Imperfect commitment Santiago Truffa. Agenda 1.“Authority and communication in Organizations”...
-
Upload
archibald-lucas -
Category
Documents
-
view
216 -
download
0
Transcript of Imperfect commitment Santiago Truffa. Agenda 1.“Authority and communication in Organizations”...
Agenda
1. “Authority and communication in Organizations” Wouter Dessein, RES 1999
2. “Contracting for information under imperfect commitment”, Krishna-Morgan (2008)
Authority and communication in Organizations
Introduction:
• Delegation as an alternative to communication
• Information is dispersed in the hierarchy of an organization
• Why an un-informed principal may grant formal decision making rights to an agent who is better informed but may have other objectives?
– To avoid noisy communication - loss of information
Authority and communication in Organizations
Introduction:
• But by delegating authority principal commits never to reverse the agents decision (agency problem)
• Difference in objectives implies strategic behaviour when communicating (cheap talk-since there is no commitment, no mechanism design can elicit the truth), whereas the bias is systematic and predictable (no uncertainty).
• Central trade-off:
Loss of control (under delegation) v/s Loss of information (under comunication
Authority and communication in Organizations
The Model:
• The principal must screen several projects • The agents is better informed, but is biased• Projects cannot be contracted uppon• The principal can only contract on the authority of the project• The the preincipal has 2 choices:
– Delegate (agency problem)
– Order after consulting the agent (strategic inf. transmition)
• Main result:
As long as the divergence in preferences (relative to the principal uncertainty) is not too large, is optimal to delegate control.
Authority and communication in Organizations
The Model:
• There is a continum of projects, only 1 can be selected
• Utility of the principal is max at y=m
–
• Utility of the agent is max at y=m+b
–
rvmRymyUU pp ,,,
0,,, bbmyUU AA
0)0(0);(,, llmylmmUmyU pp
0)0(0);)((,, llbmylmbmUmyU AA
Authority and communication in Organizations
Information structure:
• Only agent (A) observes m, F(m), f(m) supported in • All other parametes are common knowledge• Soft information (not verifiable) Incomplete contracting
approach• Resources Principal (P)
Timming:
1. (P) decides Delegate (D) / Not delegate (ND)
2. (A) observes m. Initiates project if (D), can be asked if (ND)
3. (A) implements project
LL,
Authority and communication in Organizations
Communication v/s Delegation: separate problems
Delegation:
• P and A cannot communicate • If (A) has control implements y=m+b• Then:
• (P) delegates if b<b´ given by:
)(),( blmmUU pp
L
Ly
mdFmylbl )()(min´)(
Authority and communication in Organizations
Communication:• (P) cannot commit to let (A) decide, and communication is feasible• Since the project is non contractible communication can only
change (P) beleives• Bayesian equilibrium:
– i) Family of signaling rules (cond. Prob.)
– ii) Decision rule • if is in the support of q(), then max the utility of the agent
given y() • y(n) max the expected utility of (P) a partition of
)( mnqRNny :)(
LLm , n n
n LL,
Authority and communication in Organizations
Communication:• Let denote a partition of with N steps• • Define
• Proposition 1: If b>0, Then
Exists at least one equilibria where:
(1)
),...,( 0 Naaa LL,
LaaaL N ...10
aaLLaa ,,
dmmfmyUaaya
a
p )(,maxarg),(
)(1)( bNNNstbN )(),( mnqny
iiii aamifmaayq ,1),( 11
Authority and communication in Organizations
Communication:• Proposition 1:
(A)
(2)
(3)
1,..,10),,(),,( 11 NiaaayUaaayU iiiAiiiA
),(),()( 11 iiii aanifaayny
LaLa N 0
Authority and communication in Organizations
Communication:• Equilibrium selection (multiple equilibria):
Pick the equilibria where (P) and (A) utilities are ex-ante maximize
N(b) as large as possible.
• Minimal average size of partition elements (loss of inf):
• Sufficient condition for delegation:
)(
2)(
bN
LbA
4)(
4
)()()(
b
bAbAmyEbmyE
Authority and communication in Organizations
Communication: • Lemma 1
Partition are increasingly large, and a function of b.
