pragmatics & game theory: branches of game-theoretic ... › ~roland › pgt1314 › folien ›...
TRANSCRIPT
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Pragmatics & Game Theory:Branches of Game-Theoretic Linguistics
Roland Mühlenbernd
WiSe 13/14
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Table of Content
1 IntroductionReviewOverview
2 The Strategic Implicature ModelThe Local GameThe Global Game
3 Strategic Language UseIndirect SpeechRelationship Negotiation
4 Evolutionary Game TheoryBehavioral StrategiesLearning Dynamics
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
ReviewOverview
Review
conversational implicature
4 maxims: quality, quantity, relevance, mannerparticularized & generalized implicatures
neo-Gricean pragmatics
scalar & clausal implicaturesQ- and R-based implicatures (Horn)Horn's division of pragmatic laborQ-, I- and M-based implicatures (Levinson)
game-theoretic pragmatics
situations: signaling gamespossible behavior of production/perception: strategies (pure &behavioral)actual behavior: rationalistic solution concepts (here: IBR)
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
ReviewOverview
Overview
Game Theory and Linguistics
Language Evolution
Signaling Games
GT in Lang. Use Pragm. Reasoning
Signaling Games
IBR model SIM
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
The Strategic Implicature Model
Parikh's (1991) Strategic Implicature Model was the �rstaccount to use game theory for matters in pragmatics.
Parikh deals with particularized implicatures of relevance
he distinguishes between two types of relevance:
logical relevance: a proposition is logical relevant with respectto a set of propositions, if the two together have a 'nontrivial'implication without having it individually (in spirit of Sperberand Wilson, 1986)rational relevance: a proposition is rational relevant, if itincreases the expected utility of a participant's goal
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
Example: B's decision problem
Situation: A and B have to attend a talk at 5 pm and B believesthe probability of it's being time for the talk now is .2 and thatthere is still time is .8.
c: continue previous action, d: depart for the talk, p: it's time for the talk
The information that it is time for the talk has rational relevancehere, since it has a positive value of information: 10 - 6 = 4.
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
A Relevance Implicature
Example
Situation: It is an important talk today (at 5 pm)A: 'It is 5 pm.'+> It is time for the talk.
logical relevance: the proposition (expression) is relevantbecause it is non-trivial in the given set of propositions(situation, context) by generating the implicature.
rational relevance: the proposition is rational relevant for thehearer since it increases his expected utility
note that both types of relevance are essential for Grice's ideaof the cooperation principle!
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
The SIM Model For The Given Example
situation s: 'important talk at 5 pm'; and empty context s ′
expression ϕ: 'It is 5 pm.'
information states t: it is 5 pm and the talk is now; and t′: it is 5 pm
literal interpretation l (�ts to t′) and pragmatic interpretation p (�ts to t)
production and interpretation cost: -1
incorrect interpretation: -2, pragmatic inference: -1
information value by rational relevance: +4
-2, -1-4,-3
-2, -1-3,-21,2-2, -1
-2, -1-4,-3-5,-4
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
The SIM Model's Local Game
B could reason that A could havean alternative in situation s
to use a more complex expressionµ: 'It is time for the talk now.'(extra costs: -.5)
to express meaning e: it's time forthe talk
A could also have an alternative insituation s ′
to be silent (ν: empty message)that expresses nothing (e′: emptymeaning)
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
The SIM Model's Local Game
Solution idea:
A's information set is {s}and {s ′}B's information set is {t, t′},{e} and {e′}there are four senderstrategies and two receiverstrategies
and therefore 8 strategypro�les
there is only one unique Nashequilibrium{(s, ϕ), (s ′, ν); ({t, t′}, p)}
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
The SIM Model's Global Game
the local game results after Ahas uttered ϕ
if A would utter somethingelse (e.g. ψ or µ: 'thespeaker entered the stage','the audience is waiting'...),it would emerge a di�erentlocal game
each local game has aexpected utility value
A should use the expressionthat triggers the local gamewith maximal expected utility
If LG denotes the set of all local games that result from A's choice, then〈GG , LG 〉 is called the Strategic Implicature Model.
