Minority Game with Interaction via Various Networks

1. The 13th statistical physics workshop @ Kyonggi Univ. Minority Game with Interaction via Various Networks Sang Hoon Lee and Hawoong Jeong,Complex Systems and Statistical Physics Lab.,Korea Advanced Institute of Science and Technology

2. The Minority Game What if we connect the players by networks? The results by numerical simulation This presentation will provide the results of the networked version of the Minority Game

3. Minority Game (MG) captures bounded rationality and inductive reasoning The quantified Minority Game El Farol bar at Santa Fe D. Challet and Y.-C. Zhang,Physica A 246, 407 (1997) The number of people in the bar

4. αc ~ 0.34 for S=2 What are we interested in the MG? Volatility phase transition Time series of choice

5. Anghel et al. show the emergence of the scale-free leadership structure by MG on the ER random network In-degree distribution of the “follower” networks M. Anghel et al., Phys. Rev. Lett. 92, 058701 (2004)

6. Topology of substrate networks determines the shape of the volatility of the system the smallest volatility

7. Disorderness of WS small-world network effects on the different phases of MG

8. How does disorderness of WS network effect on the volatility of the MG system? Average path length changes rapidly with p, related to the information transfercf) The asymmetric phase is the (exploitable) information-rich phase Clustering coefficient changes rapidly with p, related to the crowding effectcf) The symmetric phase is the crowded phase

9. The power-law in-degree distribution is observed for many substrate networks In-degree distribution of follower networks BA ER a snapshot of choice GKK

10. MG on 2D regular lattice shows the power-lawdistribution of “choice clusters” the distribution of sizes of clusters based on the spatial pattern of choice a snapshot of choice In the percolation theory, p(s) ~ s-1.25 when the occupation probability is larger than the threshold 0.5927 of the 2D site percolation

11. Underlying topology influences the properties of the Minority Game • Volatility of MG on various networks has quite different structures from the original MG depending on the topology of substrate • Disorderness of the substrate networks (rewiring probability p of WS network) affects the form of volatility function in different domains depending on the degree of disorderness • From the structure of the follower networks or the spatial pattern of choice, we have observed that the scale-free structure represented by the power-law appears

12. Reference • http://www.unifr.ch/econophysics/minority/ • D. Challet, M. Marsili, and Y.-C. Zhang, Minority Games (Oxford University Press, Oxford, 2005). • W. B. Arthur, Amer. Econ. Review 84, 406 (1994). • D. Challet and Y.-C. Zhang, Physica A 246, 407 (1997). • E. Moro, e-print cond-mat/0402651. • M. Anghel, Z. Toroczkai, K. E. Bassler, and G. Korniss, Phys. Rev. Lett. 92, 058701 (2004). • T. S. Lo, K. P. Chan, P. M. Hui, and N. F. Johnson, Phys. Rev. E 71, 050101(R) (2005). • D. J. Watts and S. H. Strogatz, Nature 393, 440 (1998). • A.-L. Barabási and R. Albert, Science 286, 509 (1999). • K.-I. Goh, B. Kahng, and D. Kim, Phys. Rev. Lett. 87, 278701 (2001). • D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994), revised 2nd ed.

13. “It is not worth an intelligent person's time to be in the majority. By definition, there are already enough people to do that.” - Godfrey Harold Hardy Thank You !!! =)