Analytical solution, agent behavioral transitions and classification structures in N-person social dilemma games

This dissertation presents the analytical solution, agent behavioral transitions and classification structures in N-person social dilemma games. The specific model in this research uses Pavlovian agents making decisions in a cellular automaton environment with linear payoff functions. This effort culminated in four papers being submitted to journals that publish in this field of study. The first paper demonstrates that the analytical solution to the N-person Prisoners' Dilemma game discussed in previous literature fails when the learning factors are unequal. The paper then derives a more general analytical solution that corrects this issue. The second paper analyzes agent behavior and transitions extending over all social games. Three plateaus are identified. It is found that the agents in each plateau have a significantly different behavior. The transitions between these plateaus are analyzed. Previous literature indicates that there are indeed transitions, but offers no explanations. The third paper presents under what conditions the analytical solution is applicable. The previous literature implies the analytical solution is always applicable in the Prisoners' Dilemma game. This paper thoroughly analyzes for which games the analytical solution actually works and concludes that it applies in the Chicken game with the parameter S slightly negative. The fourth paper views the N-Person Social Dilemma model from a new perspective based on dynamic system theory. Thirteen cases or games are identified. These cases plot the state transition formula, which is a quadratic curve with linear payoff functions, versus the 45 degree line. From case diagrams the solution structures are readily apparent without the use of simulation. Also, additional information concerning proper selection of parameter values is provided above the traditional approach. The case diagrams can be used by modelers to easily develop and validate models for specific applications. There is no previous literature viewing N-person social dilemma games from this system theoretical perspective.