The Study Of Evolutionary Game Dynamics On Complex Networks

Evolutionary game theory provides a versatile framework and mathemat-ical description of interactions between players or agents. In a game, the re-ward, or utility, that any player receives is a function of player's own strategyas well as the strategies of other players, according to which the player updateshis/her strategy under a certain payoff optimal principle and/or learning rulesat each time step . As time evolves, reach is an evolutionary stable equilib-rium in a dynamical game system of players, instead of the deterministic/staticsituation(Nash equilibrium) in the classical game theory literature.An evolutionary game are generally concerning the well-mixed popula-tion, where all the players contact (and play game) with each other. However,the evolutionary game in complex networks considers a structural population,i.e., the connections between players are described by a network of contacts(NOCs), where the randomness and complexity of topological structure de-scribing the interactions between players result in diversity and complexity ofthe game system's asymptotic dynamic behaviours.The dissertation surveys a wide range of related works and current situa-tion of evolutionary game dynamics on complex networks, and discusses fair-ness evolution of the Ultimatum Game on complex networks, an application ofevolutionary Battle-of-the-Sexes Game in opinion dynamics, and the SnowdriftGame on bipartite graphs with identical interactivity.The main contributions of this dissertation are summarized as follows: 1. The ultimatum game as a typical counterexample of rationality describesthe con?ict between fairness and selfishness in the game theory literature.This dissertation investigates the fairness mechanism in the evolutionaryultimatum game among a population of players located on an network ofcontacts. We study the condition to achieve the fairness emergence, whereall players reach a consensus in their payoffs. More numerical observa-tions reveal the in?uence of small-world and scale-free features of com-plex networks on the fairness emergence in the evolutionary ultimatumgame.2. A new evolutionary Battle-of-the-Sexes Game is proposed to model theopinion formation among a structured population on networks. The popu-lation of players is partitioned into different classes according to their un-altered opinion preferences, and their factual opinions are considered asevolutionary game strategies with two different updating rules, the'birth-death'and'death-birth'rules, to imitate the process of opinion formation.The players finally reach a consensus in the dominate opinion, or fall into(quasi-) stationary fractions of coexisting mixed opinions, which presentsa phase transition at the critical modularity of the multi-class players'par-titions on networks. In this dissertation, a broad theoretic analysis on co-existence stability of mixed strategies of the evolutionary game amongmulti-class players is given, where the analytical predictions agree wellwith numerical simulations of our model, indicating that players with acommunity- (or modular) population structure are prone to form coexist-ing opinions. It also provides a clue that the coexistence of mixed evo-lutionary strategies implies the modularity of networks under the gametheoretic framework. 3. A bipartite graph model with tunable power law exponent is proposed,on which we studied the evolutionary game dynamics under the assump-tion that each player has an identical interactivity, i.e., at each time stepplayers pick his neighbours as the game opponents in a muti-player game,instead of playing with all other connected players. With the backgroundof Snowdrift Game, the coalitionary time saving is introduced to describethe rewards brought by coalition of cooperators. Simulation results showthat coalitionary time saving and heterogeneity of network topology availto the enhancement of cooperation.