The Ultimatum Game On Complex Networks

Game theory is the study of the interactions between participants. As for alarge number of participants, the complex network can provide proper topologyfor the interactions between them. Combining the game theory and complexnetwork theory, this dissertation focuses on the evolutionary ultimatum gameon complex networks, including the e?ect of the ?xed structure onto the locatedultimatum game and the interplay between the structure evolution and strategyupdate. It is composed of the following ?ve aspects.The evolution of the six strategies for the ultimatum game in the squarelattice is studied and the spatial and temporal phase diagrams are given. Thesix typical strategies with some randomness are considered: uniform strategy,greedy strategy, altruist strategy, rational strategy, stubborn or ?xed strategyand fair strategy. The corresponding rank of dominance strategies is obtained.Furthermore, the evolution of the greedy and altruist strategy is provided, andsome interesting results are shown in the phase diagrams.For the continuous strategy space of the ultimatum game, the crucial topo-logical ingredients are studied which a?ect the outcomes of the ultimatum gamelocated on the di?erent networks, encompassing the regular network, the randomnetwork, the small-world network and the scale-free network. With the aid ofrandom interchanging algorithm, the relations between the outcomes of the ulti-matum game and some topological ingredients are investigated. It is found thatfor the regular network, the random network and the small-world network, theaverage range and the clustering coe?cient have evident impacts on the ultima-tum game, while for the scale-free network, the original degree heterogeneity andthe underlying rich-club characterizations are the mainly important topologicalingredients that in?uence the outcomes of ultimatum game substantially.From the perspective of the coevolution, the problem is studied that howthe structure evolution and strategy evolution together a?ects the emergence offair behaviors in the ultimatum game under a complex network framework. By allowing the players to change their neighbors in the network as well as theirstrategies, several experiments have been conducted. Results of the simulationsshow that the coevolution has substantial impacts on the resulting outcomes forstrategy adopted as well as the ultimate structure. With the increasing of thestructure updating rate, players o?er more in the ultimatum game, but play-ers will o?er less with the increasing of the strategy updating rate. Moreover,the ?nal structures have the small-world e?ects. In addition, the mutation instrategies plays a promoting role in fairness emergences.With the asynchronous update mechanism, the interplay between structuredynamics and strategy dynamics leads to overwhelmingly interesting results. Itis found that fair division emerges for speci?c ratios of structure updating prob-ability to strategy updating probability. Furthermore, it is shown that the initialstructures have no essential e?ect on the coevolutionary results. Besides, thee?ects of other spatial factors are also investigated, e.g. the population size has apositive in?uence on the o?er, while the average degree has a negative e?ect. Inaddition, one extrinsic factor, the background payo?, is also of great importancein promoting fair divisions. Apart from above, the evolved networks are foundto have the small-world e?ect and positive assortative behaviors.With the coevolutionary rules, the problem of population growth is inves-tigated. In particular, how the dynamics of the ultimatum game in?uences thegrowth pattern of the network is examined. Simulation results show that payo?-based preferential attachment mechanism leads to the emergence of a scale-freestructural property. In addition, the average distance, the assortative mixing fea-tures and the rich-club phenomenon are revealed, which are consistent with theobservations of some real social networks. In parallel, the corresponding resultsfor the ultimatum game and the wealth distribution of the agents are analyzed.