English

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

Optimization and Control 2025-04-22 v1 Computer Science and Game Theory

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.

Keywords

Cite

@article{arxiv.2504.13939,
  title  = {Compendium of Advances in Game Theory: Classical, Differential, Algorithmic, Non-Archimedean and Quantum Game},
  author = {Bourama Toni},
  journal= {arXiv preprint arXiv:2504.13939},
  year   = {2025}
}

Comments

This compendium will serve a book chapter in an upcoming contributed volume