Information Sharing between Vertical Hierarchies · ) Interaction between information exchange...

Introduction Model Complete information Asymmetric information Information sharing? Conclusions

Information Sharingbetween Vertical Hierarchies

Marco Pagnozzi Salvatore Piccolo

September 2012

Introduction

Why do competitors share private information?

The essence of an organization is based on the trade-o¤between the costs and bene�ts of communication amongits members (Arrow)

Information sharing agreements are widespread:

Banks exchange information about borrowersSellers share information about consumers�demandFirms disclose information about management�s performance

Introduction

Banks exchange information about borrowers

Sellers share information about consumers�demandFirms disclose information about management�s performance

Introduction

Banks exchange information about borrowersSellers share information about consumers�demand

Firms disclose information about management�s performance

Introduction

Literature

IO: information sharing can increase e¢ ciency or reducecompetition � e.g., Novshek and Sonnenschein (1982),Clarke (1983), Vives (1984) ...

Banking: lenders exchange information to screen investmentprojects or discipline borrowers � e.g., Pagano and Jappelli(1993) ...

Consumers�privacy: sellers use information on consumers toprice discriminate � Acquisti and Varian (2005), Taylor(2004)

... But these papers neglect the source of information

Ganuza and Jansen (2012) show how information sharinga¤ects �rms�incentive to acquire signals about their costs

Literature

Contribution

Principals obtain information through contracting withexclusive and privately informed agents

Principals compete and may share information

) Interaction between information exchange acrossorganizations and agency con�icts within organizations

e.g.: Two competing manufacturers that sell through privatelyinformed retailers and may share the information obtainedfrom them

Link between information sharing and vertical contracting:Calzolari and Pavan (2006) analyze information transmissionin sequential common agency

Contribution

Result

Information sharing a¤ects principals�incentiveto distort agents�output to extract rents

The choice to share information only depends on:

the nature of competition between principals andthe correlation of agents�information

) Principals share information i¤ externalities and correlationhave the same sign

This e¤ect is of �rst-order relative to thosewith complete information

Principals face a prisoner�s dilemmawhen they do not share information

Result

the nature of competition between principals and

the correlation of agents�information

Result

Two principals: P1 and P2

Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2

�θ, θ, with:

Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + αPr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α

) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;

Two principals: P1 and P2Two exclusive agents: A1 and A2

Ai is privately informed about marginal cost θi 2�

θ, θ, with:

Two principals: P1 and P2Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2

�θ, θ, with:

Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + α

Pr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α

�θ, θ, with:

Utilities

Pi pays ti to Ai , and Ai produces qi

Risk-neutral players:

Ai : Ui = ti � θiqi

Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj

� ti

) δ measures production externalities:

strategic complementarity (δ > 0) or substitutability (δ < 0)

We assume δ small and compute expected pro�ts throughTaylor expansions

Limited liability for agents

Utilities

Pi pays ti to Ai , and Ai produces qiRisk-neutral players:

� ti

Utilities

� ti

Utilities

� ti

Utilities

� ti

Utilities

� ti

Contracts

θi can be learned by Pi through private contractingand by Pj through information sharing

Pi o¤ers a direct mechanism: Ai report his cost θi and

without information sharing:

fti (θi ) , qi (θi )g

with information sharing:�ti�θi , θj

�, qi�θi , θj

Ai�s cost can be credibly transmitted by Pi to Pj/Aj

Contracts

�, qi�θi , θj

Contracts

�, qi�θi , θj

Contracts

�, qi�θi , θj

Contracts

�, qi�θi , θj

Timing

1 Principals simultaneously choose whether to commit to shareinformation

2 Ai learns θi3 Principals contract with agents4 Pi discloses her information about Ai�s cost if she hascommitted to do so

5 Agents produce and payments are made

Timing

2 Ai learns θi

3 Principals contract with agents4 Pi discloses her information about Ai�s cost if she hascommitted to do so

Timing

2 Ai learns θi3 Principals contract with agents

4 Pi discloses her information about Ai�s cost if she hascommitted to do so

Timing

Complete information within each hierarchy

Standard duopoly where �rms share cost information(Shapiro, 1986)

