Strategic Speech: Evidence for a Game-theoretic Model of Indirect Speech Kyle A. Thomas KRAZ Lab 4/9/14

Strategic Speech: Evidence for a Game-theoretic Model of Indirect Speech

Kyle A. ThomasKRAZ Lab 4/9/14

The Initial Puzzle

We don’t communicate like computers

How Do We Understand Each Other?

• Grice’s Cooperative Principle: Conversation partners’ cooperate to convey meaning

• Grice’s 4 Maxims1. Quality—Be truthful2. Quantity—Be succinct3. Relation—Be relevant4. Manner—Be clear

Grice, 1975

The Initial Puzzle


Grice explained how……but not why.

Why Do We Speak Indirectly?

1. Laziness or efficient communication1

2. Violations can carry additional information– “How was your date?”

• “Well, she was really nice. She definitely has an interesting personality. And it turns out we both like tea.”

3. Politeness and saving face2

– “It would be awesome if you were around this weekend to help me move”

4. Humor through encryption3

– A reliable way to ping other peoples’ minds1Searle; 2Brown & Levinson, 1987; 3Flamson & Barrett, 2008

The Initial Puzzle


Grice explained how…

We have explanations for why……but not why.

…but only for some cases.

Explanations Incomplete

• Many indirect utterances don’t fit the mold– “I guess I’ll take care of the dishes…like always”– “Nice shop you’ve got here; it would be a shame if

something happened to it”• Proposal: Some usages of indirect speech are

strategic1

1Pinker, Nowak, & Lee, 2008

Strategic Indirect Speech

• Communicators’ interests not always aligned– Identification problem

1. Plausible deniability with concrete costs– “Perhaps we can just settle this here?”

2. Relationship negotiation with social costs– “Don’t take this the wrong way, but I find you

really interesting, and I’m wondering if you’d like to go back to my hotel room for some coffee”

Deniability Not Always Plausible

• Intended meaning is often obvious…– “Which is odd because the bar was open and

serving coffee” –Rebecca Watson• …But can lead to very different outcomes– “Do you want to sleep with me”• Ruins friendship

– “Do you want to come up for coffee?”• Friendship can be maintained*

*Unless you are dealing with Rebecca Watson

Special Sauce: Common Knowledge

• Infinite recursion of shared mental states– I know that you know that I know, and so on…

• Game theory of common knowledge– Important for switching equilibria in coordination

games1

1Dalkiran, Hoffman, Ramamohan, Ricketts, & Vattani, 2012

Hume, Rousseau Stag Rabbit

Stag 10, 10 0, 5

Rabbit 5, 0 5, 5

Coordination Problems

• Example: Stag Hunt

• 2 Nash equilibria • No dominant strategy– Always better to do what partner does

Problem: Interdependent Expectations

• Hume’s behavior contingent on what he thinks Rousseau will do…

• Rousseau’s behavior is contingent on what he thinks Hume will do…– Which is contingent on what Hume thinks Rousseau will do…

• Generates infinite recursion of beliefs– Start at rabbit-rabbit equilibrium– Need common knowledge to shift to stag-stag

Hume, Rousseau Stag Rabbit

Stag 10, 10 5, 0

Rabbit 0, 5 5, 5

Two Simultaneous Games

1. Identification problem for type

– Depends only on first-order belief from the signal

2. Coordination problem for relationship

– Depends on higher-order beliefs

Interested Not Interested

Signals Goes Upstairs Nothing

Doesn’t Signal Nothing Nothing

Friends Lovers

Friends Friends Ruined Friendship

Lovers Ruined Friendship Lovers

Threading the Needle

• Sufficient first-order knowledge solves ID problem

From Lee & Pinker, 2010

Threading the Needle

• Avoiding common knowledge maximizes coordination game benefits


Is First-order Uncertainty Sufficient?

• Is common knowledge really necessary to explain these results?


?

Two Kinds of First-order Uncertainty

• Ambiguity—Almost common knowledge • Uncertainty due to multiple interpretations• “Let’s meet at the park”– Did he mean Cambridge Common or Boston Common?

