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Playing a quantum game in a corrupt world

Neil F. Johnson

Published Sep 12, 2000• 1 citation
OpenAlex

Abstract

The quantum advantage arising in a simplified multi-player 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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The quantum advantage arising in a simplified multi-player 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.
The Prisoner's Dilemma plays a very important part in the game theory.It is related to economics,political science,sociology,philosophy,ethnics,etc.when study in such field quantized the Prisoner's Dilemma and found that the payoffs for the players are better than that in the classical game.Then,people developed the two-player Quantum Prisoner's Dilemma into multiplayer quantum game.Also,they found that the quantum game does better than classical game.But now,the quantum advantage arising in a simplified multiplayer quantum game is found to be disadvantage when the game's qubit source is corrupted.
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.
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.