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1 Vol. No. Jan. 96, Effects of Internal Dynamics and Micro-Macro Loop on Dynamics of Social Structures Takashi Sato, and Takashi Hashimoto We discuss a condition required for forming and maintaining dynamics of macro structure in a society from the dynamical view of society, which regards social structure as dynamically changing with time. We summarize results of a multi-agent simulation composed of agents having internal dynamics. In the simulation, we observe the dynamics of a macro structure itinerating among various kinds of ordered patterns via aperiodic motion. Further, we report results of analyses investigating an effect of the micro-macro loop on dynamics of social structures. Based on the analyses, we conclude that internal dynamics of agents and micro-macro loop are necessary to form and maintain an endogenous dynamics of social structure.. / 2),2) School of Knowledge Science, Japan Advanced Institute of Science and Technology Presently with Initial Research Project, Okinawa Institute of Science and Technology, JST Blumer 2) Tarde / 25) Veblen 29) / /

2 2 Jan. 96 Simon 22) Knight 4) Hayek 9) voluntarism 24) 5) 8) ) Simple Recurrent Network with Self-Influential Connection; SRN-SIC SRN-SIC 9) SRN-SIC circadian rhythm Necker Cube Varela 28) Karmiloff-Smith 3) Gelder Gelder 26),27) / Necker Cube 6),8)

3 Vol. No. 3 ),2) 2 SRN-SIC SRN-SIC 9) / 2 SRN-SIC 3 / 4 / / 2.2 Elman Simple Recurrent Network; SRN 6) SRN SRN with Self-Influential Connection; SRN-SIC 9) SRN 2 Necker Cube 2 7),23) Giddens 7)

4 4 Jan. 96 Own past output value Output Layer L Hidden Layer L Input Layer L L External Stimulus : Unlearnable (Weights are fixed at.) : Learnable (By normal BP) Context Layer Hidden neurons past output values SRN SRN-SIC Fig. Architecture of agent having internal dynamics, called Simple Recurrent Network with Self- Influential Connection (SRN-SIC). 4 SRN-SIC SRN-SIC SRN-SIC -.. () L(net) =tanh(βnet) () net β L SRN-SIC (2) (3) o k (t) =L(net k (t)) (2) net k (t) = w kj v j(t)+θ k (3) j o k (t) t k w kj k j v j(t) t j θ k k (4) (5) v j(t) =L(net j(t)) (4) net j(t) = w jix i(t)+ w jh v h (t ) i h + w jl o l (t ) + θ j (5) l w ji j i x i(t) t i w jh j h v h (t ) t h w jl j l o l (t ) t l θ j j SRN-SIC. SRN-SIC 2.3 Challet Minority Game MG 3) MG 3) MG 2 MG () n 2 or - or (2) SRN-SIC -.. MG. -

5 Vol. No. 5 MG MG - or,, SRN-SIC SRN-SIC 5 2 SRN-SIC. SRN-SIC MG,,, ) 2) 3) 4) 5) 6) 6 9) - 2 )

6 6 Jan Fig. 2 2 An example of the itinerant dynamics at the macro level in one turn. Table Classification of dynamics observed at the macro level in one turn. 2 ( ) Veblen 3) Veblen 5) Veblen 4 Challet MG 3) 4),5) MG MG

7 Vol. No. 7 MG / 28, 29, 28 28,,, 28,,28, 28 78,,, ) ) 2 3(a) (c) (a) (c) 3(a) (c) 4 a -.. b c a c 4 a c a 5 b

8 8 Jan. 96 (a) -. is given. Start e+6.e+6.2e+6 (b). is given. Start e+6.e+6.2e+6 Start Fig. 3 (c). is given e+6.e+6.2e+6 Collapse and regeneration of the itinerant dynamics by starting and ending of the artifactual fixed inputs. (a) Random number between -. and. is given. Start e+6.e+6.2e+6 (b) Random number between -.5 and.5 is given. Start e+6.e+6.2e+6 (c) Random number between -. and. is given. Start e+6.e+6.2e+6 4 Fig. 4 Collapse and regeneration of the itinerant dynamics by starting and ending of the uniform random inputs with various ranges. 5 a b a 4 b

9 Vol. No. 9 (a) Different itinerant dynamics is shaped (b) Intermittent dynamics is shaped. Regenerated the original period four dynamics Regenerated the original fixed point a b Fig. 5 Dynamics at the macro level when the itinerant dynamics is input to the agents shaping (a) single fixed and (b) single periodic dynamics Table 2 Summary of the experiments in which the micromacro loop is temporarily cut off