• Noisy signal—Common p-belief– Uncertainty due to corrupted signal• E.g., Bad cell phone reception

– “Let’s --et at the Pa--”

Two Kinds of First-order Uncertainty

• ACK—Higher-order knowledge decays– No equilibrium switching

• CpB—Higher-order knowledge doesn’t decay– Equilibrium switching depends on value of p• Probability, p, that message was received

• Could have equal first-order uncertainty– But lead to different coordination outcomes

Dalkiran, Hoffman, Ramamohan, Ricketts, & Vattani, 2012

First-order Second-order Third-order Fourth-order0

10

20

30

40

50

60

70

80

90

100

Almost Common Knowledge vs. Common p-Belief

AmbiguityNoise

Level of Knowledge

Perc

ent C

erta

inty

…CK

Indirect Speech is ACK not CpB

• Indirect speech is ambiguous (ACK)– “Surely, she knows that was a proposition…”• “…But maybe she thinks I think she is naïve…”

– “…And so thinks I don’t think she thinks I think she thought it was a proposition”

– First-order uncertainty; higher-order decay• Interrupted direct speech is just noisy (CpB)– “I’m not sure if she heard me over the loud bus…”• “…But, if she did, what I said was unmistakable”

– First-order uncertainty; no higher-order decay

Experiments

1. Direct test of model assumptions– Are there two games that rely on different levels

of knowledge?

2. Eliminate first-order uncertainty confound– Is first-order uncertainty all that’s required?

3. Demonstration that knowledge levels are causal– If knowledge levels are manipulated directly, can

direct speech mimic an innuendo?

Experiment 1: Testing the Two Games

• Male & Female co-workers, 3 conditions:1. First-order Interested: Female secretly finds out

male is interested in her2. First-order Not Interested: Female secretly finds

out that male is not interested in her3. False Common Knowledge: Female secretly finds

out that male is not into her, but circumstances create false perception he is

• Vignettes on Turk; N = 100; within-subject

What the Hell is False Common Knowledge?

Eric picks up Sara at eight and they go out to the restaurant. Much to Eric’s surprise the restaurant is actually very romantic, just what he was trying to avoid. There are candles everywhere, the lighting is dim, romantic jazz music is playing, the table is set for two, and only couples are seated at nearby tables. A young woman goes from table to table, trying to sell roses to each man to give to the woman he is dining with. The waiter casually mentions to Eric in front of Sara how lucky he is to be on a date with such a beautiful woman. Sara realizes this must have been an accident in planning because she noticed the surprised look on Eric’s face when they entered, and because of the conversation she overheard about Eric’s secret interest in Rebecca. Eric, not wanting to disclose his secret affection for Rebecca or hurt Sara’s feelings, decides not to divulge that he did not intend for the restaurant to be romantic. So, they go ahead and order without saying anything.

Dependent Variables

1. Probability they have sex at some point– (a) Female interested; (b) Female not interested

2. Ease of resuming normal friendship and day-to-day interactions– (a) Female interested; (b) Female not interested

3. Awkwardness for male and female– Nothing happens, not discussed

4. Knowledge-level questions– E.g, Does he know she knows he’s interested?

Experiment 1: Predictions

1. First-order knowledge affects ID game (sex)– First-order Interested > First-order Not Interested =

False CK• More likely to have sex when female is also interested

2. Higher-order knowledge affects coordination game (relationship & awkwardness)– Relationship: False CK < First-order Not Interested

• Harder to resume relationship with False CK

– Awkward: False CK > First-order Not Interested• More awkward with False CK

H1: First-order Knowledge & Sex

First-

order In

terested

First-

order N

ot Intereste

d

False

CK1

2

3

4

5

6

7

Likelihood of sex: Female interested

First-

order In

terested

First-

order N

ot Intereste

d

False

CK1

2

3

4

5

6

7

Likelihood of sex: Female not interested

NS

NS

H2: Higher-order Knowledge and Friendship Damage

First-

order In

terested

First-

order N

ot Intereste

d

False

CK4

4.5

5

5.5

6

6.5

Ease of resuming previous re-lationship: Female interested

First-

order In

terested

First-

order N

ot Intereste

d

False

CK4

4.5

5

5.5

6

6.5

Ease of resuming previous re-lationship: Not interested

H2: Higher-order Knowledge and Awkwardness

First-

order In

terested

First-

order N

ot Intereste

d

False

CK1

2

3

4

5

6

7

Awkwardness for male

First-

order In

terested

First-

order N

ot Intereste

d

False

CK1

2

3

4

5

6

7

Awkwardness for female

Experiment 2: Eliminating First-order Uncertainty Confound

• 3 conditions:1. Direct: “Would you like to come over and have

sex?”2. Direct with noise: “Would you like to come over

and sl--- w--- me?” [masked by loud bus]3. Innuendo: “Would you like to come over and see

my room?”• Vignettes on Turk; within-subject; N = 93

Predictions

• Direct w noise & Innuendo equally uncertain– Lisa’s “probability it was a proposition”– Direct > Direct w noise = Innuendo• Titrated in pilot studies

