SLANGSession 7

Roland MuhlenberndSeminar fur Sprachwissenschaft

University of Tubingen

Overview

I Evolution of Cooperation

I Repeated Prisoner’s Dilemma

I The logic of indirect speech

I Signaling Games

I Horn’s Division of Pragmatic Labor

Human Language is grounded on Cooperation

Reasons for cooperation:

I kin selection (r > cb )

I direct reciprocity

I indirect reciprocity

I spatial selection

I group selection

b > c > 0b = 3, c = 1

Cooperate Defect

Cooperate b-c2;2 0;3Defect b 3;0 c1;1

Tabelle : Prisoner’s Dilemma

Repeated PD: The Evolution of Cooperation

Robert Axelrod’s Computer tournament (1979):

C D

C 3;3 0;5D 5;0 1;1

Tabelle : Prisoner’s Dilemma

I Finding the best strategy for the Repeated Prisoners’Dilemma (RPD)

I Game theorists were invited to submit their favourite strategy(decision rule)

I All submitted strategies play against each other for 200 rounds

I The strategy with the highest average score wins thetournament

Repeated PD: The Evolution of Cooperation

I TIT FOR TAT: Cooperate in the first round and then do whatyour opponent did last round

I FRIEDMAN: Cooperate until the opponent defects, thendefect all the time

I DOWNING:I Estimate probabilities p1 = P(C t

O |Ct−1I ), p2 = P(C t

O |Dt−1I )

I If p1 >> p2 the opponent is responsive: CooperateI Else the opponent is not responsive: Defect

I TRANQUILIZER:I Cooperate the first moves and check the opponents responseI If there arises a pattern of mutual cooperation: Defect from

time to timeI If opponent continues cooperating, defections become more

frequent

I TIT FOR 2 TATS: Play TIT FOR TAT, but response withdefect if the opponent defected on the previous two moves

I JOSS: Play TIT FOR TAT, but response with defects in 10%of opponent’s cooperation moves

Repeated PD: The Evolution of Cooperation

Results:

1. The winner was TIT FOR TAT with 504 points

2. Success in such a game correlated with the followingcharacteristics:

I Be nice: cooperate, never be the first to defect.I Be provocable: return defection for defection, cooperation for

cooperation.I Don’t be envious: be fair with your partner.I Don’t be too clever: or, don’t try to be tricky.

The Logic of indirect Speech

Three major relationship types

I Dominance: ”Don’t mess with me” (inherited from primates’dominance hierarchy)

I Communality: ”share and share alike” (kin selection andmutualism, group selection)

I Reciprocity: ”You scratch my bag, I scratch yours”(Tit-For-Tat exchanges)

The Logic of indirect Speech

I Would you like to come up and see my etchings? [sexualcome-on]

I If you could pass the guacamole, that would be awesome.[polite request]

I Nice store you got here. Would be a real shame if somethinghappened to it. [a threat]

I Gee, officer, is there some way we could take care of the tickethere? [a bribe]

Dishonest Officer Honest Officer

Don’t bribe Ticket TicketBribe Go Free Arrest for BriberyImplicate Bribe Go Free Ticket

Tabelle : Bribe Game

The Logic of indirect Speech: Mutual knowledge

I Indirect speech acts prohibits mutual knowledge

I Conventions need mutual knowledge?

aS aGtS 1;1 0;0tG 0;0 1;1

I Linguistic conventions can be modeled by signaling games

Signaling Games: Coordination games

Coordination games:

I The two players’ shared goal is to coordinate on the samestrategy

I Any 2× 2-coordination game has two Nash Equilibria

I Which Equilibrium is the best / unique solution???

Solution concepts:

I Aligned preferences

I Focal point: Convention

I Coordination by communication ⇒ Signaling games

Signaling Games: An example

The situation

I There is a monkey society, whose members can use two alarmcalls for an emergency case: ”Ooh!” and ”Aah!”

I There are two main emergency cases: Attacks by skypredators (tS)and ground predators (tG )

I There are two possible actions: Hide in the bushes (aS) orclimb on the trees (aG )

aS aGtS 1;1 0;0tG 0;0 1;1

Question: What could the monkeys do to coordinate theirbehavior?

