Strategy Regulation And Optimization Of Networked Evolutionary Games With Risk And Memories

Networked evolutionary game theory is an important tool to investigate the e-mergence and maintenance of cooperation in natural,social,and economical sys-tems,and it's a focus and hot topic in the study of game theory.In a finite networked evolutionary game,both the number of players and the strategies of each player are finite,thus,the dynamics of the game can be expressed as a finite logical dynamic network.As a powerful tool for the analysis and control of logical dynamic network-s,the semi-tensor product method has also been used in studying the networked evo-lutionary games in recent years.Using this method,this paper firstly investigates the algebraic formulation for several kinds of networked evolutionary finite games,and then studies the control problem of them by regulating certain players' strategies.The main contents of this paper are listed as follows:1.The strategic regulation problem to avoid players going bankrupt in net-worked evolutionary games is studied.First,the games are expressed as logical dy-namic networks and converted into their algebraic forms.Besides,by constructing the algebraic form of each player's payoff function,the strategic regulation problem of the given game is transformed into the control problem of a logical dynamic sys-tem.Then,sufficient and necessary conditions are obtained to detect whether free control sequences and state feedback controls can be designed to avoid any player going bankrupt.Moreover,the design methods of these two kinds of controllers are given.2.The strategy optimization of networked evolutionary games with bankruptcy risk and finite memories is studied.First,the evolutionary dynamics is expressed as a higher-order logical dynamic network and then converted into its algebraic form by establishing the game's strategy transition matrix.Then,a sufficient and necessary condition is given to detect whether an initial strategy profile can reach to the optimal strategy profile by some free control sequences while avoiding the bankruptcy status,and the method to design the control sequences is given.3.The stability problem for networked evolutionary games with finite memo-ries and time-varying networks is investigated.First,this kind of games is modeled as a state-depended high-order probabilistic switching logical network and converted into its algebraic form.Then,the existence of fixed point of the algebraic form under some assumptions is verified.Finally,some sufficient conditions are given to detect whether the game can globally converge to the strict pure strategy Nash equilibrium,and proper control sequences are designed.4.The cooperation and optimization for evolutionary public goods games on circle are studied.First,by constructing the strategy transition matrix,the evolution-ary public goods game whose strategy updating rule is Fermi rule is modeled as a standard Markov process.Then,the dynamic evolution law of the game is summa-rized based on the computer simulation results.Moreover,the effect of control on the final cooperation level is studied.