Quantum Approach to Game Theory

Alonso‐Sanz, Ramón

doi:10.1007/978-3-030-19634-9_2

Cited by 2 publications

(6 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They also build a certain quantum strategy that always outperforms any classical strategy, leading to a Nash equilibrium set of strategies that are also Pareto optimal. This work serves as a basis for the underlying quantum variant of the prisoner's dilemma problem and is usually referred to as the EWL scheme [14]. The EWL scheme has received criticism by Benjamin and Hayden in [3], due to the restrictions imposed to the players' actions.…”

Section: Related Workmentioning

confidence: 99%

“…This scheme was criticized in [3] (to which a subsequent reply from Eisert et al followed [70]) due to the restrictions imposed to players' actions. Despite the fact that this limitation leads to a slightly different version of the quantum PD game, it is technically correct and has served as a basis model for several other works [5,14,33,54,71,72].…”

Section: Quantum Version Of Conditional Strategiesmentioning

confidence: 99%

“…Quantum game theory can be seen as an extension (or a variation) of classical game theory [1,2,5,14]. There is an interesting debate regarding what a quantum game really is and its ontological position in the area of game theory.…”

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%

“…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. [14,15], and this is the main reason for someone to characterize this class of games as quantum games. Three primary characteristics distinguish quantum from classical game theory: superposed initial states, quantum entanglement of states, and superposition of actions to be used upon the initial states.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

et al. 2019

View full text Add to dashboard Cite

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.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Quantum Version Of Conditional Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

et al. 2019

View full text Add to dashboard Cite

show abstract

Quantum Tapsilou—A Quantum Game Inspired by the Traditional Greek Coin Tossing Game Tapsilou

Kastampolidou,

Andronikos

2023

Games

View full text Add to dashboard Cite

This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the classical game, both players have 14 probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding Ry rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action.

show abstract

Quantum Approach to Game Theory

Cited by 2 publications

References 23 publications

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

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

Quantum Tapsilou—A Quantum Game Inspired by the Traditional Greek Coin Tossing Game Tapsilou

Contact Info

Product

Resources

About