quantum-2x2-game-mathematical-framework

name	quantum-2x2-game-mathematical-framework
description	Rigorous mathematical framework for quantum game theory applied to static 2x2 games. Proves existence of Nash equilibria for continuous quantum mixed strategies via fixed-point argument, generalizing classical Nash theorem to quantum case. Extends classical concepts to quantum setting with arbitrary unitary operations (pure strategies) and probability measures over SU(2) (mixed strategies). Use when: quantum game theory foundations, 2x2 quantum games, quantum Nash equilibrium proof, EWL protocol mathematics, quantum mixed strategies.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2605.15747","published":"2026-05-15","tags":["quantum","game-theory","nash-equilibrium","ewl-protocol","2x2-games","mixed-strategies","SU2","mathematical-framework","fixed-point-theorem"]}

Quantum Game Theory for 2x2 Games: Mathematical Framework

Overview

Rigorous mathematical framework establishing the foundations of quantum game theory for static 2x2 games. Proves existence of Nash equilibria for continuous quantum mixed strategies via fixed-point argument, generalizing the classical Nash existence theorem to the quantum domain.

Source

• Paper: "Quantum game theory for 2x2 games: a mathematical framework"
• arXiv: 2605.15747 (May 2026)

Core Methodology

1. Strategy Space Extension

• Classical pure strategies: Discrete choice set (Cooperate/Defect, etc.)