System Dynamics And Learning Theory In Games

Along with some ground-breaking advances made by artificial intelligence(AI)in recent years,game theory is playing a more and more important role in some emerging interdisciplinary fields,such as social intelligence,cooperative intelligence,machine intelligence,multi-agent learning,AI safety,and AI ethics.Especially,by combining with system dynamics and machine learning,it has recently become a hot topic in the community of complex system control and AI.Given some deficiencies of the solution concept of Nash equilibrium in traditional noncooperative games,in this dissertation,we propose a potential research framework of complex game systems,based on the study of the deterministic and stochastic dynamics of evolutionary games and the learning theory of stochastic games and incomplete-information games.Specifically,the main results and innovations are shown as follows.First,for solving the cooperative conundrum in multi-player social dilemmas,we propose a model of asymmetric public goods games,and meanwhile analyze the deterministic evolutionary dynamics of players’ strategies in the situations without incentive control mechanisms,with symmetric incentive control mechanisms,and with asymmetric incentive control mechanisms,respectively.By theoretical analysis,we find that without incentive control mechanisms,although the cooperative strategy is maintained,it undermines the evolution of altruistic punishment.While in the presence of incentive control mechanisms,asymmetric control mechanisms are found to be more beneficial than symmetric control mechanisms for promoting the evolution of cooperation.Next,for studying the evolutionary dynamics of the two-player game with two strategies and the multi-player game with heterogeneous decisions,we propose a generalized fitness function for the Moran process and a generalized probability function of strategy selection for the pairwise comparison process,respectively.Based on the Moran process and pairwise comparison process,we then analyze the effect of these two functions on evolutionary outcomes.By theoretical analysis,we find that under weak selection,the criterion for one strategy to dominate another not only depends on the classical “σ-rule”,but also on the first order derivative of these two functions with respect to the selection intensity.Therein,the former determines the parameter condition of the criterion,whereas the later determines the inequality direction of the criterion.Subsequently,for studying the sequential decision-making problem in ever-changing game environments,we propose a networked multi-player stochastic game and develop an adaptive learning mechanism of action selection based on the actor-critic reinforcement learning algorithm.By comparing the criterion for one action dominating another with and without learning mechanisms under weak selection,we find that learning enables the adaptation of players to varying environments in social dilemmas.Finally,for studying the sequential decision-making problem of a cooperative team in uncertain environments,we propose a model named robust team stochastic games,and meanwhile develop a robust iterative learning algorithm to seek the optimal policy of the team in the sense of robust optimization.By theoretical analysis,we find that the algorithm can not only effectively converge to the optimal policy of the game at a near exponential rate,but also allow for using approximation calculations to alleviate “the curse of dimensionality”.