Characterizing Manipulation via Machiavellianism

Machiavellianism refers to the propensity of taking advantage of people within a society. Machiavellians have reputations for being cunning and competitive. They are also skilled long-term strategists and planners. Other than their "victories," there are no other successful conclusions for them. The belief component of Machiavellianism includes cynical views of human nature (e.g., manipulated and manipulating individuals), interpersonal exploitation as a technique (e.g., strategic thinking), and a lack of traditional morality that would forbid their behaviors (e.g., immoral behaviors). This paper focuses on a game that involves manipulation. The game was conceptualized using the best and worst Nash equilibrium points as part of our contribution. We constrained the problem to homogeneous, finite, ergodic, and controllable Bayesian-Markov games. Machiavellian players pretended to be in one state when they were actually in another. Moreover, they pretended to perform one action while actually playing another. All Machiavellian individuals engaged in some form of interpersonal manipulation. Manipulating players exhibited a higher preference compared to manipulated participants. The Pareto frontier is defined as the line where manipulating players play the best Nash equilibrium and manipulated players play the worst Nash equilibrium. It is also considered a sequential Bayesian-Markov manipulation game involving multiple manipulating players and manipulated players. Finally, a tractable characterization of the manipulation equilibrium results is provided. To guarantee that the game's solution converged into a singular solution, we used Tikhonov's penalty regularization method. A numerical example describes the results of our model.