Quantum Nash Equilibria and Quantum Computing

TL;DR

This paper reviews the intersection of quantum computing and Nash Equilibria, exploring how quantum methods can generate new equilibrium classes and analyzing quantum game strategies and computational models.

Contribution

It extends previous work by analyzing examples of quantum games and strategies, and discusses the implications for computational classes and coherence in quantum systems.

Findings

Quantum computing can generate new classes of Nash equilibria.

Quantum game strategies extend classical game theory.

Quantum coherence influences computational complexity.

Abstract

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substantive analysis of examples provided by Meyer, Flitney, Iqbal and Weigert and Cheon and Tsutsui with respect to quantized games, quantum game strategies and the extension of Nash Equilibrium to solvable games in Hilbert space. Finally, we review earlier work by Sato, Taiji and Ikegami on non-linear computation and computational classes by way of reference to coherence, decoherence and quantum computating systems.