Reasoning about Strategic Behavior: Imperfect Information and Perfect Recall in Decidability Analysis

Abstract

Strategic decision-making in games with imperfect information and perfect recall has been a significant area of study in artificial intelligence (AI) and game theory. This paper presents a comprehensive analysis of reasoning about strategic behavior in such games, focusing on the computational complexity and feasibility of various decision-making algorithms. The study evaluates several key algorithms, including Iterative Regret Minimization, Deep Q-Networks (DQN), and Nash Equilibrium Approximation, in terms of their ability to compute optimal strategies and solve strategic problems efficiently. Through theoretical analysis and empirical evaluations, we demonstrate the computational challenges associated with strategic tasks like optimal strategy computation and equilibrium identification. While certain algorithms offer efficient solutions for real-time decision-making, others, particularly those relying on deep reinforcement learning, require significant computational resources. The results provide valuable insights into the trade-offs between efficiency, accuracy, and computational resources in strategic decision-making. Our findings suggest that the choice of algorithm should be based on the specific characteristics of the strategic problem, such as problem size, real-time requirements, and resource constraints. The study contributes to a deeper understanding of the computational aspects of reasoning about strategic behavior in imperfect information games with perfect recall and provides practical recommendations for algorithm selection in real-world applications.