Quantum Volunteer's Dilemma

TL;DR

This paper introduces a quantum version of the volunteer's dilemma, showing that quantum strategies can lead to better payoffs and more optimal equilibria than classical strategies in multiplayer game scenarios.

Contribution

It generalizes the classical volunteer's dilemma to quantum strategies, deriving analytical payoffs and demonstrating quantum advantages in equilibrium outcomes.

Findings

Quantum strategies yield higher expected payoffs.

Quantum Nash equilibria are Pareto optimal.

Quantum game outperforms classical in strategic advantage.

Abstract

The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work, we introduce a quantum variant of the classical volunteer's dilemma, generalizing it by allowing players to utilize quantum strategies. Employing the Eisert-Wilkens-Lewenstein quantization framework, we analyze a multiplayer quantum volunteer's dilemma scenario with an arbitrary number of players, where the cost of volunteering is shared equally among the volunteers. We derive analytical expressions for the players' expected payoffs and demonstrate the quantum game's advantage over the classical game. In particular, we prove that the quantum volunteer's dilemma possesses symmetric Nash equilibria with larger expected payoffs compared to the unique symmetric Nash equilibrium of the classical game, wherein players use mixed strategies. Furthermore, we show that the quantum Nash equilibria we identify are Pareto optimal. Our findings reveal distinct dynamics in volunteer's dilemma scenarios when players adhere to quantum rules, underscoring a strategic advantage of decision-making in quantum settings.