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      Quantum two-players games, Entanglement and Nash equilibria

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          Abstract

          The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple geometric properties of "chiral" group \(SU (N)\times SU(N)\) and is based on considering the stability subgroup of the initial state of the game. The explicit forms of neither the gate operator nor the payoff matrix are necessary.

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          Quantum Games and Quantum Strategies

          M. Wilkens, M Lewenstein, J. Eisert (1998)
          We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.
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            Quantum strategies

            David Meyer (1998)
            We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the traditional Matching Pennies game. While not every two-person zero-sum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the equilibrium strategy cannot increase a player's expected payoff. We show, however, that in our example a player who implements a quantum strategy can increase his expected payoff, and explain the relation to efficient quantum algorithms. We prove that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategies there must be.
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              Experimental realization of quantum games on a quantum computer

              , , … (2001)
              We generalize the quantum Prisoner's Dilemma to the case where the players share a non maximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.
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                Author and article information

                Journal
                Publication date Created: 17 February 2014
                Publication date Updated: 2014-02-23
                Article
                ArXiV ID: 1402.3932
                SO-VID: 18609252-030b-4640-9236-15e01c4f87d6
                License:

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments 8 pages, no figures, two references added
                Categories quant-ph

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