An Experimental Study of Cognition and Behavior from the Pe - PowerPoint Presentation

Slide1

An Experimental Study of Cognition and Behavior from the Perspective of Inductive Game TheoryBy M. Kaneko (with A. Takeuchi, Y. Funaki and J. J. Kline)

0) No knowledge about the payoffs, even for his own Prisoner’s dilemmas are repeated 50 timesNo Role-Switching Alternating Role-Switching Cognition and behavior - - learning payoffs by trial/error revising his behavior from time to time The IGT Perspective (Kanko-Kline 2008, 2009):The above points are considered in the IGT perspectiveSharpened Extended

1Slide2

Social Justice　

Research ProjectsM. KanekoChiayi ２０１１・10・03Mathematical thinkingLogical Inferences & Decision Making

Emphases

Symbolic thinking (Syntactical/grammatical)

Interpretation of Symbolic Expressions (semantic)

2

Inductive Game

Theory

Epistemic Logic

Understanding of Society and Human in Society

Experiences as Given

Derivations/Use/Revision of Beliefs/UnderstandingEmphasisFrom Experiences to BeliefsGenerations of ExperiencesInteractions between cognition and behavior Interpretation of Symbolic thinking

Social Institutions　

Soft InstitutionsEmergence of Value・MoralityEtc.Hard InstitutionsTax SystemsEtc.Slide3

1: Sources for Knowledge - - experiences 2: From accumulated experiences, a player derives his understanding of the situation. 3: Uses of his derived view for behavioral revisions.

3a): Generating experiences - - trials/errorsb): Memorizing such experiences c): Limitations on a) and b): restricted trials/errors, forgetfulness, mistakes, misunderstanding

Interactive

Kaneko-Kline papers

Formal Theory

Informal Theory

Basic Assumption: no knowledge about payoffs

A model of individual behavior – Statistical Analysis:

- - sharpening and extending the informal theory - -

Present paperSlide4

Basic Set-upSubjects repeatedly play a prisoner’s dilemma game for 50 rounds with the same subject.In each round:Each subject is assigned a role of either BLUE (row) or GREEN

(column).Each subject chooses action c or d Feedback information is given: (his role; pair of actions chosen; his payoff)After the 50 rounds, they answer questionnaire about the payoff matrix.4Slide5

Experimental Treatments 2 × 3 and 50 rounds2 types of role-switching

No role-switching (NRS) Alternating role-switching (ARS)3 types of PD Games Quasi-Symmetric (QS1) Quasi-Symmetric (QS2) Twisted (T)×

NRS

ARS

5

50 rounds

B

B

B

G

G

G

1

2

2

2

1

1

G

1

2

B

B

B

G

G

G

1

2

1

1

2

2

G

1

2

B

BSlide6

Three Types of Prisoner’s Dilemma GamesQuasi-Symmetric 1 (QS1)Quasi-S

ymmetric 2 (QS2)Twisted (T)6(5, 4)(2, 5)(6, 1)

(3, 2)

(5, 5)

(2, 6)

(6, 2)

(3, 3)

(0, 1)

(0, 1)

(0, 1)

(0, 1)

(8, 7)

(2, 8)

(9, 1)

(3, 2)

(8, 8)

(2, 9)(9, 2)(3, 3)

(0, 1)

(0, 1)

(0, 1)

(0, 1)

(5, 4)

(2,

10

)

(6, 1)

(3, 2)

(5, 4)

(2, 5)

(6, 1)

(3, 2)

(0, 0)

(0,

5

)

(0,0)

(0, 0)

=

=

=

－

+

－

c

d

c

d

c

d

c d

c d

c d

Asymmetric?

Twisted?

In all games

d – Dom

(

d,d

) - - NE

(

c,c

) is an ICE

in QS1,QS2

(

c,d

) is an ICE

in TSlide7

Summary of the TreatmentsQS1QS2TRole-Switching

14 Pairs14 Pairs14 PairsNo Role-Switching14 Pairs14 Pairs14 Pairs7= 168 subjects (14 × 2 × 6)Between-Subject DesignSubjects

・

Undergraduate students of

Wased

a University.

・

Recruited from many majors;

excepts for economics.

LocationExperiment Lab ofWaseda UniversitySlide8

Basic Information StructureKnown structure:Number of actions for each roleNo change in the Payoff matrix across periodsA role assignment but not a specific assignment.

