Corruptible Advice

1

• Corruptible Advice
• Seminar by
• Ganesh Iyer
• (University of California, Berkeley)
• Joint with Erik Durbin (Federal Trade Commission)
• Seminar at
• Marketing Retreat, University of Alberta.
• May 12, 2006

2
Introduction

• Sellers of experience goods offer incentives to
  customers for recommendation to new customers.
• http//money.cnn.com/2004/09/22/real_estate/buying
  _selling/referralsites/
• http//peersuasion.com/what.php
• Logging on for a dream agent Real estate
  referral sites promise to match buyers and
  sellers with the right real estate
  agents.September 27, 2004 532 PM EDT By Sarah
  Max, CNN/Money senior writerSALEM, Ore.
  (CNN/Money) When friends of mine recently
  started shopping for a house, they did what many
  buyers do They asked acquaintances to recommend
  a good real estate agent.

3
Introduction

• Credit rating companies (Moodys, SP, Fitch)
• SP rates 30 trillion in debt representing
  750,000 securities in 2004.
• Raters are paid by the bond issuers rather than
  by investors who use the ratings.
• Consulting business that advice on matters that
  could affect their ratings.
• SPs Risk Solutions helps banks meet Basel 2
  requirements.
• Insist that there is a firewall between Risk
  Solutions and ratings business.
• Film and music critics may receive perks from
  film or recording companies whose products they
  comment on.
• A doctor might receive support from
  pharmaceutical companies whose products they
  might recommend for patients.
• Stock analysts working for an investment bank
  might advise clients on firms from which the bank
  seeks business.

4
Anatomy of the problem

• There are 3 parties
• D Decision maker (new consumer, investors,
  patient)
• A Advisor (existing consumer, analyst, music
  critic, doctor)
• T Third-party (seller, investment bank,
  recording companies, pharmaceutical companies).
• The decision maker D must decide whether or not
  to take an action in an uncertain environment and
  consults an informed advisor.
• Third-party T stands to benefit if the decision
  maker takes the action.
• Advisor has information that affects the optimal
  action and has preferences that are aligned with
  those of the decision maker.
• But T may prefer a particular action and get
  monetary payoffs from it.
• It can therefore offer a payment to influence the
  advisors report which affects the credibility of
  the advisors report.

5
Anatomy of the problem

• Ts interests are well known
• Seller would like new consumers to buy.
• Firm wants an analyst to offer positive stock
  recommendation
• For the advisor there are reputational concerns
• Countering the information corrupting influence
  of T.

6
Characteristics of the game

• A decision maker makes a decision (d0,1) under
  uncertainty and consults an advisor who has
  better information.
• A third-party benefits if D takes a positive
  (d1) decision and can offer a payment (bribe)
  conditional on the decision.
• The advisor cares about his reputation for not
  being corruptible.

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An Extended Marketing ExampleSocial
recommendation of an experience good

• Word of mouth recommendation of real estate
  agents, health clubs, long-distance phone
  services, who are potential new buyers.
• New buyers are uncertain of quality
  Probability of success (or of a good match).
• 0 lt Probability lt 1.
• Seller may offer referral fees (Biyalogorsky,
  Gerstner, Libai, 2001)
• Here they are unobservable payments to influence
  the advice.
• Advisors utility is a composite of pecuniary
  self-interest utility of the friend
  (reputation).
• In the absence of the seller (or if payments are
  observable) advisors preferences are the same as
  that of the friend.

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Main Point

• The presence of third-parties reduces the
  information transmission by advisors who value
  their reputation.
• Bad advisors who do not value their reputation
  might lie about a bad product and mis-report it
  as good.
• But even a good advisor who values reputation
  might lie about a good product and mis-report it
  as bad.
• Bribes can have two types of roles
• Bribes can be used to make the bad advisor lie
  about the bad product / state.
• But with reputational effects, bribes can also be
  used to influence the good advisor to not lie
  about the good state.

9
Literature

• Cheap talk (Crawford and Sobel 1982)
• Advisors, Krishna and Morgan (2001), Sarvary
  (2002)
• Eliciting advice from multiple advisors
  sequentially if they are biased in opposite
  directions.
• Advisor cares about the reputation for accuracy
  (Scharfstein and Stein 1990)
• Example Think about recommending a babysitter to
  your friend.
• Here the advisor cares not for reputation for
  accuracy, but reputation for incorruptibility.
• So it might be that an advisor might send an
  inaccurate message to bolster his reputation.
• Word of mouth literature Ellison and Fudenberg
  (1995), Banerjee and Fudenberg (2001), Godes and
  Mayzlin (2004).
• In this paper word of mouth is not
  automaticinvolves strategic communication by
  advisor who decides what information to
  communicate.
• Morgan and Stocken (2004) analysis of stock
  recommendations.

10
Model

• Two possible states of the world with equal
  probability and they refer to the payoffs for D,
• Example Seller quality might be good or bad.
• Advisor can be bad or good
• Probability that A is good is l
• Decision maker does not observe s or t but
  advisor observes both.
• We start with T knowing state, but not knowing
  advisor type.
• Example, seller knows the product quality, but
  not whether the advisor cares about reputation or
  not.
• Decision makers decision d (0,1) where d 1 is
  a yes decision which generates some payoff.
• Example d1 can mean that the new consumer buys
  the product.

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Model

• If d 1, the decision leads to outcome
  Ssuccess or Ffailure the probability of
  which depends upon the state.
• Value of success G gt 0 and failure is L, L gt
  0.
• Probability
• Expected utility from D choosing d 1,
• T can choose to make a contingent (on d 1)
  payment to A.
• Ts payoffs are (w-q) d.

