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Licensed Unlicensed Requires Authentication Published by De Gruyter February 19, 2014

Cheap Talk and Editorial Control

Jonathan Newton

Abstract

This paper analyzes simple models of editorial control. Starting from the framework developed by Krishna and Morgan (2001a), we analyze two-sender models of cheap talk where one or more of the senders has the power to veto messages before they reach the receiver. A characterization of the most informative equilibria of such models is given. It is shown that editorial control never aids communication and that for small biases in the senders’ preferences relative to those of the receiver, necessary and sufficient conditions for information transmission to be adversely affected are (i) that the senders have opposed preferences relative to the receiver and (ii) that both senders have powers of editorial control. It is shown that the addition of further senders beyond two weakly decreases information transmission when senders exercising editorial control are anonymous, and weakly increases information transmission when senders exercising editorial control are observed.


This paper has its genesis in a chapter of my PhD completed at the University of Cambridge. I thank Robert Evans for his kind advice, as well as the editor and two anonymous referees. The author is the recipient of a Discovery Early Career Researcher Award funded by the Australian Research Council.


Appendix A

Γ(2): only sender 2 can block, opposed biases

In Period 2, S2 decides to “block” B or “allow” AS1’s message.

Strategies for S1 and S2 are:

  1. s1(θ):θM. For example, a strategy could be to inform R of the correct state or to inform R whether θ is below or above 1/2.

  2. {s21(θ):θM,s22(θ,m1,m2):θ×M×M{B,A}}. For example, a strategy could be to inform R of the correct state and never block, or to block m1 when it indicates the state is below a certain threshold and otherwise give no further information.

Fully revealing equilibrium

Let s1(θ)=θ, s21(θ)=θ+2b2 when θ[0,12b2], s21(θ)=θ2b2 when θ>12b2. Let:

m1,m2,θ:s22={A,U2y(m1,m2),θ,b2U2(0,θ,b2)B,otherwise.

If R observes (m1,m2) consistent with these equilibrium strategies then μ(θ=m1|(m1,m2))=1. If R observes (m1,m2) which are inconsistent with these equilibrium strategies then μ(θ=m1|(m1,m2))=1 when U2(m2,m1,b2)>U2(m1,m1,b2), μ(θ=m2|(m1,m2))=1 when U2(m2,m1,b2)>U2(m1,m1,b2). Hence S2 is believed only when it would not be profitable to him for R to believe his message when S1’s message correctly indicates θ. Set:

μ(θ=0|block)=1.

Γ(O): both senders can block own message, opposed biases

In Period 2 S1 and S2 decides to “block” B or “allow” A their own messages.

Strategies for S1 and S2 are:

si1(θ):θM,si2(θ,m1,m2):θ×M×M{B,A}.
z(s1,s2,θ):={s11(θ),s21(θ)ifs12θ,s11(θ),s21(θ)=s22θ,s11(θ),s21(θ)=A(block,s21(θ))ifs12θ,s11(θ),s21(θ)=B,s22θ,s11(θ),s21(θ)=As11(θ),blockifs12θ,s11(θ),s21(θ)=A,s22θ,s11(θ),s21(θ)=B(block,block)ifs12θ,s11(θ),s21(θ)=B,s22θ,s11(θ),s21(θ)=B

Fully revealing equilibrium

Let s11(θ)=θ, s21(θ)=θ+2b2 when θ[0,12b2], s21(θ)=θ2b1 when θ>12b2. For all m1,m2,θ, let:

s12={A,U1y(m1,m2),θ,b1U1(1,θ,b1)B,otherwise.
s22={A,U2y(m1,m2),θ,b2U2(m1,θ,b2)B,otherwise.

If R observes (m1,m2) consistent with these equilibrium strategies then μ(θ=m1|(m1,m2))=1. If R observes (m1,m2) which are inconsistent with these equilibrium strategies then μ(θ=m1|(m1,m2))=1 when U2(m2,m1,b2)>U2(m1,m1,b2) and/or m2<m12b1. Otherwise, let μ(θ=m2|(m1,m2))=1. Hence S2 is believed only when it would not be profitable to him for R to believe his message when S1’s message correctly indicates θ. Set:

μθ=m1|(m1,block)=1,μθ=1|(block,m2)=1,
μθ=1|(block,block)=1m1,m2M.

Note that for given m1, the lowest y that could be induced by S2 is m12b1, so S2 can never incentivize S1 to play B.

Γ(obs): both senders can block all messages, blocker observed, opposed biases

Strategies for S1 and S2 are as in Γ(B).

z(s1,s2,θ):={s11(θ),s21(θ)ifs12θ,s11(θ),s21(θ)=s22θ,s11(θ),s21(θ)=Ablock1ifs12θ,s11(θ),s21(θ)=B,s22θ,s11(θ),s21(θ)=Ablock2ifs12θ,s11(θ),s21(θ)=A,s22θ,s11(θ),s21(θ)=Bblock12ifs12θ,s11(θ),s21(θ)=B,s22θ,s11(θ),s21(θ)=B

