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arXiv:1112.0713 · Physica A Statistical Mechanics and its Applications

Quantum strategies win in a defector-dominated population

Qiang Li, Azhar Iqbal, Minyou Chen, Derek Abbott

Published Feb 4, 2012• 37 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2012.01.048

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We reformulate the quantum Monty Hall problem in the presence of decoherence. The decoherence destroys the fairness of the game. A new Nash equilibrium for a particular strategy profile in the presence of decoherence emerges. It is shown that in the presence of decoherence under the action of amplitude damping channel, Bob's winning probability is always higher than three-forth, irrespective of Alice's strategy, if he does not switch to the other door and always wins for a fully decohered case of the channel. Depolarizing channel damps up Bob's winning probability and gets better off if he sticks to his current selection. Phase damping channel leaves the winning probability unaffected. Unlike the classical and the quantum forms of the game, Bob's dominant strategy in the presence of decoherence is not switching.
In this paper, quantum strategies are introduced within evolutionary games in order to investigate the evolution of quantum and classical strategies on networks in the public goods game. Comparing the results of evolution on a scale-free network and a square lattice, we find that a quantum strategy outperforms the classical strategies, regardless of the network. Moreover, a quantum strategy dominates the population earlier in group interactions than it does in pairwise interactions. In particular, if the hub node in a scale-free network is occupied by a cooperator initially, the strategy of cooperation will prevail in the population. However, in other situations, a quantum strategy can defeat the classical ones and finally becomes the dominant strategy in the population.