen from the figure, the Nash equilibrium result of this game is [[OMEGA].sup.*1.sub.[delta] > 0] = 0. This is similar to Case 1, where information withholding is profitable initially but not in equilibrium, due to supplier inference. However, unlike Case 1, supplier learning is now complete as convergence is to full information.

What is striking about Cases 1 and 3 is the possibility that information withholding becomes the chosen strategy, when such a strategy locks the retailer into a lower long run profit than would have been the case under information sharing. This is an illustration of path dependence in supply-chain information games.

Case 4. In contrast to the above, consider a state of low initial uncertainty such that [[OMEGA].sup.o.sub.[delta] > 0] < [[OMEGA].sub.[delta] > 0]. Then, information sharing dominates since [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (figure 2 (Case 4)) and no rational retailer would embark on information withholding strategy.

PROPOSITION 7. If initial uncertainty is high, information withholding is a viable strategy for the retailer, but depending on the information parameters, this strategy can backfire through the supplier learning of the retailer's market, locking the retailer (due to technology irreversibilities) into an inferior strategy, compared to an information sharing strategy in the first place.

Extension to Multiple Suppliers and Single Buyer

To underline the increasingly powerful role of retailers in the food industry as evidenced, for example, by such factors as slotting fees, and by the rise of such giants as Wal-Mart, we extend the previous analysis to the many-supplier case. Our findings shed further light on information strategies in the food industry and explain why larger retailers such as Wal-Mart that purchase from numerous suppliers are more willing to share information with their suppliers, than smaller retailers are.

Assume n identical suppliers, each indexed by i (i = 1,...., n). The retailer orders [q.sup.i.sub.o] from each supplier i with [[summation].sup.n.sub.i] = 1 [q.sup.i.sub.o] = [q.sup.*.sub.o] so that [q.sup.*.sub.o] is the retailer's total orders. [q.sup.*.sub.o] is still given by equation (7). But the profit for each supplier is given by,

(25) E([[pi].sup.i.sub.s]) = c([q.sup.*.sub.o])[q.sup.i.sub.s] - [upsilon][q.sup.i.sub.s]

where c([q.sup.*.sub.o]) is found by solving the order equation (7) (with [C.sub.T] = c + [C.sub.o]) for c:

(26) c([q.sup.*.sub.o]) = (a [PSI] - 1/2 s [[OMEGA].sub.u > 0] - [c.sub.o]) - sb[PSI][q.sup.*.sub.o].

Each supplier maximizes its profit in equation (25), using equation (26), and the constraint [[summation].sup.n.sub.i]=1 [q.sup.i.sub.o] = [q.sup.*.sub.o] leading to the determination of its optimum quantity, [q.sup.i*.sub.s] and price, [c.sup.i*]. Dropping the superscript i (since suppliers are identical) yields:

(27) [c.sup.*] = 1/n + 1 (a[PSI] - 1/2 s[[OMEGA].sub.u >0] - [c.sup.o] + n/n + 1 [upsilon].

If we use equation (6) to substitute for we will find that for n > 1, the derivative [differential][c.sup.*]/[differential][[OMEGA].sub.[delta] < 0] that may be calculated from equation (27) is smaller than it is for a monopoly supplier (equation (13)), that is, more competition among suppliers limits their ability to act opportunistically by raising [c.sup.*]. Also equation (27) reduces to the original cost equation (13) when n = 1, verifying the consistency of the results. Finally, as n rises, the size of mark-up over manufacturing cost v falls, as we would expect In fact as n [right arrow] [infinity], we see that [c.sup.*] [right arrow] [upsilon], that is, the competitive supplier model emerges But equation (27) also shows that the effect of higher manufacturing costs [upsilon] on [c.sup.*] is larger, the larger is n, with the size of the effect varying from 1/2 when n = 1 (our previous results) to 1 when n = [infinity]. The explanation lies in the fact that while a competitive supply structure implies less mark-up, there is, at the same time, less flexibility to absorb the higher manufacturing costs. The result is that an increasing proportion of such costs must be passed down the supply chain. In short,

PROPOSITION 8. Competition among suppliers reduces their ability to act opportunistically and also reduces their market power as indicated by supplier mark-up.

Retailer's Equilibrium Profits under Information Sharing

Substituting for [c.sup.*] above into the retailer's profit equation (8) we find:

(28) [[PI].sup.E.sub.r] = 1/4b [(n/n + 1).sup.2] * [(a [PSI] - 1/2 s[[OMEGA].sub.u > 0] - [c.sub.o] - [upsilon]).sup.2]/ [PSI]

In equation (28), [differential][[PI].sup.E.sub.r]/[differential]n > 0, that is, a more competitive supply structure raises the retailers' profits, as expected. Also, again with n = 1, we regain our previous results, that is, equation (17). Under full information sharing, the retailer's net gain becomes:

(29) Net Gain of Strategy 1 [equivalent to] [[GAMMA].sub.1]

= 1/4b [(n/n + 1).sup.2] [(a - [c.sup.'.sub.o] - [upsilon]).sup.2] -r([F.sub.1] + [F.sub.2]]

reducing to equation (18) when n = 1. Also note that,

(30) [differential][[GAMMA].sub.1]/[differential]n > 0.

