Advances in Zero-Sum Game Theory and Mean Field Games

The field of game theory is witnessing significant developments, particularly in the realm of zero-sum games and mean field games. Researchers are making strides in solving complex games with partial observability, leveraging techniques such as dynamic programming and function approximation to achieve epsilon-optimality. The introduction of novel frameworks and algorithms is enabling the principled application of existing methods to new domains, leading to improved performance and convergence rates. Notably, the use of perturbations and successive over-relaxation techniques is being explored to enhance the efficiency of best-response-based algorithms and Q-learning methods. Furthermore, advances in finite element approximations are providing new insights into the stability and regularity of solutions to mean field game systems. Overall, these developments are paving the way for a deeper understanding of complex game-theoretic systems and their applications. Noteworthy papers include: The paper on epsilon-optimally solving two-player zero-sum partially observable stochastic games, which introduces a lossless reduction enabling the principled application of dynamic programming techniques. The paper on deep successive over-relaxation minimax Q-learning, which proposes a novel algorithm incorporating deep neural networks as function approximators and demonstrates its effectiveness in high-dimensional state-action spaces.

Sources

{\epsilon}-Optimally Solving Two-Player Zero-Sum POSGs

Perturbing Best Responses in Zero-Sum Games

Some error estimates for semidiscrete finite element approximations of stable solutions to mean field game systems

Deep SOR Minimax Q-learning for Two-player Zero-sum Game

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