Signaling Games: An example

A simple signaling game:

I A set of states T = {tS , tG}I A set of actions A = {aS , aG}I A set of messages M = {mOoh!,mAah!}I A Probability function Pr ∈ ∆(T )

Pr(tS) = .5, Pr(tG ) = .5

Signaling Games: Strategies

”Language use” can be depicted as a strategy:

I A sender strategy S : T → M

I A receiver strategy R : M → A

S1:tS mOoh!

tG mAah!

S2:tS

mAah!tG

mOoh!

S3:tS mOoh!

tG mAah!

S4:tS

mAah!tG

mOoh!

R1:mOoh! aS

mAah! aG

R2:mOoh!

aGmAah!

aS

R3:mOoh! aS

mAah! aG

R4:mOoh!

aGmAah!

aS

Question: What is S1(tS), S4(tG ), R2(mOoh!), R3(mAah!)?

Signaling Games: Signaling Systems

How to compute the resulting strategy matrix...

Signaling Games: Signaling Systems

Resulting strategy matrix:

R1 R2 R3 R4

S1 1 0 .5 .5S2 0 1 .5 .5S3 .5 .5 .5 .5S4 .5 .5 .5 .5

I (S1,R1) and (S2,R2) are combinations of perfectcommunication and called signaling systems (Lewis 1969).

(S1,R1):tS mOoh! aS

tG mAah! aG(S2,R2):

tS

mOoh!

aS

tG

mAah!

aG

Signaling Games: Simulation result

Simulation:

I Agents are placed on a lattice andcan only communicate to directneighbors

I Agents play repeatedly Lewis’signaling game and learn bylearning dynamics

I Agents are colored according astrategy combination

Results

I The society is distributed in two types of languages users.

I One group is using (S1,R1), the other is using (S2,R2).

I The agents on the borders miscommunicate

Review: Reinforcement Learning

S Rts

tg

m1

m2

as

ag

0

0

0

0I the sender has an urn for each

state t ∈ T

I each urn contains balls of eachmessage m ∈ M

I the sender decides by drawingfrom urn 0t

I the receiver has an urn foreach message m ∈ M

I each urn contains balls of eachaction a ∈ A

I the receiver decides bydrawing from urn 0t

I successful communication → urn update

I in general a signaling system emerges over time

Signaling Games: Research in Tubingen

We are applying signaling games...

I as dynamic games (repeatedly played)

I on a multi-agent system (lattice, network)

I combined with update dynamics and learning accounts

Main results:If all members of a group of agents use / have learned an uniquesignaling system...

I a convention emerged (Lewis, 1969)

I for which meanings are assigned to messages

I ergo: a fragment of a language / dialect / slang emerged

I Since simple learning dynamics like reinforcement learningleads to the evolution of conventions, mutual knowledge andrationality is not necessary to explain the phenomena, but canwe necessarily exclude them?

Signaling Games: Horn’s division of pragmatic labor

The modelA simple signaling game:

I A set of states T = {tf , tr}I A set of actions A = {af , ar}I A set of messages M = {mu,mm}I A Probability function Pr ∈ ∆(T )

Pr(tf ) > Pr(tr )

I A cost function C : M → RC (mu) > C (mm)

Signaling Games: Horn’s division of pragmatic labor

Examples:

I tf : Miss X sang Home Sweet Home in a normal way

tr : Miss X sang Home Sweet Home in a strange way

mu: ”Miss X sang Home Sweet Home”

mm: ”Miss X produced a series of sounds that corresponded closelywith the score of Home Sweet Home”

I tf : John became a prisoner

tr : John goes to the prison building

mu: ”John went to jail”

mm: ”John went to the jail”

I tf : a person that cooks / a tool that drills

tr : a tool that cooks / a person that drills

mu: ”cook”/”drill”

mm: ”cooker”/”driller”

Signaling Games: Applications

I Emergence of conventional language use

I Explanation for language change

I Pragmatic phenomena like Neo-Gricean Implicatures

Example: Division of the meaning space

tA mpig aA

tM mpork aM

tA

mpork

aA

tM

mpig

aM