  Resource allocation takes place in various types of real-world complex
systems such as urban traf- fic, social services institutions, economical and
ecosystems. Mathematically, the dynamical process of complex resource
allocation can be modeled as minority games in which the number of resources is
limited and agents tend to choose the less used resource based on available
information. Spontaneous evolution of the resource allocation dynamics,
however, often leads to a harmful herding behavior accompanied by strong
fluctuations in which a large majority of agents crowd temporarily for a few
resources, leaving many others unused. Developing effective control strategies
to suppress and elim- inate herding is an important but open problem. Here we
develop a pinning control method. That the fluctuations of the system consist
of intrinsic and systematic components allows us to design a control scheme
with separated control variables. A striking finding is the universal existence
of an optimal pinning fraction to minimize the variance of the system,
regardless of the pinning patterns and the network topology. We carry out a
detailed theoretical analysis to understand the emergence of optimal pinning
and to predict the dependence of the optimal pinning fraction on the network
topol- ogy. Our theory is generally applicable to systems with heterogeneous
resource capacities as well as varying control and network topological
parameters such as the average degree and the degree dis- tribution exponent.
Our work represents a general framework to deal with the broader problem of
controlling collective dynamics in complex systems with potential applications
in social, economical and political systems.
