# Pareto-optimal solution for the quantum battle of the sexes

## TL;DR

This paper finds Pareto-optimal solutions to the asymmetric quantum battle of the sexes game using the Eisert-Wilkens-Lewenstein protocol, demonstrating solutions beyond Nash equilibrium and experimentally validating the approach with NMR.

## Contribution

It introduces a Pareto-optimal solution framework for the asymmetric quantum game, extending the protocol's applicability beyond symmetric games.

## Key findings

- Identified Pareto-optimal solutions that resolve the dilemma.
- Experimental validation using NMR technique.
- Extended the protocol's applicability to asymmetric quantum games.

## Abstract

Quantum games have gained much popularity in the last two decades. Many of these quantum games are a redefinition of iconic classical games to fit the quantum world, and they gain many different properties and solutions in this different view. In this letter, we attempt to find a solution to an asymmetric quantum game which still troubles quantum game researchers, the quantum battle of the sexes. To achieve that, we perform an analysis using the Eisert-Wilkens-Lewenstein's protocol for this asymmetric game. The protocol highlights two solutions for the game, which solve the dilemma and satisfy the Pareto-optimal definition, unlike previous reports that rely on Nash equilibrium. We perform an experimental implementation using the NMR technique in a two-qubit system. Our results eliminate dilemmas on the quantum battle of the sexes and provide us with arguments to elucidate that the Eisert-Wilkens-Lewenstein's protocol is not restricted to symmetric games when at the quantum regime.