Manipulation Game Considering No-Regret Strategies

This paper examines manipulation games through the lens of Machiavellianism, a psychological theory. It analyzes manipulation dynamics using principles like hierarchical perspectives, exploitation tactics, and the absence of conventional morals to interpret interpersonal interactions. Manipulators intersperse unethical behavior within their typical conduct, deploying deceptive tactics before resuming a baseline demeanor. The proposed solution leverages Lyapunov theory to establish and maintain Stackelberg equilibria. A Lyapunov-like function supports each asymptotically stable equilibrium, ensuring convergence to a Nash/Lyapunov equilibrium if it exists, inherently favoring no-regret strategies. The existence of an optimal solution is demonstrated via the Weierstrass theorem. The game is modeled as a three-level Stackelberg framework based on Markov chains. At the highest level, manipulators devise strategies that may not sway middle-level manipulated players, who counter with best-reply strategies mirroring the manipulators' moves. Lower-level manipulators adjust their strategies in response to the manipulated players to sustain the manipulation process. This integration of stability analysis and strategic decision-making provides a robust framework for understanding and addressing manipulation in interpersonal contexts. A numerical example focusing on the oil market and its regulations highlights the findings of this work.