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| Resource allocation takes place in various kinds of real-worldcomplex systems, such as the traffic systems (e.g., urban trafficsystem and flight systems), social services institutions ororganizations (e.g., bank, theater, and mart, financial market),or even the ecosystems. Resources are always limited, and agentstend to choose the least used resource based on certain availableinformation, obeying the fundamental principle that theemph{minority wins}. In these systems, herd behavior is harmfulfor the efficiency of resource allocation. However, it isubiquitous in real cases, and present to be congestion in trafficsystem, extreme events in financial system, and other crisis insocial system, all of which are commonly characterized by the lowefficiency of resource allocation. For the sake of preventing herdbehavior and improving the efficiency,it is proposed thatpinning scheme to fix certain individuals' options, and itsystematically is studied that the effect of emph{pinning} to the resourceallocation dynamics of boolean game systems. The work demonstratesthat, the sacrifice of certain individuals' options may markedlyimprove the efficiency of the whole system. Especially, in certaincases, the system performs better than the random game systemthrough self-organized processes. We develop an analytic theorybased on the discrete time master equation to understand theeffect of pinning. The rule to design effective pinning scheme arealso discussed. The work represents a basic and generalmathematical framework to address the fluctuation of the resourceallocation in social, economical and political systems. |
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| Keywords:theoretical physics; complex system; minority game; resource allocation |
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