Manipulation power in bargaining games using machiavellianism

This paper suggests a novel approach for representing manipulation games based on Nash’s bargaining model conceptualized under the Machiavellianism psychological theory. The Machiavellianism structure is represented by the concepts: views, tactics, and immorality. Such concepts determine a Stackelberg game consisting of manipulating and manipulated players which employ manipulation strategies to achieve power situations with the disposition to not become attached to a conventional moral. We consider a game model involving manipulating and manipulated players engaged cooperatively in a Nash bargaining game restricted to a Stackelberg game. As a result, we propose an analytical formula for solving the manipulation game, which arises as the maximum of the quotient of two Nash products. The solution of the manipulation game is a strong Stackelberg equilibrium. We represent the Stackelberg game as a Nash game for relaxing the interpretation of the non-cooperative bargaining solution and the equilibrium selection problem. The weights of the players for the Nash solution are determined by their role in the Stackelberg game. In the dynamics of the game, the manipulated players always break ties optimally for the manipulating players. The dynamics and the rationality proposed for the manipulation game correspond to many real-world manipulation situations. We fit the computation of the problem into a class of homogeneous, ergodic, controllable, and finite Markov chains games. A numerical example validates the usefulness of the method.