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arXiv · 2504.13939

Compendium of Advances in Game Theory: Classical, Differential, Algorithmic, Non-Archimedean and Quantum Game

Bourama Toni
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Abstract

This compendium features advances in Game Theory, to include: Classical Game Theory: Cooperative and non-cooperative. Zero-sum and non-zero sum games. Potential and Congestion games. Mean Field games. Nash Equilibrium, Correlated Nash Equilibrium and Approximate Nash Equilibrium. Evolutionary Game Theory. Intelligent Game: Differential Game Theory. Algorithm Game Theory and Security Games. Quantum Games and Quantumization of classical games such as the Battle of the Sexes. Non-Archimedean and p-adic game theory and its growing relevancy as the domains of game-theoretic application expand. p-adic quantum game to leverage and combine the distinguishing features of non-Archimedean analysis and quantum information theory. This is a novel game-theoretic approach with great potential of application. In times of exponential growth of artificial intelligence and machine learning and the dawn of post-human mathematical creativity, this compendium is meant to be a reference of choice for all game theory researchers.

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Bourama Toni. 2025-04-15. Compendium of Advances in Game Theory: Classical, Differential, Algorithmic, Non-Archimedean and Quantum Game. https://arxiv.org/abs/2504.13939

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