10 Jan Table 3 The correspondence between dynamics at the macro level and the configuration of agents at the micro level. Hidden_ Output Hidden_3 6 Fig. 6 The strategy of agent showing chaotic behavior in the group shaping the itinerant dynamics x y z (SRN-SIC)

11 Vol. No. SRN-SIC No.5783 ) Aoki, M.: Towards A Comparative Institutional Analysis, MIT Press (2). 2) Blumer, H.G.: Symbolic Interactionism: Perspective and Method, Prentice-Hall (969). ( ) :, (99). 3) Challet, D., Zhang, Y.C.: Emergence of Cooperation and Organization in An Evolutionary Game, Physica A, 246, pp (997). 4) Challet, D.: The Minority Game s web page, 5),,, ( ) :,, 7, pp (24). 6) Elman, J.L.: Finding Structure in Time, Cognitive Science, 4(2), pp (99). 7) Giddens, A.: New Rules of Sociological Method, Hutchinson (976), (993, 2ed.).,, ( ) :, (987), (2, 2ed.). 8) Hashimoto, T., Egashira, S., Formation of social norms in communicating agents with cognitive frameworks, Journal of Systems Science and Complexity, 4(), pp (2). 9) Hayek, F.: Rules, perception and intelligibility, Studies in Philosophy, Politics and Economics, Univ. of Chicago Press (967). ) Kaneko, K., Tsuda, I.: Chaos: Focus Issue on Chaotic Itinerancy, Chaos, 3(3), pp (23). ), :, (997). 2), :, (998). 3) Karmiloff-Smith, A.: Beyond Modularity: A Develop-mental perspective on Cognitive Science, MIT Press (992). 4) Knight, F.H.: Risk, Uncertainty and Profit, Univ. of Chicago Press (92). 5) Moro, E., The Minority Game: an introductory guide, In: Korutcheva, E. and Cuerno, R. (Eds.): Advances in Condensed Matter and Statistical Mechanics, Nova Science (24). 6) Nagao, N., Nishimura, H., and Matsui, N.: A neural chaos model of multistable perception, Neural Processing Letters, 2(3), pp (2). 7), :, (2). 8) Nishimura, H., Nagao, N., Matsui, N., A perception model of ambiguous figures based on

12 2 Jan. 96 the neural chaos, In: Kasabov, et al. (Eds.): Progress in Connectionist-Based Information Systems,, Springer-Verlag, pp (997). 9) Sato, T. and Hashimoto, T., Dynamic Social Simulation with Multi-Agents having Internal Dynamics, In: Hasida, K. and Nitta, K. (Eds.): New Frontiers in Artificial Intelligence: Joint Proceeding of the 7th and 8th Annual Conferences of the Japanese Society for Artificial Intelligence, LNCS, Springer-Verlag (25, To be published). 2) :, NTT (997). 2) :, (997). 22) Simon, H.A.: Models of Man, John Wiley & Sons (957). 23) :, (994). 24), :, (2). 25) :, 8 (995). 26) van Gelder, T., Port, R., Its about time: An overview of the dynamical approach to cognition,in:port,r.,vangelder.,t.(eds.),mind as Motion: Explorations in the Dynamics of Cognition, MIT Press (995). 27) van Gelder. T.: The Dynamical Hypothesis in Cognitive Science, Brain and Behavioral Sciences, 2, pp (998). 28) Varela, F.J., Thompson, E., Rosch, E.: The Embodied Mind Cognitive Science and Human Experience, MIT Press (99). 29) Veblen, T.: Why is Economics Not an Evolutionary Science, The Quarterly Journal of Economics, 2 (898). 3) Veblen, T.: The Place of Science in Modern Civilisation and Other Essays, Huebsch (99). 3) Zhang, Y.C.: Modeling market mechanism with evolutionary games, Europhys. News, 29, pp (998). ( 6 9 ) ( 7 8 ) ( 7 7 ) ,,.,, Sony Computer Science Laboratory-Paris. 2-22,..,.,,,.

Consideration of Cycle in Efficiency of Minority Game T. Harada and T. Murata (Kansai University) Abstract In this study, we observe cycle in efficien

Consideration of Cycle in Efficiency of Minority Game T. Harada and T. Murata (Kansai University) Abstract In this study, we observe cycle in efficiency of Minority Game. The Minority Game is a game when