Equilibrium with blocking area of size 2b2

Let s11(θ)=θ, s21(θ)=θ+2b2 when θ[0,14b2). Let s11(θ)=θ, s21(θ)=θ2b1 when θ[14b2,12b2). Let S11(θ)=1b2, s21(θ)=1b2 when θ[12b2,1]. If R observes (m1,m2) consistent with these equilibrium strategies then μ(θ=m1|(m1,m2))=1. If R observes (m1,m2) which are inconsistent with these equilibrium strategies and m112b2 then let μ(.|(m1,m2))Uniform[12b2,1]. If m1<12b2 and either

(i)m1<14b2andm2>m1+2b2,or
(ii)m114b2andm12b1<m2<m1

then μ(θ=m2|(m1,m2))=1. Otherwise, let μ(θ=m1|(m1,m2))=1. Beliefs when blocking occurs are

μ(.|block1)=μ(.|block12)Uniform[12b2,1],
μ(θ=1|block2)=1.

Let y(z) be determined by these beliefs. Let

si2={A,Uiy(m1,m2),θ,bi>Ui(blocki,θ,bi)B,otherwise.

Note the strict inequality above and that in this equilibrium both S1 and S2 play B when θ[12b2,1].

Fully revealing equilibrium with n>2 players

Let μ be such that if z=(m1,,mn), mi=m for a majority of i{1,,n}, then μ(θ=m|z)=1. If z=(m1,,mn) and no message is sent by a majority of senders, let μ(θ=m1|z)=1. If bi>0, then let μ(0|blocki)=1. If bi<0, then let μ(1|blocki)=1. For other blocking possibilities, let μ(0|blockjk)=1. Let y(z) be determined by these beliefs.

For all θ, for 1in, let si1(θ)=θ. Let

si2(θ,m1,,mn)={A,Uiy(m1,,mn),θ,biUi(blocki,θ,bi)B,otherwise.

Appendix B

We construct a non-monotonic equilibrium when b1=b2=12. We divide the available messages of Γ(B) into two sets of messages ϕ1,ϕ2 so there are in effect only two messages available to the senders. R’s beliefs are as follows:

μ(θ|(ϕ1,m2))U110,210m2
μ(θ|(ϕ2,ϕ1))U110,210
μ(θ|(ϕ2,ϕ2))U0,110210,1
μ(θ=0|block)=1

Equilibrium strategies for the senders are then as follows:

θ0,110210,1,s11(θ)=s21(θ)=ϕ2
θ110,210,s11(θ)=s21(θ)=ϕ1
si2={A,Uiy(m1,m2),θ,biUi(0,θ,bi)B,otherwise.

References

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  1. 1
  2. 2
  3. 3

    Krishna and Morgan (2001b) also study the case where the two senders send messages sequentially rather than simultaneously. In such a model, it is impossible to achieve full revelation of private information. As the goal of the paper is to present the simplest model of editorial control, the author chooses to present results stemming from the simultaneous senders model.

  4. 4

    Although both experts have the same information, the sender with editorial control can still gain from employing a further sender when payoffs are compared to equilibrium payoffs of the one sender game.

  5. 5

    Such a situation is by no means unusual. Research for policy formation bodies – “think tanks” – is often undertaken by people who are by no means experts in any sense of the word. The entire weight attributed to their opinions comes from the fact that they are operating under the aegis of a well-known organization. Were they to leave the organization and write some research on their own it is unlikely that many people would read it or that any press coverage would be achieved.

  6. 6

    For example, in every UK general election since 1992, at least 28% of readers of the most read newspaper in the United Kingdom, the Sun, have voted for the largest party opposed to the party supported by the newspaper. The Sun supported the Conservatives in 1992, 2010; Labor in 1997, 2001, 2005. Source: http://www.ipsos-mori.com/researchpublications/researcharchive/2476/Voting-by-Newspaper-Readership-19922010.aspx.

  7. 7

    As of January 7th 2012, English Wikipedia contained 3,840,444 articles. During 2011 there were 59 requests to open arbitration cases, only 13 of which were accepted. 16 cases were heard and settled by the arbitration committee in 2011. See: http://en.wikipedia.org/wiki/Wikipedia:Requests for arbitration/Statistics 2011

  8. 8

    In the context of Wikipedia, such a reduction in anonymity is provided by the availability of the IP addresses of those who make changes to articles. This information can be used to identify possible editing by interested parties, such as edits of the biographical information of US congressmen via congressional IP addresses. See: http://en.wikipedia.org/wiki/U.S. Congressional staff edits to Wikipedia.

  9. 9

    For example, if there existed a message “black” that a sender sent in equilibrium when the state was “white” then the “meaning” of “black” would be “white”.

  10. 10

    Non-monotonic equilibria do exist. An example is given in Appendix B.

  11. 11

    We note that criticisms of Krishna and Morgan (2001a) also apply to the current paper. In particular, the equilibrium constructions rely on the perfect observation of the θ by the senders (Battaglini 2002). It is plausible to think that disagreement between senders over the state of the world could be a reason for message blocking. The current paper abstracts from such possibilities to focus on strategic considerations.

  12. 12

    This is similar to the observation of Dessein (2002) that R may want to commit to playing the best action for the sender (allow the sender to choose the action) to induce full revelation.

Published Online: 2014-2-19
Published in Print: 2014-1-1

©2014 by De Gruyter

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