Signaling under Common and Conflicting Interests IRCS Common Ground - - PowerPoint PPT Presentation

Conflicts Signaling Games Cycles Conclusions

Signaling under Common and Conflicting Interests

IRCS Common Ground Seminar Christopher Ahern Joint work with Robin Clark

University of Pennsylvania

September 18, 2013

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Conflicts Signaling Games Cycles Conclusions

Goals

Effect of conflicting interests on signaling in a population. What does conflict do? How do we use signals? Where does language go?

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Conflicts Signaling Games Cycles Conclusions

Talk Outline

1

Conflicts

2

Signaling

3

Games

4

Cycles

5

Conclusions

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Conflicts Signaling Games Cycles Conclusions Philosophy

Hobbes (1651)

In such condition there is no place for industry, because the fruit thereof is uncertain, and consequently, not culture of the earth,...no arts, no letters, no society, and which is worst of all, continual fear and danger of violent death, and the life of man, solitary, poor, nasty, brutish, and short.

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Conflicts Signaling Games Cycles Conclusions Philosophy

Locke (1690)

The state of nature has a law of nature to govern it, which obliges every one: and reason, which is that law, teaches all mankind, who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions.

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Conflicts Signaling Games Cycles Conclusions Philosophy

Hobbes: Better at self-promotion

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Conflicts Signaling Games Cycles Conclusions Philosophy

Leviathan: Better album name

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Conflicts Signaling Games Cycles Conclusions Biology

Tennyson (1850)

Who trusted God was love indeed And love Creation’s final law– Tho’ Nature, red in tooth and claw With ravine, shriek’d against his creed– Who loved, who suffer’d countless ills, Who battled for the True, the Just, Be blown about the desert dust, Or seal’d within the iron hills?

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Conflicts Signaling Games Cycles Conclusions Biology

Dawkins (1976)

We are survival machines – robot vehicles blindly programmed to preserve the selfish molecules known as genes. Any altruistic system is inherently unstable, because it is open to abuse by selfish individuals, ready to exploit it.

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Conflicts Signaling Games Cycles Conclusions Biology

Richard Dawkins and the Selfish Gene: Good band name

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Conflicts Signaling Games Cycles Conclusions

Crucial points for Signaling

1

Cooperation

2

Honesty

3

Mechanisms

4

Language

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Conflicts Signaling Games Cycles Conclusions Cooperation

Nowak (2006)

Cooperation means that selfish replicators forgo some of their reproductive potential to help one another. But natural selection implies competition and therefore

• pposes cooperation unless a specific

mechanism is at work.

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Conflicts Signaling Games Cycles Conclusions Honesty

Searcy & Nowicki (2005)

One might expect many instances in which signalers would attempt to profit individually by conveying dishonest information. ...if dishonesty is common, it also is not

• bvious why receivers should respond to

signals. ...if receivers fail to respond to signals, it is not obvious how signaling systems can exist at all.

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Conflicts Signaling Games Cycles Conclusions Mechanisms

Scot-Phillips (2008)

1

Indices: signal form is tied to meaning

2

Handicaps: costs borne by honest senders

3

Deterrents: costs borne by dishonest senders

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Conflicts Signaling Games Cycles Conclusions Mechanisms

Reby & McComb (2003)

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Conflicts Signaling Games Cycles Conclusions Mechanisms

Zahavi (1975) Grafen (1990) Spence (1973)

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Conflicts Signaling Games Cycles Conclusions Mechanisms

Dostoyevsky (1866)

Where is it I’ve read that someone condemned to death says or thinks, an hour before his death, that if he had to live on some high rock, on such a narrow ledge that he’d only room to stand, and the ocean, everlasting darkness, everlasting solitude, everlasting tempest around him, if he had to remain standing on a square yard of space all his life, a thousand years, eternity, it were better to live so than to die at once. Only to live, to live and live! Life, whatever it may be!

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Conflicts Signaling Games Cycles Conclusions Mechanisms

Mencken (1949)

Conscience is the inner voice that warns us somebody may be looking.