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
The Local GameThe Global Game
The SIM Model
Conclusion
the SIM model is (one of) the �rst model that combinesPragmatics and Game Theory
the model deals with particularized implicatures (relevance)and therefore takes a given context/situation into account
the solution concept is a unique Nash equilibrium that depictspragmatic language use
but: there is criticism for model and solution concept:
there are a lot of numbers made up, which di�erences arecritical for the right solutionthe Nash equilibrium explains why to stay with a strategy, butnot how to come to itthere is no good solution for the case of multiple Nashequilibria
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
Overview
Game Theory and Linguistics
Language Evolution
Signaling Games
GT in Lang. Use
Indirect Speech
Pragm. Reasoning
Signaling Games
IBR model SIM
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
The Logic of Indirect Speech (Pinker, Nowak & Lee 2007)
Example 1
'Would you like to come up and see my etchings?'+> a sexual come-on
Example 2
'If you could pass the guacamole, that would be awesome.'+> a polite request
Example 3
'Nice store you got here. Would be a real shame if something happenedto it.' +> a threat
Example 5
'Gee, o�cer, is there some way we could take care of the ticket here?'+> a bribe
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
The Logic of Indirect Speech
Direct bribe: 'If you let me go without a ticket, I'll pay you 50dollar.'
Indirect bribe: 'Gee, o�cer, is there some way we could takecare of the ticket here?' (showing a �fty dollar bill)
dishonest o�cer honest o�cer
Don't bribe -100 -100Bribe -50 -500Indirect bribe -50 -100
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
The Logic of Indirect Speech
The directness of a proposition is probably continuous:
'If you let me go without a ticket, I'll pay you 50 dollar.''Is there some way we could take care of the ticket here?''I've learned my lesson; you don't have to worry about me doingthis again.'
a corrupt cop is more sensitive to recognize bribe than a honest cop
there is a threshold for both to recognize the bribe
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
Relationship Negotiation
People use indirect speech also in nonlegal situations, wherethere are no �nancial or legal payo�s and penalties
Example: bribing a maitre d' to get seated in a full restaurantdirectly without reservation
When relations are ambiguous, a divergent understandingbetween the parties can lead to the aversive emotion we callawkwardness
dishonest maitre d' honest maitre d'
Don't bribe long wait (D/D) long wait (D/D)Bribe instant seating (R/R) awkwardness (R/D)Indirect bribe instant seating (R/R) long wait (D/D)
D: dominance relationship; R: reciprocity relationship
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
Relationship Negotiation
There are three essential human relationship types:
boss - employee (dominance)good friends (communality)business transaction (reciprocity)
relationship mismatches impose emotional costs (awkwardness)
sometime relationship types are highly unambiguous
indirect speech can help to avoid relationship mismatches by�the bene�t of the doubt�
indirect speech merely provides shared individual knowledge,but not common knowledge
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Indirect SpeechRelationship Negotiation
Overview
Game Theory and Linguistics
Language Evolution
Signaling Games
GT in Lang. Use
Indirect Speech
Pragm. Reasoning
Signaling Games
IBR model SIM
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Coordination & Signaling
R L
R 1 0L 0 1
aL aStL 1 0tS 0 1
Messages: One or two lanterns?
s1:tL m1
tS m2
s2:tL
m2tS
m1
s3:tL m1
tS m2
s4:tL
m2tS
m1
r1:m1 aL
m2 aS
r2:m1
aSm2
aL
r3:m1 aL
m2 aS
r4:m1
aSm2
aL
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
a signaling game is a tuple SG = 〈{S ,R},T ,Pr ,M,A,U〉a Lewis game is de�ned by:
T = {tL, tS}M = {m1,m2}A = {aL, aS}Pr(tL) = Pr(tS) = .5
U(ti , aj) =
{1 if i = j
0 else
aL aStL 1 0tS 0 1
N
S
R
1 0
R
1 0
S
R
0 1
R
0 1
.5 .5tL tS
m1 m2 m1 m2
aL aS aL aS aL aS aL aS
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Pure strategies
Pure strategies are contingency plans, players act according to.
