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

An Experimental Study of Cognition and Behavior from the Perspective of Inductive Game Theory

By M. Kaneko (with A. Takeuchi, Y. Funaki and J. J. Kline)

0) No knowledge about the payoffs, even for his own

1) Prisoner’s dilemmas are repeated 50 times• No Role-Switching • Alternating Role-Switching

2) 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 perspective• Sharpened • Extended 1

Social Justice　 Research Projects M. Kaneko

Chiayi ２０１１・10 ・ 03

• Mathematical thinking• Logical Inferences &

Decision Making

Emphases• Symbolic thinking

(Syntactical/grammatical)

• Interpretation of Symbolic Expressions (semantic)

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Inductive Game Theory 　Epistemic Logic 　Understanding of Society and Human in Society 　

Experiences as Given• Derivations/Use/Revision of

Beliefs/Understanding

Emphasis• From Experiences to Beliefs• Generations of Experiences• Interactions between

cognition and behavior

• Interpretation of Symbolic thinking

Social Institutions 　Soft Institutions• Emergence of

Value ・ Morality• Etc.

Hard Institutions• Tax Systems• Etc.

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.

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a): Generating experiences - - trials/errors

b): 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 paper

Basic Set-up

• Subjects 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.

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Experimental Treatments 2 × 3 and 50 rounds

2 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

BBB GGG

1

2

2 2

1 1G

1

2

BBB GGG

1

2

1 1

2 2G

1

2B

B

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

Quasi-Symmetric 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 T

Summary of the Treatments

QS1 QS2 T

Role-Switching 14 Pairs 14 Pairs 14 Pairs

No Role-Switching 14 Pairs 14 Pairs 14 Pairs

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= 168 subjects (14 × 2 × 6)Between-Subject Design

Subjects・ Undergraduate students of Waseda University.・ Recruited from many majors; excepts for economics.

Location

Experiment Lab ofWaseda University

Basic Information Structure

– Known structure:1. Number of actions for each role2. No change in the Payoff matrix across periods3. A role assignment but not a specific assignment.

– The payoff structure is not known:1. A subject does not know about the payoff structure --- not “unknown” in the sense of uncertainty.2. A subject receives a payoff value after each round --- Experiences become the source for his subjective view.

8

9

5, 4 2, 10

6, 1 3, 2

cd

c d

(T, ARS): pair 8

Aggregated Frequencies over the subjects for NRS

10

11

12

Today, 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

Summary of Experimental Data

• 3 games ×2 types of role-switching = 6 treatments• Each treatment has 14 pairs of subjects • Each pair show a trajectory of action pairs for 50 rounds.

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• Payoff answers from each subject• In each treatment of NRS, 4 numerical answers are given • In each treatment of RS, 8 numerical answers are given.

Behavioral Data

Cognitive Data

Questions

Some Analysis of behavioral and cognitive results• What is the general tendency of subjects’ choices?• What is the payoff understandings of subjects?

Objective game and subjective view• More experiences, more precise view?• Behavior when subjective view is correct/ incorrect w.r.t. the objective game

14Round 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)

Payoffs Correctness relative to the Objective Payoffs

NNRS

NARS

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• Subjective view and Equilibrium– What is the equilibrium of the subjective view?– Are they playing the equilibrium of the subjective view?

(T, ARS): pair 8

Incorrect but good enough to suggest for ICE

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Incorrect 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]

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Statistical Tests: Comparisons of Behaviors

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

Summary and Further Considerations

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• We considered interactions between behavior and cognition.• They are related to

• the thought process• criterion of trial/error• Inductive derivation of a subjective view (interpretation of

experiences) • a lot of constraints - - inferential ability, forgetfulness, simplification of detailed information• etc.

--------------------- • 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?

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ReferencesEntire 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 Logic1. Kaneko, M., Epistemic logics and their game theoretical applications:

Introduction. Economic Theory 19 (2002), 7-62.2. Kaneko, M., and N-Y. Suzuki, Epistemic Logic of Shallow Depths and Game

Theory, Economic Theory 19:63-103, (2002).

Inductive Game Theory3. Kaneko, M., and J. J. Kline, (2008), Inductive Game Theory: A Basic Scenario,

Journal of Mathematical Economics 44, 1232-1263.4. Kaneko, M., and J. J. Kline, (2008), Partial Memories, Inductively Derived Views,

and their Interactions with Behavior, to appear in Economic Theory, DOI: 10.1007/s00199-010-0519-0

5. 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

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