PROPOSITION 9. Retailers facing a large number of suppliers are more willing to share sensitive market data with them. This is because as suppliers become more numerous, they become more competitive and less able to act opportunistically.

Evidence of aggressive supply chain and information sharing practices of such firms as Wal-Mart with its numerous suppliers provides support for this finding. This proposition is further discussed in conjunction with proposition 10 below.

Information Withholding Strategies

The approach here mirrors the procedure discussed earlier. Thus, we must first find the retailer's net gain from adopting the information withholding strategy, [[GAMMA].sub.2] (equation (20)) which continues to apply here. However, the previous cost function [c.sup.*'] (equation (19)) now also depends on the number of suppliers and is given by equation (27) This equation thus shows that the retailer acts strategically, not only in the information space as before, but now also with respect to the number of suppliers. Substituting for c* from equation (27) into equation (8), using the definition for [PSI] (equation (6)), and simplifying the result yields:

(31) [[GAMMA].sub.2] = [{(n/n + 1)[a(1 - 1/2 [[OMEGA].sub.u < 0]) - 1/2 s[[OMEGA].sup.u > 0] - ([c.sup.'sub.o] + [upsilon])] + (1/n + 1)a[[OMEGA].sub.u < 0] [[OMEGA].sup.s.sub.[delta] > 0}.sup.2]/4b(1 - [[OMEGA].sub.u < 0) - r([F.sub.1] + [F.sub.2].

This equation reduces to equation (20), when n = 1, verifying the consistency of the results. Now consider the effect of n on the retailer's information withholding strategy. First, as n rises, [[GAMMA].sub.2] rises via the term in the bracket. We can call this, the market power effect because it shows when there are many suppliers, the retailer enjoys higher profits. Second, a rise in n reduces [[GAMMA].sub.2] via the second term. This is the information withholding effect, and shows that information withholding pays less when the retailer has market power vis-a-vis many suppliers. Why is this? Withholding information from a supplier is aimed at preventing supplier opportunism. But a rise in the number of suppliers reduces supplier opportunism. Thus, gains from withholding information diminish. In fact, it is easy to verify that,

(32) [differential]/[differential]n [differential][[GAMMA].sub.2]/[differential][[OMEGA].sup.s.sub.[delta] > 0] < 0.

This is seen in figure 3 by a tilt of the [[GAMMA].sub.2] curve to [[GAMMA].sup.'.sub.2]. Combined with the upward shift of [[GAMMA].sub.1] as n rises, this raises the threshold value [[OMEGA].sub.[delta] > 0] to [[OMEGA].sup.'.sub.[delta] > 0], as shown. Thus, as the number of suppliers increases there is a decrease in the range of uncertainty over which withholding information would pay. In short, Propositions 9 and 10 complement one another. Moreover, they are consistent with the survey results reported in table 1. Of the two types of information sharing technologies reported in that table, 90% of the stores that belong to the largest groups or chains (last column), that is, those with 750 stores or more, use ETMD, and one-third of them use SDAIR. In contrast, these figures fall to only 33-41% and 2-3%, respectively, for the single stores and small chains of up to 10 stores. Stores in the largest chains are more likely to be "self-distributing." Thus, they can realize economies of scale as individual stores' data are aggregated at central distribution centers that, in turn, order from multiple suppliers/manufacturers. In addition, such chains can insure greater price competition by using a large number of suppliers. The resulting loss of market power as the number of suppliers increases, reduces "supplier opportunism" and increases the propensity of the larger stores to share information. Smaller stores do not enjoy the economies of scale to deal with numerous supplier and are therefore subject to supplier market power, limiting, in turn, their propensity to engage in data sharing technologies.

PROPOSITION 10. Large food retailers facing many suppliers are less likely to withhold key market data from their suppliers than smaller food retailers, facing a few large suppliers.

Conclusion

We develop a game-theoretic model of information technology adoption by retail firms along the supply chain, with emphasis on food retailers. The article stresses the strategic dimension of IT adoption decisions from the view point of information sharing. We find that although information sharing reduces procurement and demand uncertainties, only large retailers are willing to share information. We also explain why smaller food retailers might withhold sales data from suppliers. Both findings are consistent with evidence from summary results, by King, Wolfson, and Seltzer, of a supermarket panel study of 866 stores.

We also find that there is a revealed equilibrium in which suppliers learn retailers' market data even when data are withheld from them. One interesting normative implication is that withholding data, based on short-run profitability, leads to adverse path-dependence effects where the retailer is locked into a bad equilibrium.

One of the next steps is to test the propositions with empirical evidence and to extend the model along several lines.

