Dominant Strategies of Quantum Games on Quantum Periodic Automata

Giannakis, Konstantinos; Papalitsas, Christos; Kastampolidou, Kalliopi; Singh, Alexandros; Andronikos, Theodore

doi:10.3390/computation3040586

Cited by 34 publications

(29 citation statements)

References 43 publications

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“…In that work, quantum automata accepting infinite words were associated with winning strategies for abstract quantum games. The current paper differs from [33] in the following aspects: (i) the focus is in the PQ penny flip game and all its variations; (ii) the automata are either deterministic or nondeterministic finite automata; and (iii) the words accepted by the automata correspond to moves by both players.…”

Section: Related Workmentioning

confidence: 99%

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Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

et al. 2018

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Abstract:The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The PQ penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper, we investigate all possible finite games that can be played between the two players Q and Picard of the original PQ game. For this purpose, we establish a rigorous connection between finite automata and the PQ game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the PQ game. What this means is that, from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

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Section: Related Workmentioning

confidence: 99%

“…The relation of quantum games with finite automata was also studied in [33]. In that work, quantum automata accepting infinite words were associated with winning strategies for abstract quantum games.…”

Section: Related Workmentioning

confidence: 99%

Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

et al. 2018

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“…A previous work in [19] discussed the connection between a quantum game and quantum automata. In particular, the game was the PQ Penny-flip game from [1] where one player outperforms the other by employing quantum actions.…”

Section: Related Workmentioning

confidence: 99%

“…Quantum computing advocates the use of quantum-mechanical methods for computation purposes. Under this perspective, quantum automata have also been thoroughly investigated [14][15][16][17][18] and have been associated with game theory in [19], where it was shown that they can be related to quantum strategies of repeated games.…”

Section: Introductionmentioning

confidence: 99%

Quantum Conditional Strategies for Prisoners' Dilemmata Under the Ewl Scheme

Giannakis¹,

Theocharopoulou²,

Papalitsas³

et al. 2019

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Classic 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. 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 some well-known game conditional strategies that have been studied within the framework of the repeated PD game. Then, we try to associate these strategies to proper quantum finite automata that receive them as inputs and recognize them with probability 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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“…In particular, they reduced the problem they studied to choosing strategies in evolutionary games. Quantum games and their strategies seem very promising, offering enhanced capabilities over classic ones [13]. [18].…”

Section: Related Workmentioning

confidence: 99%

Quantum Inspired General Variable Neighborhood Search (qGVNS) for Dynamic Garbage Collection

Papalitsas¹,

Karakostas²,

Andronikos³

et al. 2017

Preprint

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General Variable Neighborhood Search (GVNS) is a well known and widely used metaheuristic for efficiently solving many NP-hard combinatorial optimization problems. Quantum General Variable Neighborhood Search (qGVNS) is a novel, quantum inspired extension of the conventional GVNS. Its quantum nature derives from the fact that it takes advantage and incorporates tools and techniques from the field of quantum computation. Travelling Salesman Problem (TSP) is a well known NP-Hard problem which has broadly been used for modelling many real life routing cases. As a consequence, TSP can be used as a basis for modelling and finding routes for Geographical Systems (GPS). In this paper, we examine the potential use of this method for the GPS system of garbage trucks. Specifically, we provide a thorough presentation of our method accompanied with extensive computational results. The experimental data accumulated on a plethora of symmetric TSP instances (symmetric in order to faithfully simulate GPS problems), which are shown in a series of figures and tables, allow us to conclude that the novel qGVNS algorithm can provide an efficient solution for this type of geographical problems.

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Dominant Strategies of Quantum Games on Quantum Periodic Automata

Cited by 34 publications

References 43 publications

Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

Quantum Conditional Strategies for Prisoners' Dilemmata Under the Ewl Scheme

Quantum Inspired General Variable Neighborhood Search (qGVNS) for Dynamic Garbage Collection

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