sender strategy: s : T → M
receiver strategy: r : M → A
s1:tL m1
tS m2
s2:tL
m2tS
m1
s3:tL m1
tS m2
s4:tL
m2tS
m1
r1:m1 aL
m2 aS
r2:m1
aSm2
aL
r3:m1 aL
m2 aS
r4:m1
aSm2
aL
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Signaling Systems
signaling systems are combinations of pure strategies. TheLewis game has two: L1 = 〈s1, r1〉 and L2 = 〈s2, r2〉
L1:tL
tS
m1
m2
aL
aSL2:tL
tS
m1
m2
aL
aS
signaling systems are strict Nash equilibria of the EU-table:
r1 r2 r3 r4s1 1 0 .5 .5s2 0 1 .5 .5s3 .5 .5 .5 .5s4 .5 .5 .5 .5
in signaling systems messages associate states and actionsuniquely
signaling systems constitute evolutionary stable states
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Behavioral Strategies
Behavioral strategies are functions that map choice points toprobability distributions over actions available in that choice point.
behavioral sender strategyσ : T → ∆(M)
behavioral receiver strategyρ : M → ∆(A)
σ =
t1 7→[m1 7→ .9m2 7→ .1
]t2 7→
[m1 7→ .5m2 7→ .5
] ρ =
m1 7→[a1 7→ .33a2 7→ .67
]m2 7→
[a1 7→ 1a2 7→ 0
]
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Learning Dynamics & Signaling Games
Extensions in time:
agents play the game repeatedly
agents' decisions are in�uenced by previous encounters
application of learning dynamics like reinforcement learning
belief learning
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Best Response & Expected Utility
Playing Best Response means to make a choice thatmaximizes the Expected Utility.
EUS(m|t, β) =∑a∈A
β(a|m)× U(t, a) (1)
EUR(a|m, β) =∑t∈T
β(m|t)× U(t, a) (2)
How does an agent get belief β?
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Belief Learning
The belief is a result of observation
Example:
SO a1 a2m1 8 2m2 7 13
β =
m1 7→[a1 7→ .8a2 7→ .2
]m2 7→
[a1 7→ .35a2 7→ .65
]
RO t1 t2m1 6 0m2 4 4
β =
t1 7→[m1 7→ .6m2 7→ .4
]t2 7→
[m1 7→ 0m2 7→ 1
]
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Best Response as Behavioural Strategy
behavioural sender strategyσ : T → ∆(M)
σ(m|t) =
{1
|BR(t)| if m ∈ BR(t)
0 else
behavioural receiver strategyρ : M → ∆(A)
ρ(a|m) =
{1
|BR(m)| if a ∈ BR(m)
0 else
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Reinforcement Learning
S Rts
tg
m1
m2
as
ag
0
0
0
0the sender has an urn for eachstate t ∈ T
each urn contains balls of eachmessage m ∈ M
the sender decides by drawingfrom urn 0t
the receiver has an urn for eachmessage m ∈ M
each urn contains balls of eachaction a ∈ A
the receiver decides by drawingfrom urn 0t
successful communication → urn update
in general a signaling system emerges over timeRoland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Behavioural & Pure Strategies
Pure strategies are a subset of behavioural strategies.
Example:
σ2:t1
m2t2
m1
ρ2:m1
a2m2
a1
σ2 =
t1 7→[m1 7→ 0m2 7→ 1
]t2 7→
[m1 7→ 1m2 7→ 0
] ρ2 =
m1 7→[a1 7→ 0a2 7→ 1
]m2 7→
[a1 7→ 1a2 7→ 0
]
Note: If an agents plays σ2 as sender and ρ2 as receiver, we say, hehas learned the signaling language L2 = 〈σ2, ρ2〉.
Roland Mühlenbernd Branches of Game-Theoretic Linguistics
IntroductionThe Strategic Implicature Model
Strategic Language UseEvolutionary Game Theory
Behavioral StrategiesLearning Dynamics
Conclusion
1 The Strategic Implicature Model (Parikh 1991)
is the �rst model that combines pragmatics and game theorydeals (basically) with relevance implicaturesuses the Nash equilibrium as solution conceptbut: there is criticism for model and solution concept:
2 Strategic Language Use
is a branch in the tree of research directions that use gametheory for issues in linguisticsascribes two essential functions to communication: informationtransmission and relationship negotiationintegrates social costs (awkwardness)
3 EGT and Signaling Games
gives a framework to model dynamics of language evolutionand changeintegrates e.g. learning dynamics on repeated plays
Roland Mühlenbernd Branches of Game-Theoretic Linguistics