Dynamical interplay between local connectivity and global competition in a networked popula.pdf

a r X i v : c o n d - m a t / 0 4 0 1 5 2 7 v 3 [ c o n d - m a t .d i s - n n ] 3 1 J a n 2 0 0 4 Dynamical interplay between local connectivity and global competition in a networked population S. Gourley1, S.C. Choe1, P.M. Hui2, and N.F. Johnson1 1 Clarendon Laboratory, Physics Department, Oxford University, Oxford OX1 3NP, United Kingdom, 2 Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong (February 2, 2008) We show, both numerically and analytically, that the consequences of ‘wiring up’ a competitive pop- ulation depend quite dramatically on the interplay between the local connectivity and the global resources. With modest global resources, adding small amounts of local connectivity yields an increasingly heterogeneous population. With substantial global resources, high-performing yet rea- sonably homogenous collective states emerge instead. PACS numbers: 02.50.Le, 87.23.Kg, 89.65.Ef, 05.40.2a Is ‘getting connected’ a good or bad thing? How does increased access to both global (i.e. public) information and local (i.e. private) information, affect both the pop- ulation as a whole and its individual members? Thinking in terms of future technologies, what are the possible ben- efits and dangers of introducing communication channels between collections of intelligent devices, microsensors, semi-autonomous robots, nanocomputers, and even bi- ological micro-organisms such as bacteria [1,2]? These questions are relevant to a wide range of computa- tional, technological, biological and socio-economic sys- tems. However such questions are very difficult to answer since these systems are simply ‘too complex’ [3–7]. Here we examine these questions using a minimal generic model which mimics a group of selfish, rational individuals or components, referred to simply as ‘agents’. These agents repeatedly compete for a global resource by making inductive decisions about future group be- havior. The population and its agents ma