https://doi.org/10.1140/epjp/s13360-025-06822-y
Regular Article
Quantum Prisoners’ Dilemma in massive scalar field
1
School of Economics and Management, Wuyi University, 529020, Jiangmen, China
2
School of Mathematics and Computational Science, Wuyi University, 529020, Jiangmen, China
Received:
19
July
2025
Accepted:
1
September
2025
Published online:
10
September
2025
This paper investigates the Quantum Prisoners’ Dilemma (QPD) played in the environment of a massive scalar field. The study models the qubits of the two players as two-level Unruh-DeWitt detectors interacting weakly with a quantum field in an accelerating reference frame. This paper analyzes the effects of the detectors’ acceleration and the scalar field’s mass on player payoffs, symmetry and the game’s equilibrium. It is found that the system eventually evolves to a thermal equilibrium state determined by the Unruh temperature, which is independent of the initial state, field mass, and inter-detector distance. The results show that the detectors’ acceleration affects the players’ payoffs depending on the strategy profile, and increasing acceleration causes the payoff to decay faster. The field’s mass, however, influences the timescale for reaching this steady state, with a more massive field slowing down the rate of payoff decay. A key finding is that the symmetry of the game is broken due to the Unruh effect, and the quantum strategy profile which resolves the dilemma in the ideal case is no longer always a Nash equilibrium in this environment.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
