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arXiv:quant-ph/0009050 · Physical Review A

Playing a quantum game with a corrupted source

Neil F. Johnson

Published Jan 9, 2001• 100 citations
arXivHTMLPDF

Abstract

The quantum advantage arising in a simplified multiplayer quantum game is found to be a disadvantage when the game's qubit source is corrupted by a noisy ``demon.'' Above a critical value of the corruption rate, or noise level, the coherent quantum effects impede the players to such an extent that the ``optimal'' choice of game changes from quantum to classical.

DOI
10.1103/physreva.63.020302

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The quantum advantage arising in a simplified multiplayer quantum game is found to be a disadvantage when the game's qubit source is corrupted by a noisy demon.'' Above a critical value of the corruption rate, or noise level, the coherent quantum effects impede the players to such an extent that the optimal'' choice of game changes from quantum to classical.
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It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0≤p≤0.622 (p is the quantum noise parameter), and then disappears in the range of 0.622<p≤1. Increasing the amount of quantum noise leads to the reduction of the quantum player's payoff.
We present a study of a dynamical quantum game. Each agent has a `memory' of her performance over the previous m timesteps, and her strategy can evolve in time. The game exhibits distinct regimes of optimality. For small m the classical game performs better, while for intermediate m the relative performance depends on whether the source of qubits is `corrupt'. For large m , the quantum players dramatically outperform the classical players by `freezing' the game into high-performing attractors in which evolution ceases.
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess an alternative form of equilibrium strategy, one which has no analog either in traditional games or even in two-player quantum games. In these ``coherent'' equilibria, entanglement shared among multiple players enables different kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one another.