Resource Allocation And Evolutionary Dynamics In Complex Systems

The phenomena of abundant agents competing for limited resources are ubiquitous in nature. e.g. herding, crowd panic, stampede. Understanding to the micro-mechanism underlying those macro-phenomena is crucial for controlling and optimization the complex systems. The theory of optimal resource allocation is the prerequisites to e?cient resource utilization in real world. Therefore,to explore the proper controlling methods for various complex systems to optimize resource allocation is a signi?cant issue in practical, as well as theoretical?elds and has drawn vast interests from the researchers in the ?eld of complex systems. Based on the experimental observations and analysis of data from the reality systems, researchers have established a series of theoretical frameworks and corresponding models on resource allocation followed by plentiful achievements under various background. Moreover, these works also give us further insights in the development of nonequilibrium statistical theory. Standing on the shoulders of the giants, we carry out some researches on resource allocation in complex systems.(1) The emergence of grouping in multi-resource minority game dynamics was reported and explained by a systematic theoretical framework.(2) An intuitive control strategy, namely pinning control, was put forward to inhibit the herding behavior and the consequent low resource utilization.Another important issue in the ?eld of complex systems and complex networks is how the spreading of view-point affects agents’ actions and global dynamics of the systems. An interesting typical example is, the diffusion of the knowledge of vaccination was found to change the spreading threshold of infectious diseases. Here, we combine the prisoner’s dilemma game and view-point spreading dynamics to construct an interdependent model and give a tentative explanation to the emergence of cooperation in reality.The structure of this thesis and the innovation are as follows.Chapter 1: In this chapter, we introduced the basic conceptions and statistical quantities for complex systems, complex networks, as well as classical network models. Two commonly used models on resource allocation(minority game and boolean game) and the theory about evolutionary game are also discussed. Moreover, a general introduction on the common mathematical methods and theories such as mean-?eld theory, Markov process, master equation and generating function etc. are provided.Chapter 2: Complex systems arising in a modern society typically have many resources and strategies available for their dynamical evolution. From the data of Shanghai Stock-Market system, we have identi?ed the grouping phenomenon of resources(e.g., stocks), and its prevalence in other real-world systems. To explore quantitatively such behaviors, we propose a class of models, Minority Game(MG) dynamics with multiple strategies. A striking ?nding is the emergence of grouping states de?ned in terms of distinct strategies. We developed an analytic theory based on the mean-?eld framework to understand the “bifurcations”of the grouping states. Our work demonstrates that complex systems obeying the MG rules can spontaneously self-organize themselves into certain divided states,and our model represents a basic and general mathematical framework to address this kind of phenomena in social, economical and political systems.Chapter 3: Herding behavior is extremely harmful to resource allocation processes for the reason that a large majority of agents crowding temporarily for a few resources leaving many others unused. We have put forward pinning control approach, a intuitive control strategy, to restrain the ?uctuation of the utility of resources, and furthermore build up a systematic theoretical framework to describe and predict the e?ciency of control. The pinning control strategy we proposed here is of high e?ciency and practically available. In speci?c, by ?xing the choices of resources for a few agents while leaving the majority of the agents free, herding can be eliminated completely. Our investigation is systematic for we consider random and targeted pinning on a variety of network topologies, and we carried out a comprehensive analysis in the framework of mean-?eld theory to understand the working of control.Chapter 4: The pinning control strategy is studied in a more general framework, taking into account the effects of biased pinning patterns, various topologies of coupling structures and so on. A striking ?nding is the universal existence of an optimal pinning fraction(which minimize ?uctuation of the system) regardless of the pinning patterns and the network topology. We carry out a generally applicable theory to explain the emergence of optimal pinning and to predict the dependence of the optimal pinning fraction on the network topology. 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.Chapter 5: In social systems, individuals always adopt mixed strategy instead of pure strategy in game dynamics. To explain how cooperation emergence in the system composed of mixed-strategy agents, we integrated the classical Prisoner’s Dilemma Game and view-spreading dynamics to construct a novel evolutionary hyper-game model. From simulation, it was found that cooperation still have chance to be prosperous in mixed-strategy agent systems. Through semi-analytical theoretical analysis, we obtained the restricted condition for the emergence of high-density cooperation. A systematic analysis of the dynamics in the parameter space indicates that generous environment and vigilance of agents confronting unreal view-point conduce to the emergence of the cooperation in the form of mixed-strategy. These conclusions may shed insight on further understanding the emergence of cooperation, as well as agents’ interactions affected by the view-spreading processes in real systems.Chapter 6: We summarized our previous works and discussed the research orientation and prospective.