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Symbolic Gestures and Common Knowledge. Reall … Salala Pakistan, Nov 26 2011…. US gunships responding to request for air-support accidentally killed 24 Pakistani soldiers. In response…. Pakistan closed supply routes. Leading to ~$1 billion in extra shipping fees. Until the US apologized…

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Presentation Transcript
slide2

Reall…

SalalaPakistan, Nov 26 2011…

us gunships responding to request for air support accidentally killed 24 pakistani soldiers
US gunships responding to request for air-support accidentally killed 24 Pakistani soldiers
slide7

Until the US apologized…

“We are sorry for the losses suffered by the Pakistani military”

-Hillary Clinton, July 3 2012

Over half a year later!

slide8

Then, immediately…

“…the ground supply lines into Afghanistan are opening”

slide9

Why wouldn’t US just say sorry?

-Mere words?

-Worth a billion dollars?

Why would Pakistan care?

-Again, mere words?

-US could just “fake it”; why “believe”?

slide14

The main features of the treaty were mutual recognition, cessation of the state of war that had existed since the 1948 Arab–Israeli War, normalization of relations and the complete withdrawal by Israel of its armed forces and civilians from the Sinai Peninsula which Israel had captured during the Six-Day War in 1967.

-Source: http://en.wikipedia.org/wiki/Israel- Egypt_Peace_Treaty

slide19

More generally…

Why do symbolic gestures matter?

slide20

Is this just silliness, and our laws and militaries and relationships should focus on the “tangibles”?

slide21

Or if symbolism does matter,

WHEN does it matter?

WHAT makes it work or not work?

slide23

A

B

Ω = {symbolic gesture, no symbolic gesture}π1 = { {symbolic gesture}, {no symbolic gesture} }π2 = { {symbolic gesture}, {no symbolic gesture} }

a, a

b, c

A

c, b

d, d

B

a > c , d > b

S1({symbolic gesture}) = A S2({symbolic gesture}) = AS1({no symbolic gesture}) = B S2({no symbolic gesture}) = B

slide25

In what kinds of situations is this possible?

Our model tells us…

Subsequent interaction needs to have multiple equilibria!

slide26

H

D

Ω = {symbolic gesture, no symbolic gesture}π1 = { {symbolic gesture}, {no symbolic gesture} }π2 = { {symbolic gesture}, {no symbolic gesture} }

H

v/2-c

v

D

0

v/2

S1({symbolic gesture}) = H S2({symbolic gesture}) = DS1({no symbolic gesture}) = D S2({no symbolic gesture}) = H

slide27

Ω = {symbolic gesture, no symbolic gesture}π1 = { {symbolic gesture}, {no symbolic gesture} }π2 = { {symbolic gesture}, {no symbolic gesture} }

2 is low Type

2 is high Type

-2, 2

2, 2

1

Accepts

0, 0

0, 0

1

Rejects

S1({symbolic gesture}) = Accepts

S1({no symbolic gesture}) =Rejects

(supposing gesture probability

Independent of type)

slide28

So symbolic can influence whether the U.S. has the “right” to use Pakistani airspace without permission

(this is a hawk-dove game!)

Or can influence how much we invest in a romantic relationship, if we both really like each other

(this is a coordination game, presuming I don’t want to be invested when other isn’t but do

slide29

What property need symbolic gestures have?

Our model tells us…

Gesture needs to create common p-beliefs

slide30

What kinds of gestures create common p-beliefs?

Eye contact, explicit statements, handshakes, public displays

(Intuition: when I believe they happened, I believe that you believe they happened, and I believe that you believe that…)

slide31

What kind of gestures do not create comon p-belief?

Innuendos, Rumors, Intermediaries

slide32

A

B

Ω = {no gesture, told intermediary, but wasn’t relayed, message relayed}π1 = {{no gesture}, {told intermediary but wasn’t relayed, message relayed }π2 = {{no gesture, told intermediary but wasn’t relayed}, {message relayed}}μ(no gesture)=1/2μ(told intermediary but wasn’t relayed)=1/4μ(message relayed)=1/4

2, 2

0, 0

A

0, 0

1, 1

B

S1({no gesture}) = A S1 ({told intermediary but wasn’t relayed, message relayed }) =B

slide33

Why?

Because whenever tell intermediary don’t think other will receive?

slide34

But what if know intermediary is really reliable?

Well, even then, if other doesn’t know that intermediary is reliable…

slide35

A

B

Ω = {no gesture, told reliable intermediary and relayed, told unreliable intermediary and wasn’t relayed, told reliable intermediary and was relayed}π1 = …π2 = …μ(no gesture)=1/2μ(told intermediary but wasn’t relayed)=1/5μ(message relayed)=1/5

2, 2

0, 0

A

0, 0

1, 1

B

S1({no gesture}) = A S1 ({told reliable intermediaty}) =B

slide36

Even when you know message got delivered, you suspect that other suspects that you suspect message didn’t get delivered…

I.e. with intermediaries, even if p-belief, isn’t isn’t common p-belief…