Game Models And Dynamic Evolution Of Collective Behavior Under Uncertain Environment

Game theory(GT)is a branch of social science,which aims to study the strategic decisionmaking behavior.In 1940 s,von Neumann and Morgenstern first considered GT from a normative decision analytical framework when they studied human being's economic behavior.Later,Nash has mathematically proved the existence of equilibria in games based on fixed point theorems,which laid a solid foundation for the generalization of GT.Through several decades of development,GT has been gradually and widely applied to ecology,sociology,politics,international relation,military strategy,and many other disciplines and fields,becoming an important cornerstone of modern science.Traditional GT is on the basis of probabilities,it therefore is capable of dealing with random uncertainty.However,many studies including Heisenberg's uncertainty principle and chaos theory show that the uncertainty is one of the essential properties of the realistic world,and the uncertainty is not just the randomness in the sense of probability.Usually,decision-making subjects in games have to make decisions under uncertain conditions,the players may be not sure on the objective parameters of environment,what happens in a game,other players' actions and inferences,and so forth.Moreover,with the development of uncertainty reasoning theories,the uncertainty has more complicated and rich connotation.Given that,this dissertation centers on the study of game models and dynamic evolution of collective behavior under uncertain environment to investigate the modelling and application of GT in uncertain environment.The main work points of the dissertation are given as below.1.Considering the possible existence of ambiguity in the semantic condition,the DempsterShafer evidence theory is employed to express and model the ambiguity so as to study uncertain zero-sum matrix games and competitive multi-criterion decision making(MCDM)problem under the ambiguity environment.As for a two-person zero-sum matrix game with an uncertain payoff matrix,in the dissertation a novel zero-sum matrix game model with belief structure payoffs has been proposed.Within that game model,a linguistic variable transformation approach is used to separate the discord and nonspecificity from the belief structure payoff matrix step and step,after that the equilibrium of the proposed game model can be solved by means of the associated methods of interval-valued matrix games.Then,we have further studied a generalization of the two-person zero-sum matrix game — zero-sum polymatrix game and its link uncertainty.Another new game model,called zero-sum polymatrix game with belief structure links,is proposed,and its equilibria and other associated problems are also investigated based on a multi-player generalization of the minmax theorem and a linear programming solution for the original deterministic zero-sum polymatrix game.The proposed two game models,namely zero-sum matrix game with belief structure payoffs and zero-sum polymatrix game with belief structure links,are the extensions of classical zero-sum matrix games,which enrich and improve the theoretical research of zero-sum matrix games under uncertain environment.At last,with respect to uncertain decision-making problem that simultaneously contains ambiguity and multiple competitive subjects,the dissertation gives a competitive MCDM framework under ambiguity environment based on evidence theory and GT.The proposed framework provides an exercisable flow chart for this kind of problems,and is easy to use and extend further.2.By using the probability to represent random uncertainty of individual behavior and states,we have studied that how cooperation emerges and evolves among rational individuals under the network evolutionary game framework.At first,by considering the uncertainty of reference selection in the typical process of network evolutionary game,a self-adaptive winstay-lose-shift(WSLS)reference selection mechanism is proposed.In that mechanism,each individual dynamically determines its learning object according to current local information by adaptively following the WSLS principle.Technically,the proposed reference selection mechanism is more reasonable to reflect the difference and time-variability among individual expected payoffs in the evolutionary process.The simulations based on evolutionary prisoner's dilemma and evolutionary public goods game show that the self-adaptive WSLS mechanism could certainly enhance the cooperation level of a structured population,this mechanism therefore provides a new alternative scheme to promote cooperation.At second,by setting evolutionary dictator game as the experimental framework,we have systematically studied the formation and emergence of altruistic behavior,a special form of cooperation,in some homogeneous or heterogeneous structured populations under two kinds of strategy updating mechanisms including the one based on Darwin's theory of evolution and the other one based on punctuated equilibrium.Within that study,the impact of the uncertainty of roles assignation on the results of population's evolution is investigated to find which one,individuals with lower degrees to play as dictators or individuals with higher degrees to play as dictators,is better to promote population's altruism and reduce the inequality of payoff distribution.The work has presented a comprehensive understanding for that how the biological and social systems evolve and work in different underlying mechanisms.3.Based on two quantum game schemes,Eisert-Wilkens-Lewenstein and MarinattoWeber respectively,the dissertation studies quantum game models under quantum uncertainty,and how the co-evolution of classical and quantum games on a two-layer network impacts the collective behavior.As a compatible generalization of classical probability,quantum probability expresses the uncertainty in a deeper level.Previous studies show that quantum games have many features that are totally different with that of classical games.In the dissertation,we have first quantized the inspection game and analyzed its every equilibrium.The results show that the quantization can respectively help each player to increase his own payoff,yet fails to bring Pareto improvement for the collective payoff in the quantum inspection game.Then,we also study the quantization of three opinion formation game models,and find that in one of these quantum opinion formation games it could unconditionally generate non-zerosum and win-win equilibrium if given an appropriate initial entanglement state,which could promote the formation of public opinion.Besides,in the dissertation the network evolutionary game that bases on single layer network and classical game models has been extended to a two-layer network.Within that study,the entanglement degree of selected quantum game and coupling factor of constructed two-layer network are seen as variable parameters to investigate the impact of co-evolution of classical and quantum prisoner's dilemmas on the collective cooperation behavior,and we also discuss how to promote the generalized cooperation under the quantum game environment.The work on two-layer network has enriched the research of network evolutionary game.4.Classical GT is founded on the hypothesis that subjects are complete rational.By introducing natural selection and mutation into GT,Maynard Smith and Price established evolutionary game theory(EGT)on the condition of bounded rationality.In the dissertation,the application of EGT in uncertain environment has been investigated.Firstly,EGT has been applied to uncertain multi-source information fusion problem.We construct a Jaccard matrix game(JMG),then based on the replicator dynamics and JMG an evolutionary combination rule(ECR)is proposed to implement the combination of multiple evidences.Some typical paradoxes in evidence theory have been used to demonstrate the effectiveness of ECR.Secondly,we study the problem of information source selection(ISS).An ISS game is proposed,whose basic properties are also analysed.In terms of the proposed ISS game,we establish a new ISS model based on the replicator dynamics.The application of the new ISS model has been illustrated by two examples of two-source selection and three-source selection.Lastly,the binary opinion dynamics is investigated under the framework of EGT.We have built two models of opinion interaction,called BSO and BDO respectively,and analysed the impact of opinion preference and equivocators on the evolution of binary opinions on the basis of the replicator dynamics.These work,on the one hand enrich the application research of EGT,on the other hand provide new solution and research ideas for the corresponding specified problems.