The payoff structure is not known:A subject does not know about the payoff structure --- not “unknown” in the sense of uncertainty.A subject receives a payoff value after each round --- Experiences become the source for his subjective view.8Slide9

95, 4

2, 106, 13, 2

c

d

c

d

(T, ARS):

pair 8

Aggregated Frequencies over the subjects for NRSSlide10

10Slide11

11Slide12

12Today, we will mainly look at:Cognitive Aspects – Resulting knowledge about payoffs from experiences

Interactions between behavior and cognition.Behavioral Predictions:No Role-switching – Dominant Strategy Role-switching –

IC equilibrium

predicts a pair of actions maximizing the

simple sum of payoffs,

and the Nash EQ.

Cognitive Data:

Payoffs Questionnaire, after 50 rounds

We got the subjective payoffs from the answers to this

Correctness of a subject’s understanding and his behavior Slide13

Summary of Experimental Data3 games ×2 types of role-switching = 6 treatmentsEach treatment has 14 pairs of subjects Each pair show a trajectory of action pairs for 50 rounds.13

Payoff answers from each subjectIn each treatment of NRS, 4 numerical answers are given In each treatment of RS, 8 numerical answers are given.Behavioral Data

Cognitive DataSlide14

QuestionsSome Analysis of behavioral and cognitive resultsWhat is the general tendency of subjects’ choices?What is the payoff understandings of subjects?Objective game and subjective viewMore experiences, more precise view?Behavior when subjective view is correct/

incorrect w.r.t. the objective game14Round t

Round t’’

Round t’

5,

?

?

,

?

?

,

?

?

, ?

5,

?

?

,

?

6

,

?

?

,

?

5,

?

2,

?

6,

?

?

,

?

2

1

C

D

C

(5, 4)

(2, 5)

D

(6, 1)

(3, 2)Slide15

Payoffs Correctness relative to the Objective Payoffs

NNRSNARSSlide16

16Subjective view and Equilibrium

What is the equilibrium of the subjective view?Are they playing the equilibrium of the subjective view?(T, ARS): pair 8Incorrect but good enough to suggest for ICESlide17

17Incorrect for Dom for subject 1; X: 5 > [3] & 2 < 3; O: [5] < 10 & 1 < 2 for subject 2; X: [1] <2 & [1] = [1]; X:[1] < 10 & [1] =[1] Slide18

18Statistical Tests: Comparisons of Behaviors

Ambitious Claim:Statistical Tests are implied in Informal Postulates of IGT Slide19

Summary and Further Considerations19

We considered interactions between behavior and cognition.They are related to the thought processcriterion of trial/errorInductive derivation of a subjective view (interpretation of experiences) a lot of constraints - - inferential ability, forgetfulness, simplification of detailed informationetc.---------------------

A model of individual behavior is presented.

Statistical test about history-independence, excluding

the tit-for-tat strategy behavior, trigger strategy behavior.

Is the ambition accomplished? Slide20

20References

Entire Projects１．Kaneko, M., Game Theory and Mutual Misunderstanding, Springer (2004)２．Kaneko, M., and J. J. Kline, Two Dialogues on Epistemic Logic and Inductive Game Theory, forthcoming in Advances in Mathematics Research, Vol. 12, edited by Albert R. Baswell, Nova Science, New York (2011).

３．

ーーー

『

社会正義　地界で考える

』

　勁草書房　

2007

年

4.Kaneko,

M., Exploring New Socio-Economic Thought for a Small and Narrow Earth, mimeo (2009).Epistemic Logic

Kaneko, M., Epistemic logics and their game theoretical applications: Introduction. Economic Theory 19 (2002), 7-62.Kaneko, M., and N-Y. Suzuki, Epistemic Logic of Shallow Depths and Game Theory, Economic Theory 19:63-103, (2002).

Inductive Game Theory

Kaneko, M., and J. J. Kline, (2008), Inductive Game Theory: A Basic Scenario, Journal of Mathematical Economics

44, 1232-1263.Kaneko, M., and J. J. Kline, (2008), Par

tial Memories, Inductively Derived Views, and their Interactions with Behavior, to appear in

Economic Theory

, DOI: 10.1007/s00199-010-0519-0

Kaneko, M.,

and A. Mitra, (2007),

Discrimination in Festival Games with Limited Observability and Accessibility, to appear in Mathematical Social Sciences. doi:10.1016/j.mathsocsci.2011.03.002

Kaneko, M. and J. J. Kline, (2009), Transpersonal Understanding through Social Roles, and Emergence of Cooperation, University of Tsukuba, SSM.DP.1228.