Learning machiavellian strategies for manipulation in Stackelberg security games

This paper suggests a new approach for repeated Stackelberg security games (SSGs) based on manipulation. Manipulation is a strategy interpreted by the Machiavellianism social behavior theory, which consists on three main concepts: view, tactics, and immorality. The world is conceptualized by manipulators and manipulated (view). Players employ Machiavelli’s tactics and Machiavellian intelligence in order to manipulate attacker/defender situations. The immorality plays a fundamental role in these games, defenders are able to not be attached to a conventional moral in order to achieve their goals. We consider a security game model involving manipulating defenders and manipulated attackers engaged cooperatively in a Nash game and at the same time restricted by a Stackelberg game. The resulting game is non-cooperative bargaining game. The cooperation is represented by the Nash bargaining solution. We propose an analytical formula for solving the manipulation game, which arises as the maximum of the quotient of two Nash products. The role of the players in the Stackelberg security game are determined by the weights of the players for the Nash bargaining approach. We consider only a subgame perfect equilibrium where the solution of the manipulation game is a Strong Stackelberg Equilibrium (SSE). We employ a reinforcement learning (RL) approach for the implementation of the immorality. A numerical example related to developing a strategic schedule for the efficient use of resources for patrolling in a smart city is handled using a class of homogeneous, ergodic, controllable, and finite Markov chains for showing the usefulness of the method for security resource allocation.