Analysis Of Opinion Dynamics Based On Evolutionary Games

In recent years,opinion dynamics on complex networks have attracted extensive attention from scholars in various fields such as applied mathematics,control theory,systems science,artificial intelligence,and computer science.Researchers have studied the propagation dynamics of opinions on complex networks by integrating evolutionary game theory,but most of previously related works are based on computer simulations and there are far a few studies in which theoretical analysis is performed.Under this circumstances,the thesis proposes an evolutionary game-theoretical model of binary opinions and carries out analytical calculations to identify the mathematical conditions of successful opinion spreading on complex networks.First,the condition in which a certain opinion can be spread on the networks is explored.Combining with evolutionary game theory,this thesis establishes an evolutionary model of binary opinions on complex networks from the microscopic perspective of decision-making interaction.Inspired by real-life observations,it is assumed that an agent's choice to select an opinion is not random,but is based on a score rooted from public knowledge and the interactions with neighbors.By means of coalescing random walks,the condition in which a certain opinion can be favored to spread in the weak selection is obtained,which can be applied to arbitrary network structures.The result has been verified through computer simulations on three different types of network structures.Second,the thesis investigates the conditions under which a certain opinion can emerge on complex networks.Based on the calculation of coalescence times,the fixation probabilities of two opinions are derived in the weak selection limit.By comparing these two fixation probabilities,the condition for the emergence of one opinion is obtained,which can also be applied to any network structure.Furthermore,it is found that a certain opinion can emerge on any network structure if the ratio of the obtained positive feedback scores of competing opinions exceeds one.The result has been confirmed by means of computer simulations on three different types of network structures.