Quantum Games and Quantum Strategies

Eisert, Jens; Wilkens, Martin; Lewenstein, Maciej

doi:10.1103/physrevlett.83.3077

Cited by 904 publications

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“…Above payoff operators reduce to that of Eisert's scheme for δ equal to γ, which represents the entanglement of the initial state [7]. And for δ = 0 above operators transform into that of Marinatto and Weber's scheme [6].…”

Section: Quantization In Presence Of Correlated Noisementioning

confidence: 99%

“…Same happens for the case of γ = 0, δ = 0. However, for the case when γ = δ = π 2 the scheme transforms to the Eisert's quantization scheme [7] and quantum player always remains better off against a player restricted to classical strategies. Furthermore, in the limit of maximum correlation the effect of decoherence vanishes and the quantum game behaves as a noiseless game.…”

Section: Introductionmentioning

confidence: 99%

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Quantum games with correlated noise

Nawaz¹,

Toor²

2006

J. Phys. A: Math. Gen.

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We analyze quantum game with correlated noise through generalized quantization scheme. Four different combinations on the basis of entanglement of initial quantum state and the measurement basis are analyzed. It is shown that the advantage that a quantum player can get by exploiting quantum strategies is only valid when both the initial quantum state and the measurement basis are in entangled form. Furthermore, it is shown that for maximum correlation the effects of decoherence diminish and it behaves as a noiseless game.

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Section: Quantization In Presence Of Correlated Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum games with correlated noise

Nawaz¹,

Toor²

2006

J. Phys. A: Math. Gen.

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“…In the present case, however, the correlation between players in the final result is dynamically generated, i.e., it is a consequence of the player's choice, and it is not encoded in the initial state. In this respect, it also differs from the quantum generalization of other simple games, like the prisoner's dilemma [4], or the minority game [10].…”

mentioning

confidence: 99%

“…The blending of quantum mechanics with game theory opens novel strategies based in exploiting the peculiarities of quantum behaviour, and it has already estimulated a number of new ideas, e.g., in the Prisioners' Dilemma there exists a quantum strategy that allows both players to escape the dilemma [4].…”

mentioning

confidence: 99%

“…Recently, a new field for game theory has emerged in the form of quantum games with the goal of taking advantage of quantum effects to attain a winning edge [3], [4], [5]. The blending of quantum mechanics with game theory opens novel strategies based in exploiting the peculiarities of quantum behaviour, and it has already estimulated a number of new ideas, e.g., in the Prisioners' Dilemma there exists a quantum strategy that allows both players to escape the dilemma [4].…”

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Quantum Chinos game: winning strategies through quantum fluctuations

Guinea

Martín-Delgado

2003

J. Phys. A: Math. Gen.

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We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial quantization of the game (semiclassical) allows us to find a winning strategy for the second player, but it is unstable w.r.t. the classical strategy. However, in a fully quantum version of the game we find a winning strategy for the first player that is optimal: the symmetric classical situation is broken at the quantum level.PACS numbers: 03.67.-a, 03.67.LxIn a typical scene at a Spanish restaurant, a small group of companions-at-table gather at the bar extending their arms, each with their clenched hands holding a few coins hidden inside. They are gambling for the after-lunch round of coffees. One after another they tell a number, then open their hands showing their coins one another and count them all. Ofently, one of the pals smile meaning that s/he guessed the correct total number of coins. After a given number of plays, the player scoring the worst pays for all coffees. This gambling game is known as the Chinos game and has been a traditional way in Spain to decide who is in charge for the coffees' check [1].Interestingly enough, this simple-minded guessing game exhibits a rich variety of patterns with complex behaviour that has been used to model strategic behaviour in some social and economic problems, like financial markets and information transmission [2]. This is an example of non-cooperative game for each player seeks to maximize her/his chances of guessing correctly, and at the same time to minimize the possibilities of her/his opponents.Recently, a new field for game theory has emerged in the form of quantum games with the goal of taking advantage of quantum effects to attain a winning edge [3], [4], [5]. The blending of quantum mechanics with game theory opens novel strategies based in exploiting the peculiarities of quantum behaviour, and it has already estimulated a number of new ideas, e.g., in the Prisioners' Dilemma there exists a quantum strategy that allows both players to escape the dilemma [4].In this letter our aim is twofold: firstly, to define quantum versions of the Chinos game such that they reduce to the classical game as a limiting case. Secondly, to analyse the new quantum versions in order to find how the classical strategies behave under quantum effects, and if there exists new quantum winning strategies without classical analogue.

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Quantum Game Theory

Landsburg

2011

Wiley Encyclopedia of Operations Research and Management Science

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Quantum Games and Quantum Strategies

Cited by 904 publications

References 8 publications

Quantum games with correlated noise

Quantum games with correlated noise

Quantum Chinos game: winning strategies through quantum fluctuations

Quantum Game Theory

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