Constructing quantum games from nonfactorizable joint probabilities

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.

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“…[34] also using an EPR type setting, directly from a set of non-factorizable joint probabilities. Although Ref.…”

Section: Discussionmentioning

confidence: 99%

Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

2012

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“…We have considered the particular case of a six-player QMG using a state analogous to Eq. (15). We find that the switch of optimal strategy occurs at α = 6 19 , with payoffs…”

Section: Extensionsmentioning

confidence: 95%

“…Previous publications have explored the relationship between Bell inequalities and various formulations of quantum games [9][10][11][12][13][14][15]. Comparison have also been drawn between * Corresponding author.…”

Section: Introductionmentioning

confidence: 99%

Equivalence between Bell inequalities and quantum minority games

et al. 2009

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We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality. We conclude the existence of direct correspondences between (i) the payoff rule and Bell inequalities, and (ii) the strategy and the choice of measured observables in evaluating these Bell inequalities. We also show that such a correspondence is unique to minority-like games.

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“…Consider now the right side of Eq. (26). As ∆ = 2(ǫ 1 + ǫ 4 + ǫ 5 + ǫ 8 + ǫ 9 + ǫ 12 + ǫ 14 + ǫ 15 − 2), the discriminant (2 − |∆|) can be negative for the following two cases: a) For case 0 ≤ ∆, we have 2 − |∆| = 2 − ∆.…”

Section: Correlationsmentioning

confidence: 99%

The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

2018

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The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein-Podolsky-Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.

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Constructing quantum games from nonfactorizable joint probabilities

Cited by 27 publications

References 20 publications

Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

Equivalence between Bell inequalities and quantum minority games

The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting

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