Quantum games of asymmetric information

Du, Jiangfeng; Li, Hui; Ju, Chenyong

doi:10.1103/physreve.68.016124

Cited by 36 publications

(25 citation statements)

References 15 publications

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“…(12) has the analytical expression in Eq. (14). For very large but finite value of a and c, the probability P m1,m2 in Eq.…”

Section: B Quantum Measuring Apparatusmentioning

confidence: 97%

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Simulation of continuous variable quantum games without entanglement

Li¹

2011

J. Phys. A: Math. Theor.

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A simulation scheme of quantum version of Cournot's Duopoly is proposed, in which there is a new Nash equilibrium that may be also Pareto optimal without any entanglement involved. The unique property of this simulation scheme is decoherence-free against the symmetric photon loss. Furthermore, we analyze the effects of the asymmetric information on this simulation scheme and investigate the case of asymmetric game caused by asymmetric photon loss. A second-order phase transition-like behavior of the average profits of the firm 1 and firm 2 in Nash equilibrium can be observed with the change of the degree of asymmetry of the information or the degree of "virtual cooperation". It is also found that asymmetric photon loss in this simulation scheme plays a similar role with the asymmetric entangled states in the quantum game.

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“…(12) has the analytical expression in Eq. (14). For very large but finite value of a and c, the probability P m1,m2 in Eq.…”

Section: B Quantum Measuring Apparatusmentioning

confidence: 97%

“…(12) should be written as the summation of −cm 1 P m1,m2 or −cm 2 P m1,m2 which also tends to small enough to guarantee the payoff well approximated by the Eq. (14). However, for other cases with small values of a, the situation becomes very complicate.…”

Section: B Quantum Measuring Apparatusmentioning

confidence: 99%

Simulation of continuous variable quantum games without entanglement

Li¹

2011

J. Phys. A: Math. Theor.

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“…The classical game is assumed to have the same general structure of players' payoffs as given in Eqs. (2). This assumption derives from the hope that the quantum game, corresponding to correlations in the input states that violate the inequality (6), is also equivalent to another symmetric bi-matrix game.…”

Section: Nash Equilibria Of Qcgsmentioning

confidence: 99%

Quantum correlations and Nash equilibria of a bi-matrix game

Iqbal

2004

J. Phys. A: Math. Gen.

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Playing a symmetric bi-matrix game is usually physically implemented by sharing pairs of 'objects' between two players. A new setting is proposed that explicitly shows effects of quantum correlations between the pairs on the structure of payoff relations and the 'solutions' of the game. The setting allows a re-expression of the game such that the players play the classical game when their moves are performed on pairs of objects having correlations that satisfy the Bell's inequalities. If players receive pairs having quantum correlations the resulting game cannot be considered another classical symmetric bi-matrix game. Also the Nash equilibria of the game are found to be decided by the nature of the correlations. I. INTRODUCTIONPlaying a game requires resources for its physical implementation. For example, to play a bi-matrix game the resources may consist of pairs of two-valued 'objects', like coins, distributed between the players. The players perform their moves on the objects and later a referee decides payoffs after observing them. Game theory usually links players' actions directly to their payoffs, without a reference to the nature of the objects on which the players have made their moves. Analysis of quantum games [1] suggests radically different 'solutions' can emerge when the same game is physically implemented on distributed objects which are quantum mechanically correlated. Much of recent work on quantum games [1-4] uses a particular quantization scheme[1] developed for a bi-matrix game where two players, on receiving an entangled two-qubit state, play their moves by local and unitary actions on the state. After disentanglement, a measurement of the state rewards the players their payoffs. The payoffs become classical when the moves are performed on a product state. For example, in Prisoners' Dilemma new and more beneficial equilibrium emerges in its quantum form [1] when the allowed moves

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“…Namely, it outputs nonclassical results already for separable initial states. In order to see that, let us use results (11) and (12) obtained by letting ρ in = |11 11|. Then, for arbitrary a − c > 0 and suitably large q 2 > 0 expression, tr(ρ fin M 1 ) as a function of variable q 1 increases monotonically and lim q 1 →∞ tr(ρ fin M 1 ) = ∞.…”

Section: The Iqbal-toor Quantum Duopoly Schemementioning

confidence: 99%

“…These remarkable schemes have found an application in many duopoly problems. The former scheme was further investigated, for example, in [6][7][8][9][10], the latter one in [11][12][13][14][15][16][17][18][19][20][21][22]. The aim of the paper is to pay attention to some properties of the quantum duopoly schemes that might be thought unsuitable (in the case of the Iqbal-Toor scheme) and specify the Nash equilibrium analysis (in the case of the Li-Du-Massar scheme).…”

Section: Introductionmentioning

confidence: 99%

Remarks on quantum duopoly schemes

Frąckiewicz

2015

Quantum Inf Process

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The aim of this paper is to discuss in some detail the two different quantum schemes for duopoly problems. We investigate under what conditions one of the schemes is more reasonable than the other one. Using the Cournot's duopoly example, we show that the current quantum schemes require a slight refinement so that they output the classical game in a particular case. Then, we show how the amendment changes the way of studying the quantum games with respect to Nash equilibria. Finally, we define another scheme for the Cournot's duopoly in terms of quantum computation.

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Quantum games of asymmetric information

Cited by 36 publications

References 15 publications

Simulation of continuous variable quantum games without entanglement

Simulation of continuous variable quantum games without entanglement

Quantum correlations and Nash equilibria of a bi-matrix game

Remarks on quantum duopoly schemes

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