Evolution Of Cooperation With An Exit Option And The Statistical Modeling Of Network Topology

The evolution and maintenance of cooperation is one of the main challenging sci-entific problems.Current studies suggest that the maintenance of cooperation depends on five reciprocity mechanisms,namely: direct reciprocity,indirect reciprocity,net-work reciprocity,kin selection and group selection.Although these mechanisms ap-pear to be materially different,the common potential assumption of these five recip-rocal mechanisms is that participants can not exit from the game,and this is in sharp constrast with realitics.Therefore,it is of great practical significance to investigate the influence of exit mechanism on the evolution of cooperation from both theoretical and experimentall points.In addition,in the study of collective decision-making theory with complex networks,how to estimate the parameters with signal properties(the valus of these parameters are either 0 or 1.)in order to recover the network topology is an im-portant topic in the field of network science and statistics,Based on mentioned above,in this thesis,we use evolutionary game theory to study the evolution of cooperation among selfish individuals in public goods game with an exit option by estabilishing the human behavior experimental model? Then,we use the methods of stability theory of differential equations,agent-based model and Markov transition matrix to study the cooperative dynamics with an exit option in well-mixed situations and networked pop-ulations.Lastly,for the problems of network reconstruction with signal parameters,we propose a new method called signal lasso and discuss its properties from theoret-ical analysis and numerical simulations.In detail,this thesis can be divided into the following three parts.1.In the collective decision-making experimental study of repeated public goods game with exit option.Through recruiting volunters in different universities,we esta-bilish the human behavior experimental model and investigate the evolution of coop-eration under five conditions: traditional public goods game(C0),pubic goods game with high expected exit's payoff(T0),public goods game with moderate expected exit's payoff(T1),public goods game with lower expected exit's payoff(T2),as well as public goods game with low expected exit's payoff(T3).The results show that the evolution-ary outcomes depend on the expected payoff of exiter.When the expected payoff of exiter is too large,most of the participants in the public group choose to exit from the group,and this further leads to the collapse of the cooperative system.When the ex-pected payoff of exiter is too small or negative,the exit choice does not work in this case,and the game is returned to the traditional public goods game.When the expected payoff of exiter is moderate,the existence of exit channels can filter out the bad things and play a role of regulating the investment environment dynamically in the public group.2?In the theoretical study of prisoner's dilemma game with exit option.In part 1of chapter 4,we study the evolutionary dynamics of Prisoner's dilemma game in which ooperators and defectors interact with another actor type called exiters(we call this model as CDE model).Instead of being exploited by defectors,exiters can exit from the game with the support of small but positive payoff.We find that cooperation flouish in well-mixed populations only if the additional reciprocity mechanisms are incorporated.While in structured populations,eixt option enables the coexistence of cooperators,de-fectors,and exiters through cyclic dominance.Other outcomes are also possible as the increases of exit's payoff or the changes of network structure,including global oscilla-tions,hub-node stabilization.In part 2 of chapter 4,we further extend the above CDE model by spliting the exiter into two types: conditional exiting cooperators(CE)and conditional exiting defectors(DE),and we then study the evolutionary outcomes of the Prisoner's dilemma game in finite populations.In our revised model,we assume that in order to avoid unfavorable outcomes,exiters including EC and ED,pay a monitoring cost,c,to exit from the game in favour of a temptation payoff ? when it play with defec-tors.Through calculating fixation probabilities,we separate investigate the evolution of cooperation under three condition: of only cooperators can exit from the game,only defectors can exit from the game,and cooperators and defectors can both exit from the group.We find that cooperation cannot emerges under the condition of only defectors can exit from the group,and the evolutionary outcomes are either defectors dominate or DE dominates.For the results with the condition only cooperators can exit,cooper-tion can be maintained with the support of cyclic dominance of cooperators,defectors,and conditional exiting cooperators.While for the condition of both cooperators and defectors can exit from the group,cooperation can be promoted via the multiple cyclic dominance including the route of C ? D ? CE ? C,C ? DE ? CE ? C and C ? D ? DE ? CE ? C.3?In the problems of network reconstruction,for the binary property of the adha-cency: the values of the element in adjacency are either 0 or 1.We propose the method of signal lasso for to infer the network structure by applying the evolutionary game theory,Kuramoto model,and human behavior experiment on complex netorks to gen-erating the time series data.By adding a control term of L1-norm to the penalty function of lasso method,this method is able to shrink the estimates to 0 and 1 simultaneously and theore overcome the limitation of lasso,where estimates can be only shrinked to 0.Through comparing the performance of lasso,compressed sensing and signal lasso on different types of time series data and noisy time series data.We find that the network topology estimation under signal lasso has higher accuracy and stronger robustness to noise compared with other two methods.