von Neumann's Minimax Theorem for Continuous Quantum Games

TL;DR

This paper extends von Neumann's Minimax theorem to continuous quantum games, involving quantum random variables represented by self-adjoint operators on infinite-dimensional Hilbert spaces, providing a foundational result in quantum game theory.

Contribution

It proves a quantum version of von Neumann's Minimax theorem for infinite-dimensional (continuous) quantum games, expanding classical game theory into the quantum domain.

Findings

Established a quantum Minimax theorem for infinite-dimensional games

Extended classical game concepts to quantum random variables

Provided a mathematical foundation for quantum game analysis

Abstract

The concept of a classical player, corresponding to a classical random variable, is extended to include quantum random variables in the form of self adjoint operators on infinite dimensional Hilbert space. A quantum version of Von Neumann's Minimax theorem for infinite dimensional (or continuous) games is proved.