For example, we did not consider the retailers' use of B2B exchanges directly. Food retailers may join a B2B exchange such as Transora using a standardized protocol set by UCCNET (Shulman). Analysis of this issue involves risk versus cost trade-offs, as a salient feature of the internet-based B2B procurement versus traditional EDI systems (Kauffman and Mohtadi).

Other characteristics of the food industry, perishability and high product variety, can be incorporated into our model. Product variety affects b the slope of the demand, because it affects product substitution; perishability affects s or "sale" price, but it probably also strengthens the market power of the retailer (Sexton and Zhang) favoring our Extension model.

Finally, network effects may exist (Katz and Shapiro; Economides; MacKie-Mason Shenker, and Varian). Such effects counter the reluctance to adopt information technology, since they raise the opportunity cost of nonparticipation.

[Received March 2002; accepted October 2004.]

Table 1. Select IT Practices by Retail Food Supply Chains *

                                            Effects on Variables
                                                in the Model

Basic technologies
  Electronic transmission of orders   [c.sub.o] falls (internal
    to vendors and suppliers (a         efficiency improves)
    proxy for traditional EDI)
  Technologies using POS data to
    analyze market demand
      Product movement analysis       [[OMEGA].sub.[delta]<0] falls
        (PMA)                           (better demand forecasts)
Data sharing technologies
  Electronic transmission of          [[OMEGA].sub.u] falls (reduction
    movement data to headquarters       of errors in orders leads
    or key suppliers (ETMD)             to better alignment of
  Scanning data for automatic           orders and deliveries
    inventory refill (SDAIR)            and improved
                                        inventory
                                        management)

                                      Firm Size by the Number of Stores

                                        Single
                                        Stores   2-10   11-50   51-750

Basic technologies
  Electronic transmission of orders      75%     85%     78%     83%
    to vendors and suppliers (a
    proxy for traditional EDI)
  Technologies using POS data to
    analyze market demand
      Product movement analysis          76%     76%     86%     94%
        (PMA)
Data sharing technologies
  Electronic transmission of             33%     41%     85%     82%
    movement data to headquarters
    or key suppliers (ETMD)
  Scanning data for automatic             2%      3%     4%      27%
    inventory refill (SDAIR)

                                      Firm Size by the
                                      Number of Stores

                                            >750

Basic technologies
  Electronic transmission of orders          77%
    to vendors and suppliers (a
    proxy for traditional EDI)
  Technologies using POS data to
    analyze market demand
      Product movement analysis              94%
        (PMA)
Data sharing technologies
  Electronic transmission of                 90%
    movement data to headquarters
    or key suppliers (ETMD)
  Scanning data for automatic                33%
    inventory refill (SDAIR)

* Source: Extracted from the "2002 Supermarket Panel Annual Report," by
King. Wolfson, and Seltzer.

(1) See for example Schmalnesee and Willig, chapters 2-4.

(2) See Bresnahan for a survey of these earlier works.

(3) Private labels are seen as the retailers' way to impose discipline on the proliferation of branded products (Peterson and Connor).

(4) We thank an anonymous referee for pointing us in the direction that led to this specification.

(5) This contemporaneous ability to adjust prices to demand reflects a price agility that is more likely when the retailer has significant market power. In a more competitive retail market such instantaneous price adjustments might not be as easy where firms often set prices in advance, based on competitor's prices as benchmark.

(6) In the case where [delta] [less than or equal to] 0, u [less than or equal to] 0 (first term in equation (3a)), we rule out the possibility of supply shock dominating demand shock ([absolute value of u] > [absolute value of [delta]]) (which would have led to [q.sub.s] as the binding constraint). As a practical matter this is a very unlikely, as it would imply that when demand is depressed, there is not only a supply shortage but that such a shortage dominates the shortfall in demand. Since in today's demand driven supply chains a supply shortage is only likely to arise when demand is unexpectedly high, the current scenario is not very likely to occur. Moreover, its introduction causes significant complications in the mathematical analysis of the distribution functions.

(7) For example, sign[[differential][q.sup.*.sub.o]/ [differential].sub.[delta]>o] = sign[(s/2[[OMEGA].sub.u>0 + [c.sub.T]) x [differential][PSI]/[differential][[OMEGA]u<0]] < 0.

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Hamid Mohtadi is the corresponding author, professor, Department of Economics, University of Wisconsin, Milwaukee, WI 53201. This article was written when the first author was a visiting associate professor at the Department of Applied Economics and The Food Industry Center, University of Minnesota, St. Paul, MN 55108. Jean Kinsey is professor, Department of Applied Economics, and Co-Director, The Food Industry Center, University of Minnesota, St. Paul, MN 55108.

This research is sponsored by a grant from Alfred P. Sloan Foundation through The Food Industry Center at the University of Minnesota. The authors have benefited from insights by Hal Varian, Robert King, and Terry Roe and two anonymous reviewers. Earlier versions of this article were presented at the Universities of Minnesota and Wisconsin. Any remaining errors are the authors'.