Comments: • exagerating is noisy, thus costly to the agent. • Higher the bias, higher the cost of exageration• Higher N(b) better communication… the worse communication
performs relative to delegation
ibaaaa ii 4011
bbNibbN
aabAbN
i
1)(
101 1)(24
)(
1)(
Authority and communication in Organizations
Communication: • Proposition 2:
If F() is Uniformly distributed over , (P) prefers delegation to communication whenever b is sucha that communication is feasible (N(b)=2)
• Corollary:
If F() is Uniformly distributed over , (P) delegates control rights to the agent iff , where b´ is such that the principal is indifferent between an un-informed decision and a biased decision:
LL,
LL,´bb
1
0
)(1
´)( dmmlL
bl
Authority and communication in Organizations
Communication:• Proposition 3:
Consider the most informative equilibrium given b. For any F() in the limit as b tends to zero, a principal who keeps control and communicates is on average an infinite times farther away from m tahn a principal who has delegated control:
Idea: since the partition depends on b (independently of the distribution), the result is robust to changes in probability distributions.
b
myE
b
)(lim
0
Contracting for information under imperfect commitment
Introduction:
• Optimal contracting under imperfect commitment
• Un-informed principal (with authority) and an informed but biased agent (agency problem)
• Principal can commit to pay for advice, but retains authority
Contracting for information under imperfect commitment
Introduction:
• Delegation principle: Informed agent should make the decisions– Agency problem involved---Incentives
• There might be commitment problems associated with delegation of authority
• No commitment power, Cheap talk– What if we allow for the possibility of contractual monetary transfers?
– How does the structure of optimal contracts is affected by the degree to wich the principal can commit?
1. Perfect commitment
2. Imperfect commitment (principal retains power)
3. Full delegation
Contracting for information under imperfect commitment
The model:• Project • State on nature , distributed f• Agent observes • , where is the bias parameter• U is a 2 times continously differentiable:
–
• Bias is commonly known. Principal bias is normalized to 0.• • • If U is a quadratic loss function • Agents gives “costless” advice m, after learning • After earing m, principal chooses y
We suppose quasilinear preferences, and allow for monetary transfers
Ry 1,0
ibyUU ,, ib
0,0,0 131211 UUU
),(maxarg)( yUy
ntdisagreemeybyU )(),(013 )(;),( ybby
Contracting for information under imperfect commitment
The model:
• • I. Contracts with perfect commitment (benchmark) • The principal can specify the project and the transfer as a function
of the message
• Then the revelation principle applies, we can consider direct contracts that satisfy incentive compatibility restrictions
• A direct contract
liabilityitedtwheretyUU p lim,0;),( tbyUU A ),,(
1,0)(),( ty
Contracting for information under imperfect commitment
I. Contracts with perfect commitment (benchmark)
• A direct contract is incentive compatible if is best for the agent to report truthfully
•
• Necessary and sufficient conditions for (IC) contract:
1. y(.) must be non decreasing
2.
)(,),(maxarg
tbyU
)(,),()( ,1
, ybyUt
Contracting for information under imperfect commitment
I. Contracts with perfect commitment (benchmark)• Optimal contract: Is the solution to an optimal control problem:
s.t
Law of motion:
constraints: (FOC agent)
Limmited liability t>0
1
0
)(,max dftyUy
ubyUt ,,1, uy ,
Contracting for information under imperfect commitment
• Proposition 1: Under perfect commitment, an optimal contract (y,t) has the following features
1. Projects y() are non-decreasing in , and st y() is constant over
2. Transfers t() are non-decreasing in , and t() is zero over
3. and if,
1z 1,z
1,z
),()( byy )()(0)( yyt
Contracting for information under imperfect commitment
II. Compensation contracts: Imperfect commitment
• Now the principal can contract on transfers, but not on y()
– M set of messages– T() is the transfer scheme, where T(m)>0
• Perfect Bayesian Equilibrium:
1. Strategy for the agent:
2. Strategy for the principal:
3. A belief function (using bayes rule):
GYu ,,
Mu :RMY :
MG :
Contracting for information under imperfect commitment
Modified revelation principle…
“Given an equilibrium of any (indirect) mechanism, There exists and equilibrium of a direct mechanism that is aoutcome equivalent”
• Proposition 2: In the contracting for information model, consider an indirect contract (M,T) with imperfect commitment and any equilibrium under this contract. Then there exists a pure strategy equilibrium under a direct contract which is outcome equivalent
Then with imperfect commitment, is it possible for the principal to design a contract that induces full revelation???
Contracting for information under imperfect commitment
Truth telling condition :
• Since t is downward sloping, the cheapest contract that induces full revelation is:
);(,),()(,),( tbyUtbyU
)(,),()( 1
ybyUtFOC
)()()( yyu
dybyUt )(,),()(1
1
Contracting for information under imperfect commitment
• Proposition 3: Full revelation contracts are always feasible.
• Proposition 4: Full revelation compensation contracts are never optimal
Idea: assume a contract with pooling on (z,1). For high states the indirect cost of obtaining information (raise the cost for all states), more than offset the small gains (very aligned)
Contracting for information under imperfect commitment
• Optimal compensation contracts:
Full separation is cost effective only in low states
• Proposition 5: An optimal compensation contract involves separation in low states, and pooling in high states.
No Payment for imprecise information
• Proposition 6: In an optimal compensation contract the principal never pays for imprecise information