Quantum Volunteer's Dilemma

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.

28 pages, 5 figures

References in corpus (8)

• Zero-determinant alliances in multiplayer social dilemmas
• Noisy intermediate-scale quantum computers
• A necessary and sufficient condition to play games in quantum mechanical settings
• Quantum Game Application to Spectrum Scarcity Problems
• Infinitely Repeated Quantum Games and Strategic Efficiency
• Strong isomorphism in Eisert-Wilkens-Lewenstein type quantum games
• Permissible extensions of classical to quantum games combining three strategies
• Repeated quantum game as a stochastic game: Effects of the shadow of the future and entanglement

Cited by in corpus (6)

• A Quantum Algorithm for the Classification of Patterns of Boolean Functions
• Quantum Advantage in Trading: A Game-Theoretic Approach
• Probabilistic Links Between Quantum Classification of Patterns of Boolean Functions and Hamming Distance
• Quantum Shadows: The Dining Information Brokers
• A novel $2$ \& $3$ player scheme for Quantum Direct Communication
• Quantum Multiplayer Colonel Blotto Game