# A competitive game whose maximal Nash-equilibrium payoff requires quantum resources for its achievement

## TL;DR

This paper introduces a competitive game demonstrating that quantum resources can achieve higher Nash-equilibrium payoffs than classical strategies, confirming the legitimacy of quantum games in competitive scenarios.

## Contribution

It constructs a four-player competitive game based on the minority game where quantum resources outperform classical means in Nash-equilibrium payoffs.

## Key findings

- Quantum resources enable higher Nash-equilibrium payoffs.
- The game is analogous to a Bell inequality.
- Results confirm the legitimacy of quantum games in competitive settings.

## Abstract

While it is known that shared quantum entanglement can offer improved solutions to a number of purely cooperative tasks for groups of remote agents, controversy remains regarding the legitimacy of quantum games in a competitive setting--in particular, whether they offer any advantage beyond what is achievable using classical resources. We construct a competitive game between four players based on the minority game where the maximal Nash-equilibrium payoff when played with the appropriate quantum resource is greater than that obtainable by classical means, assuming a local hidden variable model. The game is constructed in a manner analogous to a Bell inequality. This result is important in confirming the legitimacy of quantum games.