Let si = (θi , θj ) if Pj shares information, si = θi if Pj does not

Lemma: Pi�s expected equilibrium pro�t is

V �i = κ+(Esi [q�i (si ) jθi ]| {z }

average of q�i (si )

)2+Esi [q�i (si )�Esi [q

�i (si ) jθi )jθi ]]

2| {z }variance of q�i (si )

and expected output is the same regardless of principals�communication decisions

) Principals maximize output volatility

V �i = κ+(Esi [q�i (si ) jθi ]| {z }

Complete information

Proposition: With complete information: both principalsshare information if α > �ν (1� ν); no principal shareinformation if α < �ν (1� ν)

Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) butIf α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:

e.g., if δ > 0 outputs are more similar in those states

Proposition: Principals�information sharing decisions alwaysmaximize their pro�ts

Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) but

If α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:

Asymmetric information

Since principals learn their agents�costs through contracting,agents earn an information rent

Principals want to distort outputs to minimize rent

Principals want to a¤ect rival�s output to increase pro�t(because of externality)

3 subgames:

1 No communication2 Bilateral information sharing3 Unilateral information sharing

3 subgames:

3 subgames:1 No communication

2 Bilateral information sharing3 Unilateral information sharing

3 subgames:1 No communication2 Bilateral information sharing

3 Unilateral information sharing

3 subgames:1 No communication2 Bilateral information sharing3 Unilateral information sharing

No communication

Pi maximizes

EθjEθi [S (qi (θi ), qe (θj ))� θiqi (θi ) jθi ]� ν∆θqi (θ)

First-order conditions are

Eθ [S1 (qe (θ), qe (θj )) jθ] = θ,

�S1(qe (θ), qe (θj ))jθ

�= θ + ν

1�ν ∆θ.

) Type θ produces the output that equalizes marginal bene�tto marginal costType θ�s output is downward distorted to reduce agents�rent

No communication

Pi maximizes

Eθ [S1 (qe (θ), qe (θj )) jθ] = θ,

�= θ + ν

1�ν ∆θ.

No communication

Pi maximizes

Eθ [S1 (qe (θ), qe (θj )) jθ] = θ,

�= θ + ν

1�ν ∆θ.

No communication

Proposition. When principals do not share information:

� qe (θ) < q�(θ)

� qe (θ) > q�(θ) i¤ δ < 0

Because of production externalities, the low-cost agent�soutput is distorted since principals expect rivals to produceless to reduce information rents:

If goods are substitutes (complements), Aj�s lower outputinduces Ai to produce more (less)

No communication

Proposition. When principals do not share information:� qe (θ) < q�(θ)

� qe (θ) > q�(θ) i¤ δ < 0

No communication

� qe (θ) > q�(θ) i¤ δ < 0

No communication

� qe (θ) > q�(θ) i¤ δ < 0

No communication

� qe (θ) > q�(θ) i¤ δ < 0

Bilateral information sharing

Contracts specify qi and ti contingent on (θi , θj )

Relevant constraints:

Ui�θ, θj

�= ti

�θ, θj

�� θqi

�θ, θj

�� 0 8θj ,

Eθj [Ui (θ, θj ) jθ] � Eθj

�ti�θ, θj

�� θqi

�θ, θj

�jθ�

) Pi maximizes:

EθjEθi [S (qi (θi , θj ) , qe (θj , θi ))� θiqi (θi , θj ) jθi ]

� ν∆θEθj

�qi (θ, θj )jθ

�(No full surplus extraction due to limited liability)

Ui�θ, θj

�= ti

�θ, θj

�� θqi

�θ, θj

�� 0 8θj ,

�ti�θ, θj

�� θqi

�θ, θj

�jθ�

) Pi maximizes:

� ν∆θEθj

�qi (θ, θj )jθ

Ui�θ, θj

�= ti

�θ, θj

�� θqi

�θ, θj

�� 0 8θj ,

�ti�θ, θj

�� θqi

�θ, θj

�jθ�

) Pi maximizes:

� ν∆θEθj

�qi (θ, θj )jθ

(No full surplus extraction due to limited liability)

Ui�θ, θj

�= ti

�θ, θj

�� θqi

�θ, θj

�� 0 8θj ,

�ti�θ, θj

�� θqi

�θ, θj

�jθ�

) Pi maximizes:

