# A Quantum Annealing Algorithm for Finding Pure Nash Equilibria in Graphical Games

## TL;DR

This paper presents Q-Nash, a quantum annealing algorithm that efficiently finds pure Nash equilibria in graphical games by combining classical and quantum computation, and evaluates its performance on a D-Wave quantum device.

## Contribution

The paper introduces a novel quantum annealing approach for solving the NP-complete problem of finding pure Nash equilibria in graphical games, integrating classical pre-processing with quantum optimization.

## Key findings

- Q-Nash achieves competitive solution quality.
- Q-Nash reduces computation time compared to brute force.
- Quantum annealing shows promise for game-theoretic problems.

## Abstract

We introduce Q-Nash, a quantum annealing algorithm for the NP-complete problem of Fnding pure Nash equilibria in graphical games. The algorithm consists of two phases. The first phase determines all combinations of best response strategies for each player using classical computation. The second phase finds pure Nash equilibria using a quantum annealing device by mapping the computed combinations to a quadratic unconstrained binary optimization formulation based on the Set Cover problem. We empirically evaluate Q-Nash on D-Wave's Quantum Annealer 2000Q using different graphical game topologies. The results with respect to solution quality and computing time are compared to a Brute Force algorithm and the Iterated Best Response heuristic.