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

1. 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 • Prisoner’s dilemmas are repeated 50 times • No 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 perspective • Sharpened • Extended

2. Research Projects M. Kaneko Chiayi ２０１１・10・03 Social Justice Understanding of Society and Human in Society • Mathematical thinking • Logical Inferences & Decision Making Emphases • Symbolic thinking (Syntactical/grammatical) • Interpretation of Symbolic Expressions (semantic) 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 Soft Institutions • Emergence of Value・Morality • Etc. Hard Institutions • Tax Systems • Etc. Epistemic Logic Inductive Game Theory Social Institutions

3. Basic Assumption: no knowledge about payoffs Formal Theory Interactive 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. Kaneko-Kline papers a): Generating experiences - - trials/errors b): Memorizing such experiences c): Limitations on a) and b): restricted trials/errors, forgetfulness, mistakes, misunderstanding Informal Theory A model of individual behavior – Statistical Analysis: - - sharpening and extending the informal theory - - Present paper

4. 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.

5. 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) × G G 2 G G 2 2 2 B B B B NRS 1 1 1 1 50 rounds G G 2 G G 1 1 B B 2 B B ARS 1 2 1 2

6. c d Three Types of Prisoner’s Dilemma Games Quasi-Symmetric 1 (QS1) Quasi-Symmetric 2 (QS2) Twisted (T) • Asymmetric? • Twisted? c d － = c d • In all games • d – Dom • (d,d) - - NE • (c,c) is an ICE • in QS1,QS2 • (c,d) is an ICE • in T c d － = c d c d = +

7. Summary of the Treatments = 168 subjects (14 × 2 × 6) Between-Subject Design Subjects ・Undergraduate students of Waseda University. ・ Recruited from many majors; excepts for economics. Location Experiment Lab of Waseda University

8. Basic Information Structure • Known structure: • Number of actions for each role • No change in the Payoff matrix across periods • A 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.

9. (T, ARS): pair 8 c d c d Aggregated Frequencies over the subjects for NRS

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

13. Summary of Experimental Data Behavioral 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. Cognitive Data • 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.

14. 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 Round t Round t’ Round t’’

15. Payoffs Correctness relative to the Objective Payoffs NNRS NARS

16. 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

17. 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]

18. Statistical Tests: Comparisons of Behaviors Ambitious Claim: Statistical Tests are implied in Informal Postulates of IGT

19. Summary and Further Considerations • 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?

20. References • Entire Projects • １．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), Partial 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.