B. K. MISHRA, S. RAGHUNATHAN 375

1

12

1

=

12 2

k

kk

ji

jK

A

aBYBYi

n

f

or

NK

i

(5)

2

*

i

kEq

(6)

2

*

M1

n

kEP

n

(7)

where

1

1

k

Aks

(8)

1

2

12

kks

Bksnks

(9)

2

1

12

kn

Bnk s

(10)

Using the above expressions, Li shows in Proposition

4 that the manufacturer is better off by acquiring infor-

mation from more retailers, and each retailer is worse off

by disclosing his information to the manufacturer in all

circumstances. Therefore, no information sharing is the

unique equilibrium. Li then proceeds to analyze whether

information sharing can be achieved when the manufac-

turer is allowed to compensate retailers for information

disclosure. Li considers the following contract signing

game in the first stage. In the contract, the manufacturer

offers a payment

to each retailer’s private information.

All retailers simultaneously decide whether to sign the

contract. Under this contract, Li shows in Proposition 5

that there exists a

such that complete information

sharing equilibrium Pareto dominates no information

sharing equilibrium if and only if

21sn n 2.

That is, information sharing equilibrium Pareto domi-

nates the no information sharing equilibrium only when s

is sufficiently small and/or n is very large. When n = 2,

information sharing equilibrium does not Pareto domi-

nate no information sharing equilibrium. In Proposition 7,

Li shows that complete information sharing reduces both

the expected total social benefits and the expected con-

sumer surplus given by

22aEQEQ

and

22EQ

respectively, where

**

ii

iK iNK

Qq

q.

3.Our Model and Analysis

3.1. Our Model

It is worth noting that the contract of Li is based on a

fixed payment of

and not on the wholesale price.

However, it is well known that the profits of the manu-

facturer, retailers, and the overall supply chain depend

critically on the wholesale price because of the double

marginalization effect [2]. In a deterministic demand si-

tuation, a higher (lower) wholesale price increases (de-

creases) the manufacturer profit but reduces (increases)

retailers’ and the supply chain’s profits. Li shows the

intuitive result that information sharing will occur only

when the supply chain profit increases as a result of in-

formation sharing. When the manufacturer sets the whole-

sale price first to maximize its own profit, the supply

chain profit improves from information sharing only un-

der certain conditions. When these conditions are sat-

isfied, the manufacturer can indeed use the contract pro-

posed by Li and realize higher profits. However, when

the conditions are not satisfied, information sharing is not

achieved under the side payment contract. We show in

the following paragraphs that if the manufacturer uses a

contract based on the wholesale price then information

sharing equilibrium can be achieved, and the manufac-

turer as well as retailers benefit as well.

The intuition for the contract we propose is based on a

simple proposition2. If the manufacturer and retailers

enter into a contract such that neither the retailer nor the

manufacturer is worse off when information is shared

compared to when information is not shared under all

realizations of the random signals observed by the re-

tailer then information sharing equilibrium will Pareto

dominate the no information equilibrium under all cir-

cumstances. For any set of realizations of the signals, a

higher wholesale price under information sharing bene-

fits the manufacturer and hurts retailers. Consequently if

the manufacturer agrees to not increase the wholesale

price from what he would have charged under no infor-

mation sharing, retailers will not be worse off. As for the

manufacturer, if the manufacturer deems that it will ben-

efit from giving a discount after the information is shared,

it will benefit by offering the discount. If the manufac-

turer neither gives a discount nor raises its price based on

information shared by retailers, the manufacturer will not

be worse off compared to the no information sharing

scenario. Such a contract results in a win-win situation

for both manufacturer and retailers. We formally state

our wholesale price scheme based on discounts as fol-

lows.

Discount scheme: 2Pa DY

where D 0 is the

discount rate if the shared signal is Y 0, and D is equal

to 0 if Y is not shared or Y > 0.

We show that there exists a discount rate D such that

when the manufacturer offers this discount schedule all

retailers will share information and that both retailers and

2It should be emphasized that the contract we propose is not the only

ossible wholesale price based contract to achieve information sharing

equilibrium. Also, several other contracts based on wholesale price as

well as side payments exist that can achieve this equilibrium. Our

choice of the wholesale priced contract is based on the fact the pro-

osed contract is simple to implement and captures discounts, a com-

monly employed method to “buy” retailer information.

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