Quantum Games: Mixed Strategy Nash's Equilibrium Represents Minimum Entropy

Jiménez, Edward

doi:10.3390/e5040313

Cited by 9 publications

(9 citation statements)

References 23 publications

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“…The concept of correlation complexity is also discussed in [42] by Jain et al, a work that extended the [40], whereas in [43] there is the extension to the multipartite case. Quantum games are also studied in [44] with focus on the illustration of the relationship among quantum mechanics notions and Nash equilibria. They, also, investigate the entropy of such games and their minimal value under specific Nash equilibria.…”

Section: Related Workmentioning

confidence: 99%

Dominant Strategies of Quantum Games on Quantum Periodic Automata

et al. 2015

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Game theory and its quantum extension apply in numerous fields that affect people's social, political, and economical life. Physical limits imposed by the current technology used in computing architectures (e.g., circuit size) give rise to the need for novel mechanisms, such as quantum inspired computation. Elements from quantum computation and mechanics combined with game-theoretic aspects of computing could open new pathways towards the future technological era. This paper associates dominant strategies of repeated quantum games with quantum automata that recognize infinite periodic inputs. As a reference, we used the PQ-PENNY quantum game where the quantum strategy outplays the choice of pure or mixed strategy with probability 1 and therefore the associated quantum automaton accepts with probability 1. We also propose a novel game played on the evolution of an automaton, where players' actions and strategies are also associated with periodic quantum automata.

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Section: Related Workmentioning

confidence: 99%

Dominant Strategies of Quantum Games on Quantum Periodic Automata

et al. 2015

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“…Information in QG has been developed in the references 23 – 25 . In the latter work, reference is made to the density operator of quantum states when determining the capacity of the game.…”

Section: Introductionmentioning

confidence: 99%

Dilemma breaking in quantum games by joint probabilities approach

Legón

Medina

2022

Sci Rep

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Classical games get fundamentally modified in the quantum realm because of non-locality and entanglement, that bypass some of the crucial features of the classical problem that define a dilemma. We will analyze how the dilemma can be shunted and even completely eliminated by the players using quantum strategies from the viewpoint of joint probabilities. In this approach, the game information (entropy) needs to be incorporated into the game strategies. We also connect the potential of the formalism of quantum games with the transmission of quantum information in quantum noisy channels and recent considerations of the connection between thermalization mechanisms in statistical mechanics, the many body problem and cooperative games considered here in the quantum regime.

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“…Quantum game theory has gained a lot of research interest since the first pioneering works of the late 1990s [1][2][3][4][5]. Quantum game theory combines the well-known field of game theory with the emerging branch of computation theory that involves quantum principles.…”

Section: Introductionmentioning

confidence: 99%

“…There is an interesting debate regarding what a quantum game really is and its ontological position in the area of game theory. A useful list of references on this controversy can be found in [14] (citations [2][3][4][5][6][7][8][9] from that chapter). In the theory of quantum games, one identifies specific characteristics of quantum information and combines them with those of classical multiplayer, non-cooperative games, ultimately looking for differentiation in results related to Nash equilibria, player's strategies, etc.…”

Section: Introductionmentioning

confidence: 99%

Quantum Conditional Strategies and Automata for Prisoners’ Dilemmata under the EWL Scheme

et al. 2019

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Classical game theory is an important field with a long tradition of useful results. Recently, the quantum versions of classical games, such as the prisoner’s dilemma (PD), have attracted a lot of attention. This game variant can be considered as a specific type of game where the player’s actions and strategies are formed using notions from quantum computation. Similarly, state machines, and specifically finite automata, have also been under constant and thorough study for plenty of reasons. The quantum analogues of these abstract machines, like the quantum finite automata, have been studied extensively. In this work, we examine well-known conditional strategies that have been studied within the framework of the classical repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with a probability of 1, achieving some interesting results. We also study the quantum version of PD under the Eisert–Wilkens–Lewenstein scheme, proposing a novel conditional strategy for the repeated version of this game.

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Quantum Games: Mixed Strategy Nash's Equilibrium Represents Minimum Entropy

Cited by 9 publications

References 23 publications

Dominant Strategies of Quantum Games on Quantum Periodic Automata

Dominant Strategies of Quantum Games on Quantum Periodic Automata

Dilemma breaking in quantum games by joint probabilities approach

Quantum Conditional Strategies and Automata for Prisoners’ Dilemmata under the EWL Scheme

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