Research On Social Dilemma Games Based On The Structural Balance Theory On Signed Networks

Evolutionary game has applications in many fields,from engineering to economics and social sciences.Applying evolutionary games to complex networks has become a hot research field.In real society,due to different personalities or interests,friendship or hostility will be established between people,and the alienation or closeness of the relationship will have a greater impact on the game.However,the existing evolutionary game studies on networks rarely comprehensively involve the multiplicity of this relationship,and lack research on the synchronized evolution of structural balance.Trying to fill this gap,this thesis proposes a new prisoner’s dilemma game model on signed networks.In this model,we introduce trust factors and a modified Fermi function to characterize the impact of different relationships on the payoff matrix and strategy imitation respectively,and derive fixed probability formulas.Moreover,the theory of structural balance is extended by taking into account the nodes’ strategy,and a new game-theoretic structural balance for the prisoner’s dilemma model is defined.Following,a measure of structural balance rate calculated by energy functions is proposed for the first time,to directly reflect the change of structural balance.In addition,we generalize this model to snowdrift and stag-hunt games.We explore the effect of trust factors on the three social dilemma game models respectively and study the impact of game parameters as well as network parameters on evolution,and investigate the impact of monotonic structural balance increasing on the evolution of cooperation in signed networks.Simulation results show that under the optimal parameter settings of the trust factors,there is a better chance for cooperators to survive and maintain cooperation in the prisoner’s dilemma model compared to scenarios without trust factors.Moreover,the PD game structural balance defined in this thesis can reflect the survival situation of cooperators in the game.When the condition parameters are not suitable for the survival of cooperators,the game structural balance weakens continuously with the iteration,while the opposite is also true.Moreover,if the temptation value is lower than a certain threshold,the PD game structure balance changes its dynamic properties.Furthermore,when the classical structural balance has a monotonic growth control beginning at 0,it can successfully promote the cooperator’s survival in all three game models.