The decision-making process, which is regarded as cognitive and ubiquitous, has been exploited in diverse fields, such as psychology, economics, and artificial intelligence. This paper considers the problem of modeling agent cognition in a class of game-theoretic decision-making scenarios called extensive games. We present a novel framework in which artificial neural networks are incorporated to simulate agent cognition regarding the structure of the underlying game and the goodness of the game situations therein. An algorithmic procedure is investigated to describe the process for solving games with cognition, and then, a new equilibrium concept is proposed as a refinement of the classical one-subgame perfect equilibrium-by involving players' cognitive reasoning. Moreover, a series of results concerning the computational complexity, soundness, and completeness of the algorithm, as well as the existence of an equilibrium solution, is obtained. This framework, which is shown to be general enough to model the way in which AlphaGo plays Go, may offer a means for bridging the gap between theoretical models and practical problem-solving.
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