1. Sex only a function of Lisa’s interest– All speech acts create first-order knowledge

2. Ease of resuming friendship– Direct ≤ Direct w noise < Innuendo

Probability Lisa Thought it Was a Proposition

Direct Noise Innuendo0

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60

70

80

90

100

NS

H1: Likelihood They Have Sex


2

3

4

5

6

7



2

3

4

5

6

7

Likelihood of sex: Female not interested

N.S.

N.S.

H2: Ease of Resuming Friendship


2.5

3

3.5

4

4.5

5

Ease of resuming previous rela-tionship: Female interested


2.5

3

3.5

4

4.5

5

Ease of resuming previous rela-tionship: Not interested

H2: Awkwardness


2

3

4

5

6

7



2

3

4

5

6

7


Experiment 3: Demonstration of Causality

• Are knowledge levels the causal variable?– If manipulated directly, can direct speech behave

like an innuendo?• Guy gives direct proposition to co-worker– In a note• Allows direct manipulation of knowledge levels

• Vignettes on Turk; N = 106; within-subject

Experiment 3: Set Up

Late one night Greg is in the office after Amanda has already left, and he decides to write her a note to let her know how he feels. He begins the note by telling her that he has always enjoyed working with her. Next he tells her that he has been attracted to her as long as he’s known her, but he has never worked up the courage to share his feelings before. He gets swept up in the euphoria of finally sharing his feelings, and every sentence is more revealing and honest than the last. At the peak of this rush he boldly states that, “I think about you all the time. I would love the opportunity to get to know you better, and make love to you like I have imagined in my dreams.” He concludes the note, signs it, and leaves it folded up on her desk with her name on the outside and heads home.

Experiment 3: Conditions

• Guy stops by office next day to pick up files1. Uncertain: Note is gone; her keys on desk2. Second-order: He sees her reading note; she

doesn’t see him3. Third-order: She sees him see her reading

note; he doesn’t see this4. Common Knowledge: They make eye contact

as she looks up while reading the note

Experiment 3: Predictions

1. Probability of sex just function of interest– Only different based on female’s interest– Not related to knowledge-levels

2. Greatest friendship damage in CK condition– Others behave like innuendos– Related to knowledge-levels

3. Most awkwardness in CK condition

H1: First-order Knowledge & Sex

Uncerta

in

Seco

nd-order

Third-ord

er

Common Knowledge1

1.52

2.53

3.54

4.55

5.56


Uncerta

in

Seco

nd-order

Third-ord

er

Common Knowledge1

2

3

4

5

6

7

Likelihood of sex: Not interested

NS

NS

H2: Higher-order Knowledge and Friendship Damage

Uncerta

in

Seco

nd-order

Third-ord

er

Common Knowledge2

2.5

3

3.5

4

4.5

5

Ease of resuming previous rela-tionship: Female interested

Amanda F

irst

Greg Seco

nd

Amanda T

hird

Common Knowledge2

2.12.22.32.42.52.62.72.82.9

3

Ease of resuming previous rela-tionship: Not interested

H2: Awkwardness

Uncerta

in

Seco

nd-order

Third-ord

er

Common Knowledge4.4

4.6

4.8

5

5.2

5.4

5.6


Uncerta

in

Seco

nd-order

Third-ord

er

Common Knowledge4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8


Conclusions

1. Validated two-game assumption of model– Affected by different kinds of knowledge

2. Effect of innuendo not just based on first-order uncertainty– Seems specifically tied to higher-order decay

3. Knowledge levels seem to be causal– If higher-order knowledge manipulated directly, even

direct speech can behave like innuendo– However, even higher-order knowledge short of CK

can have this effect

Thanks

Documents

Strategic Speech: Evidence for a Game-theoretic Model of Indirect Speech Kyle A. Thomas KRAZ Lab 4/9/14