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Model

• The utility function of A

13
Equilibrium Concept

• Look for a PBE of the game given by,
• In a PBE all players strategies are optimal given
  the beliefs of D.
• Informative and decisive equilibria
• Informative that the message conveys
  information about the state over and above the
  prior
• so Pr(sms) gt Pr(s)
• Decisive Ds action depends on the message.

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Solution strategy

• Describe Ds beliefs given As reporting
  strategy
• Check if this reporting strategy is consistent
  with Ts strategy and Ds actions that would be
  induced.

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Single Known Advisor Type

• If Ts payment is observable, then T cannot
  affect communication and no payments will be
  made.
• So honest communication will always be an
  equilibrium.
• We will analyze the case in which

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Unobservable Payments

• In equilibrium A is honest and D believes As
  report iff
• For honest communication
• Low value of Gvalue for product if it turns out
  to be a good fit should not be too high.
• Zero bribes are paid in equilibrium. Why?
• Because the condition for the equilibrium is that
  T cannot offer a big enough bribe.
• But possibility of bribes reduces information
  transmission.
• As informativeness is the fraction of the range
  over which honest reporting is a PBE.
• Informativeness is decreasing in w but increasing
  in a.

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Uninformed T

• Even when T is uninformed of the state there is
  an incentive to offer payments to influence the
  advisor.
• But the ability to bribe the advisor is weaker
  than when T knows the state
• Because T does not know whether the bribe is
  necessary or not.
• Thus lack of information for the third party
  facilitates honest communication.
• Example, if seller does not know whether the
  product will be a good or bad fit for the
  consumer, there will be more credible information
  transmission.
• If a pharmaceutical firm does not know whether an
  experimental treatment is suitable for a patient,
  then there will be more credible information
  transmission from the doctor to the patient.

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Two third parties

• A patient might have to choose between a
  well-known treatment and a new experimental one.
• A consumer might have to choose between an
  existing product and a new one with uncertain
  value.
• Honest communication exists as long as the
  payoffs of the two third parties are not too
  different.
• There are positive bribes paid even when there is
  honest communication by the advisor.

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Advisor Types

• Fully informative equilibrium with honest
  communication
• when both types of advisors are honest
• Partially informative equilibrium
• Good advisor is always honest, but bad advisor
  accepts payment and recommends purchase.
• Positive bribes are paid in equilibrium. Bribes
  are collected by both types of advisors, but only
  changes the report of the bad advisor.
• What is the function of the bribe?

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T knows As type

• Example, Third-party firms might have greater
  incentive to know about movie critics or stock
  analysts than individual consumers/investors.
• Now T can offer a more efficient bribe.
• This makes honest communication more difficult.

21
Advisor Reputation

• Let A and D interact for two periods.
• Suppose second period payoffs are an increasing
  function of his updated reputation
• The advisors payoff is
• Nothing changes in a full communication
  equilibrium where both types of advisors are
  honest.
• Reputational effects are absent.

22
Advisor Reputation

• Consider the partially informative equilibrium
  where good advisors are honest but bad advisors
  lie.
• Now reputation matters.
• Let the reputation value resulting from mh when
  sl be
• Similarly we can define the reputation value from
  mh when sh

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Solution strategy

• In equilibrium Ts choice of q must be consistent
  with the proposed advisor strategy. The
  advisors strategy implies

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Reputational Updating

• From Bayesian updating by D

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Reputational Updating

• Result
• The advisors reputation always suffers when mh.
• Not only does honest reporting of s h harm the
  advisors reputation,
• But lying about s h establishes the advisor as
  certainly good.
• Thus a good advisor has the incentive to lie
  about the good state.
• Akin to political correctness (Morris 2001) but
  the effect here is due to the endogenous bias
  created by the third-party.

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Reputational Updating Results

• With reputational concerns there can be positive
  bribes offered to the advisors to truthfully
  report the high state.
• All advisors face the reputational cost of truly
  reporting the high state.
• What is the role of bribes here?
• Bribes are a compensation for the loss of
  reputation.
• If the reputational value of incorruptibility is
  substantially higher for the good advisor than
  the bad advisor, then the bribe needed for the
  good advisor will be higher.
• So good advisors have an incentive to misreport
  about the high state.
• Practical implication Conservative reporting is
  a reputation building mechanism.

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Will reputational concerns of A improve credible
communication compared to no reputation?

• Reputational concerns can be bad if,
• T cannot lower the bribe so that bad advisor will
  truly report low state.
• Happens when the value of incorruptibility for
  the bad advisor Vb(1) is low enough and the
  reputational damage from mis-reporting the low
  state is small.
• Reputational concerns can be good if,
• T cannot raise the bribe to induce the good
  advisor to lie about the low state.
• Happens when Vg(1) is high and the good advisor
  stands to suffer a large reputational loss for
  lying about the low state.
• Punch line Greater reputation concern for the
  bad advisor interferes with communication while
  that for the good advisor facilitates
  communication.

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Summary

• With reputation effects even a good advisor has
  the incentive to lie about the high state.
• Bribes can have two types of roles
• Bribes can be used to make the bad advisor lie
  about the bad state.
• But with reputational effects, bribes can also be
  used to influence the good advisor to not lie
  about the good state.
• Conservative reporting is a reputation building
  mechanism.

29
Summary

• Lack of information for the third-party about the
  state facilitates honest communication.
• lack of seller information about product fit for
  customer.
• When T knows As type honest communication
  becomes more difficult.

30
Research possibilities

• Psychological antecedents of honest advice.
• Voluntary disclosure.
• Endogenous price.
• Building reputation for expertise.