A differential model of $N$ player games concerning ethical dilemmas

Ethics play an important role in determining the behavior of an individual under certain circumstances. Ethical or unethical behavior can be treated as a strategy of a player in a pay-off game. In this paper, we present two analytical solutions to studying time evolution of behavior of an individual from ethics perspective. We also present the effect of a third player as a perturbation to a two player game and develop a general approach for a $N$ player game. We demonstrate geometric modeling of behavioral characteristics of individuals as polytopes residing in $D$ dimensional space. We treat three player and two player games using set of differential equations that lead to time evolution of phase trajectories which reveal about the interdependencies and self dependencies of each player. We also demonstrate the effect of strategies of each player on other players in cardinal games.