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Conflicts Signaling Games Cycles Conclusions Language

Grice (1967)

Make your conversational contribution such as is required, at the stage at which it

• ccurs, by the accepted purpose or

direction of the talk exchange in which you are engaged.

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Conflicts Signaling Games Cycles Conclusions Language

Grice (1967)

I am, however, enough of a rationalist to want to find a basis that underlies these facts, undeniable though they may be; I would like to be able to think of the standard type of conversational practice not merely as something that all or most do in fact follow but as something that it is reasonable for us to follow, that we should not abandon.

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Conflicts Signaling Games Cycles Conclusions

Crucial points for Games

1

Signaling Games

2

Nash Equilibria

3

Evolutionarily Stable Strategies

4

Parametrization

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Conflicts Signaling Games Cycles Conclusions Signaling Games

Lewis (1969)

One if by land, two if by sea.

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Conflicts Signaling Games Cycles Conclusions Signaling Games

δ S R 1,1 aland 0,0 asea mone R 1,1 aland 0,0 asea mtwo tland S R 0,0 aland 1,1 asea mone R 0,0 aland 1,1 asea mtwo tsea

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Conflicts Signaling Games Cycles Conclusions Signaling Games

Sender observes some state of the world, t ∈ T, given probability distribution over states, δ. Sender chooses message, m ∈ M, based on strategy s ∈ [T → M]. Receiver interprets message with action, a ∈ A, based on strategy r ∈ [M → A]. US and UR are the utility functions that define preferences over T ×A. Expected utility of sender and receiver: EUS(s,r) = ∑

t

δ(t)·US(t,r(s(t))) EUR(s,r) = ∑

t

δ(t)·Ur(t,r(s(t))) (1)

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Conflicts Signaling Games Cycles Conclusions Nash Equilibria

Nash (1950, 1951)

A strategy profile s∗,r∗ is a Nash equilibrium if and

• nly if:

∀s ∈ S, such that s = s∗, EUS(s∗,r∗) ≥ EUS(s,r∗) ∀r ∈ R, such that r = r∗, EUR(s∗,r∗) ≥ EUS(s∗,r) “Something that it is reasonable for us to follow.”

• Grice

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Conflicts Signaling Games Cycles Conclusions Evolutionarily Stable Strategies

Maynard Smith & Price (1973)

An Evolutionarily Stable Strategy is a strategy that, if all the members of a population adopt it, then no mutant strategy could invade the population under the influence of natural selection

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Conflicts Signaling Games Cycles Conclusions Evolutionarily Stable Strategies

Selten (1980)

In the class of asymmetric games, a strategy is evolutionarily stable if and only if it is a Strict Nash Equilibrium. A strategy profile s∗,r∗ is a Strict Nash equilibrium if and only if: ∀s ∈ S, such that s = s∗, EUS(s∗,r∗) > EUS(s,r∗) ∀r ∈ R, such that r = r∗, EUR(s∗,r∗) > EUS(s∗,r) “Something that it is reasonable for us to follow, that we should not abandon.” -Grice

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Conflicts Signaling Games Cycles Conclusions Parametrization

Crawford & Sobel (1982)

Senders have an incentive to exaggerate their type. Receivers have an incentive to sort the types accurately. US(t,a) = −(a−[t +b])2 UR(t,a) = −(a−t)2 (2)

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Conflicts Signaling Games Cycles Conclusions Parametrization

A low state (tL = 0) and a high state (tH = 1) States equiprobable, δ(tL) = δ(tH) = 1

2

Set of messages M = {m1,...,mk} Actions available, the interval A = [0,1]

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Conflicts Signaling Games Cycles Conclusions Parametrization

0.0 0.5 1.0 Action taken by Receiver Utility a = tH a = tL UR(tL, a) UR(tH, a)

UR(t,a) = −(a−t)2 (3)

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Conflicts Signaling Games Cycles Conclusions Parametrization

0.0 0.5 1.0 Action taken by Receiver Utility aH aL aP b=1 b=1/2 b=0

UR(t,a) = −(a−[t +b])2 (4)

