A Manipulation Game Based on Machiavellian Strategies

Abstract

This paper suggests a manipulation game based on Machiavellianism, which is characterized by three concepts: views, tactics, and immorality. We consider a framework where manipulating players can partially control manipulated players’ information and affect both manipulated players’ information and their allocations. The parties involved are constrained both by adverse selection and moral hazard (immorality) restricted to a class of ergodic Bayesian–Markov problems. We investigate a mechanism that maximize the probability that the manipulated players accept the proposal of the manipulators. We show that a mechanism exists and can be found by solving a nonlinear programming problem for a set of constraints. The mechanism is obtained by introducing an auxiliary variable in the nonlinear programming problem and we develop the relations needed to derive the variables of interest. For the manipulation process, players learn their behavior through a sequence of interactions in a repeated game. The manipulators possess and benefit from some commitment power, which describes the distinctive nature of a manipulation game (views). Then, we represent the game using a Stackelberg model. We also compute the Stackelberg equilibrium (tactics) for our game of incomplete information. This novel perspective is of interest for the Bayesian manipulation and persuasion literature. A simulation and analysis over an example for manipulating emotions in negotiation verify the applicability of proposed model.