Entanglement in the Quantum Volunteer's Dilemma

• URL: http://arxiv.org/abs/2606.08227v1
• Date: Sat, 06 Jun 2026 15:31:16 GMT
• Title: Entanglement in the Quantum Volunteer's Dilemma
• Abstract summary: We study a quantum version of the Volunteer's Dilemma game theory.<n>We find that maximal entanglement is not required to sustain symmetric Nash equilibria.<n>This characterization is directly relevant for implementations on resource-constrained quantum devices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A well-known model in game theory, the Volunteer's Dilemma describes a group of $n$ players who decide whether to volunteer for a collective benefit at a personal cost, or to abstain and risk forfeiting the benefit altogether. A quantum version of this dilemma, developed within the Eisert-Wilkens-Lewenstein framework, allows each player to manipulate one qubit of a shared entangled state, leading to symmetric Nash equilibria with higher expected payoffs than in the classical game. Existing analyses, however, assume maximal entanglement. Within the same framework, we introduce a generalized Quantum Volunteer's Dilemma with a tunable entanglement parameter $γ$ and study the extent to which equilibrium behavior depends on the level of entanglement. We derive explicit conditions relating $γ$, the number of players, and the players' strategies under which symmetric Nash equilibria exist, focusing on two canonical strategy profiles: one for $2\leq n\leq 9$, and one for even $n$. We find that maximal entanglement is not required to sustain symmetric equilibria. Instead, equilibrium behavior persists above a threshold value, which we compute analytically in both cases. We also demonstrate that the threshold value directly depends on system size. This characterization is directly relevant for implementations on resource-constrained quantum devices, where entanglement is inherently limited.

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