Global Behavior in a Population of Adaptive Competitive Agents

Abstract

We present computer simulations and analysis for the global behavior arising from a population of heterogeneous social agents acting with bounded rationality. The particular model studied, termed the "bar-attendance" model, offers a simple paradigm for such complex adaptive systems involving competitive agents. The model considers p adaptive agents, each possessing n predic tion rules chosen randomly from a pool of N , who attempt to attend a bar where the seating capacity is s. The global attendance time-series x(t) has a mean near, but not equal to, s . Surprisingly, the standard deviation or "volatility" of x(t) can show a minimum with increasing adaptability of the individual agents. Various arguments based on random walk models are dis cussed. It is shown that effects of crowding have to be included in order to understand the volatil ity in this system.

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References

Amaral, L.A.N. , Buldyrev, S.V. , Halvin, S. , Salinger, M.A. & Stanley, H.E. (1998). Power law scaling for a system of interacting units with complex internal system. Physical Review Letters , 80, 1385-1388.

Arthur, W.B. (1994). Inductive reasoning and bound rationality. American Economic Review 84, 406-411.

Bak, P. ( 1997). How Nature Works. Oxford: Oxford University Press.

Bak, P. , Paczuski, M. & Shubik, M. (1997). Price variation in a stock market with many agents . Physica A, 246, 430-453.

Belew, R.K. & Mitchell, M. (1996). Adaptive Individuals in Evolving Populations. New York: Addision-Wesley.

Caldarelli, G. , Marsili, M. & Zhang, Y.C. (1997). A prototype model of stock exchange. Europhysics Letters, 40, 479-484.

Casti, J. (1996). What if? New Scientist. 13 July, 36-40.

Challet, D. & Zhang, Y.C. (1997). Emergency of coorperation and organization in an evolutionary game. Physica A, 246, 407-418.

Challet, D. & Zhang, Y.C. (1998). On the minority game: Analytical and numerical study. Physica A, 256, 514-532.

10.

Cont, R. & Bouchard, J.P. (1997) (condmat/9712318). Herd behaviour and aggregate fluctuations in financial markets. The preprint can be downloaded from the Los Alamos National Laboratory preprint library site accessible via Internet at http://xxx.lanl.gov. The preprint number is given in parenthesis.

11.

Epstein, J.M. (1997). Nonlinear Dynamics, Mathematical Biology and Social Science. New York: Addision-Wesley.

12.

Glance, N.S. & Huberman, B.A. (1994). The dynamics of social dilemmas. Scientific American, 270, 76-81.

13.

Hardin, G. (1968). The tragedy of the commons. Science , 162, 1243-1248.

14.

Holland, J.H. (1995). Hidden Order: How Adaptation Builds Complexity . New York: Addison-Wesley.

15.

Huberman, B.A. & Lukose, R.M. (1997). Social dilemmas and internet congestion. Science, 277, 535-537.

16.

Ilinski, K.N. & Stepanenko, A.S. (1998) (condmat/9806138). Electrodynamical model of quasi-efficient financial market. The preprint can be downloaded from the Los Alamos National Laboratory preprint library site accessible via Internet at http://xxx.lanl.gov. The preprint number is given in parenthesis.

17.

Johnson, N.F. , Hart, M. & Hui, P.M. (1999). Crowd effects and volatility in markets with competing agents. Physica A, 269, 1-8.

18.

Johnson, N.F. , Jarvis, S. , Cheung, P. , Kwong, Y.R. & Hui, P.M. (1998). Volatility and agent adaptability in self-organizing market. Physica A, 258, 230-236.

19.

Kauffman, S. (1993). The origins of order: Self-organization and selection in evolution. New York: Oxford University Press.

20.

Proceedings of the International Workshop on Econophysics and Statistical Finance (1999). Physica A, 269, 1-187.

21.

Reif, F. (1982). Fundamentals of Statistical and Thermal Physics . New York: McGraw-Hill.

22.

Savit, R. , Manuca, R. & Riolo, R. (1997) (adaporg/9712006). Adaptive competition, market efficiency, phase transition and spin-glasses. The preprint can be downloaded from the Los Alamos National Laboratory preprint library site accessible via Internet at http://xxx.lanl.gov. The preprint number is given in parenthesis.

23.

Schelling, T.C. (1978). Micromotives and Macrobehavior. New York: W. W. Norton & Company.

24.

Stewart, I. (1998). Life's Other Secret: The new mathematics of the living world. New York: John Wiley .

25.

Zambrano, E. (in press). Rationalizable Boundedly Rational Behavior. Cornell University.