� ν∆θEθj

�qi (θ, θj )jθ

Necessary and su¢ cient �rst-order conditions:

S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,

S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν

Pr(θj jθ)Pr(θj jθ)

∆θ 8θj

) No distortion for θ and downward distortionfor θ to reduce information rentsDistortion increases with Pr(θj jθ)

Pr(θj jθ)since:

Pr�θj jθ

�measures how often Pi pays rent to type θ

Pr(θj jθ) measures how often output is ine¢ cient

Pr(θjθ)Pr(θjθ) >

Pr(θjθ)Pr(θjθ) , α > 0,

) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely

S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,

S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν

∆θ 8θj

) No distortion for θ and downward distortionfor θ to reduce information rents

Distortion increases with Pr(θj jθ)Pr(θj jθ)

since:

Pr�θj jθ

S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,

S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν

∆θ 8θj

Pr(θj jθ)since:

Pr�θj jθ

S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,

S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν

∆θ 8θj

Pr(θj jθ)since:

Pr�θj jθ

S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,

S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν

∆θ 8θj

Pr(θj jθ)since:

Pr�θj jθ

S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,

S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν

∆θ 8θj

Pr(θj jθ)since:

Pr�θj jθ

Proposition. If both principals share information,

qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision

The output of type θ is ine¢ ciently low

Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:

if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less

) Strategic linkage between Pi�s output and Aj�s cost

qe (θ, θ) = q�(θ, θ)

qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision

qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θj

qe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision

qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0

Expected output does not depend on principals�communication decision

if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces less

if δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less

Unilateral information sharing

Pi shares information, Pj does not

FOCs areEθj

�S1(qei (θ), q

ej (θj , θ))jθ

�= θ

�S1(qei (θ), q

ej (θj , θ)jθ

�= θ + ν

1�ν ∆θ

S1(qej (θ, θi ), qei (θi )) = θ 8θi

S1(qej (θ, θi ), qei (θi )) = θ + ν

1�νPr(θi jθ)Pr(θi jθ)

∆θ 8θi

Pi conditions her contracts only on θi , while Pj conditions hercontract on θj and θi

) Pj has a competitive advantage relative to Pi since she canimpose a higher distortion in the less likely states

FOCs areEθj

�S1(qei (θ), q

ej (θj , θ))jθ

�= θ

�S1(qei (θ), q

ej (θj , θ)jθ

�= θ + ν

1�ν ∆θ

∆θ 8θi

FOCs areEθj

�S1(qei (θ), q

ej (θj , θ))jθ

�= θ

�S1(qei (θ), q

ej (θj , θ)jθ

�= θ + ν

1�ν ∆θ

∆θ 8θi

FOCs areEθj

�S1(qei (θ), q

ej (θj , θ))jθ

�= θ

�S1(qei (θ), q

ej (θj , θ)jθ

�= θ + ν

1�ν ∆θ

∆θ 8θi

Do principals share information?

Proposition: When agents are privately informedabout their marginal costs:

� If δα < 0, there is a unique equilibrium in dominant strategiesin which both principals share information

� If δα > 0, there is a unique equilibrium in dominant strategiesin which no principal shares information

� If δ = 0, principals are indi¤erent betweensharing information or not

Intuition

Principals share information i¤ δα < 0

If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:

Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less

The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude

Intuition

Suppose that α > 0

If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less

Intuition

Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)

This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less

Intuition

Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces less

This reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less

Intuition

The value of communication

Proposition. Principals�expected pro�ts are higher whenthey both share information than with no communication

Since costs are correlated, communication creates aninformational externality that reduces agents�rent

(For small externalities, this e¤ect is stronger thanthe strategic e¤ect due to correlated distortions)

Corollary. Principals�decision not to share information whenδα > 0 does not maximize their joint pro�ts

Conclusions

When do principals independently choose to share theinformation obtained from informed agents?

Principals want to:

a¤ect rivals�strategies because of externalitiesreduce agents�information rents

Incentive to share information only depend on the sign of δα

Conclusions

Principals want to:

Conclusions

Principals want to:

a¤ect rivals�strategies because of externalities

reduce agents�information rents

Conclusions

Principals want to:

Conclusions

Principals want to:

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