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Conflicts Signaling Games Cycles Conclusions Parametrization

0 < b < 1

4: Separating

0.0 0.5 1.0 Action taken by Receiver Utility a = tH a = tL UR(tL, a) UR(tH, a) 0.0 0.5 1.0 Action taken by Receiver Utility aH aL aP b=1 b=1/2 b=0

: both types want to be identified

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Conflicts Signaling Games Cycles Conclusions Parametrization

1 4 < b < 1 2: Separating

0.0 0.5 1.0 Action taken by Receiver Utility a = tH a = tL UR(tL, a) UR(tH, a) 0.0 0.5 1.0 Action taken by Receiver Utility aH aL aP b=1 b=1/2 b=0

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Conflicts Signaling Games Cycles Conclusions Parametrization

1 2 < b < 3 4: Cycling

0.0 0.5 1.0 Action taken by Receiver Utility a = tH a = tL UR(tL, a) UR(tH, a) 0.0 0.5 1.0 Action taken by Receiver Utility aH aL aP b=1 b=1/2 b=0

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Conflicts Signaling Games Cycles Conclusions Parametrization

3 4 < b: Pooling

0.0 0.5 1.0 Action taken by Receiver Utility a = tH a = tL UR(tL, a) UR(tH, a) 0.0 0.5 1.0 Action taken by Receiver Utility aH aL aP b=1 b=1/2 b=0

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Conflicts Signaling Games Cycles Conclusions

Crucial points for Cycles

1

Red Queen’s Race

2

Jespersen’s Cycle in Greek

3

Autmobile Semantics

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Conflicts Signaling Games Cycles Conclusions Red Queen’s Race

Carrol (1871)

"A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!"

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Conflicts Signaling Games Cycles Conclusions Red Queen’s Race

Hauert et al. (2002)

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Conflicts Signaling Games Cycles Conclusions Jespersen’s Cycle in Greek

Kiparsky & Condoravdi (2006)

PLAIN EMPHATIC SOURCE

ου...τι ου-δε...εν Ancient Greek (ου)δεν...τι δεν...τιποτε Early Medieval Greek δεν...τιποτε δεν... πραμα Greek Dialects δεν...πραμα δεν...απαντοξη Modern Cretan

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Conflicts Signaling Games Cycles Conclusions Jespersen’s Cycle in Greek

Kiparsky & Condoravdi (2006)

Emphatic negation tends to increase in frequency due to pragmatically motivated

• veruse which is characteristic of inherently

bounded evaluative scales...an obligatory element cannot be emphatic, for to emphasize everything is to emphasize nothing.

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Conflicts Signaling Games Cycles Conclusions Jespersen’s Cycle in Greek

Schwenter (2006)

DISCOURSE NEW

INFERRABLE

DIRECTLY ACTIVATED NEG 1

1 1 1

NEG 2

1 1

NEG 3

1

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Conflicts Signaling Games Cycles Conclusions Jespersen’s Cycle in Greek

Schwenter (2006)

(The plain-emphatic distinction) is problematic from the present-day perspective of

• ther Romance languages...the post-verbal

negative element is heavily regulated by information-structural factors, and specifically by the discourse-old status of the denied proposition.

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Conflicts Signaling Games Cycles Conclusions Autmobile Semantics

Aronoff (1981)

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Conflicts Signaling Games Cycles Conclusions Autmobile Semantics

Aronoff (1981)

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Conflicts Signaling Games Cycles Conclusions Conclusions

Common and conflicting interests can lead to a range of signaling behavior: separating, cycling, and pooling. Stability and instability are important for understanding language change.

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Conflicts Signaling Games Cycles Conclusions Future Directions

Distribution over types can be estimated from corpus data (Tottie, 1991) Different information structural categories can be found in corpus data (Wallage, 2013)

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Conflicts Signaling Games Cycles Conclusions Future Directions

Thanks!

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Conflicts Signaling Games Cycles Conclusions Future Directions

References

Posted soon.

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