Playing Extensive Games with Learning of Opponent's Cognition

Decision-making is a basic component of agents' (e.g., intelligent sensors) behaviors, in which one's cognition plays a crucial role in the process and outcome. Extensive games, a class of interactive decision-making scenarios, have been studied in diverse fields. Recently, a model of extensive games was proposed in which agent cognition of the structure of the underlying game and the quality of the game situations are encoded by artificial neural networks. This model refines the classic model of extensive games, and the corresponding equilibrium concept-cognitive perfect equilibrium (CPE)-differs from the classic subgame perfect equilibrium, since CPE takes agent cognition into consideration. However, this model neglects the consideration that game-playing processes are greatly affected by agents' cognition of their opponents. To this end, in this work, we go one step further by proposing a framework in which agents' cognition of their opponents is incorporated. A method is presented for evaluating opponents' cognition about the game being played, and thus, an algorithm designed for playing such games is analyzed. The resulting equilibrium concept is defined as adversarial cognition equilibrium (ACE). By means of a running example, we demonstrate that the ACE is more realistic than the CPE, since it involves learning about opponents' cognition. Further results are presented regarding the computational complexity, soundness, and completeness of the game-solving algorithm and the existence of the equilibrium solution. This model suggests the possibility of enhancing an agent's strategic ability by evaluating opponents' cognition.