scholarly journals Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Piotr Frąckiewicz
Keyword(s):  
Quantum Game ◽  
Quantum Games ◽  
New Criterion ◽  
Game Isomorphism ◽  
Classical Game ◽  
Game Scheme

The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form.

scholarly journals Quantum games of opinion formation based on the Marinatto-Weber quantum game scheme

2016 ◽  
Vol 114 (5) ◽  
pp. 50012 ◽  
Author(s):  
Xinyang Deng ◽  
Yong Deng ◽  
Qi Liu ◽  
Lei Shi ◽  
Zhen Wang
Keyword(s):  
Quantum Game ◽  
Opinion Formation ◽  
Quantum Games ◽  
Game Scheme

scholarly journals On the equivalence between non-factorizable mixed-strategy classical games and quantum games

2016 ◽  
Vol 3 (1) ◽  
pp. 150477 ◽  
Author(s):  
Azhar Iqbal ◽  
James M. Chappell ◽  
Derek Abbott
Keyword(s):  
Decision Theory ◽  
Mixed Strategy ◽  
Strategic Interaction ◽  
Quantum Game ◽  
Mathematical Basis ◽  
Quantum Games ◽  
Mathematical Question ◽  
Game Theoretic ◽  
Classical Game ◽  
Quantum Decision Theory

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a non-factorizable game and determine the limitations of our approach.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

Quantum Game of Dual-channel Supply Chain under Free-riding Behavior

2021 ◽  
Vol 1 (1) ◽  
pp. 3-17
Author(s):  
Yu-Chung Chang ◽  
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Quantum Entanglement ◽  
Free Riding ◽  
Selling Price ◽  
Quantum Game ◽  
Optimal Price ◽  
Dual Channel ◽  
Dual Channel Supply Chain ◽  
Classical Game

Based on the perspective of the quantum game, this paper explores when the online direct sales channel takes the free-riding behavior after the retail channel provides high-quality experience and services and how the dual-channel supply chain establishes a commodity pricing strategy. The retailer’s selling price follows a decreasing function of the free-riding behavior coefficient. while the online direct selling price does an increasing function of the free-riding behavior coefficient. Under centralized decision-making, there is no quantum entanglement, so the quantum game solution is consistent with the classical game solution. Under decentralized decision-making, the optimal price and profit of the quantum game are higher than those of the classical game when the quantum entanglement degree is greater than zero. When the quantum entanglement tends to be infinite, the optimal price of the quantum game finally remains in convergence. The quantum game theory is a more optimal decision-making method than the classical game theory.

scholarly journals THE ROLE OF CORRELATION IN QUANTUM AND CLASSICAL GAMES

2013 ◽  
Vol 12 (03) ◽  
pp. 1350011 ◽  
Author(s):  
SIMON J. D. PHOENIX ◽  
FAISAL SHAH KHAN
Keyword(s):  
Pure Strategy ◽  
Classical Model ◽  
Simple Game ◽  
Central Feature ◽  
Correlated Noise ◽  
Quantum Game ◽  
Joint Measurement ◽  
Quantum Games ◽  
Output State ◽  
Quantum Objects

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these simple quantum games are not sensitive to the quantum part of the correlation. In these games played with quantum objects it is possible to transform a game such as Prisoner's Dilemma into the game of Chicken. We show that this behavior, and the associated enhanced equilibrium payoff over playing the game with quantum objects in nonentangled states, is entirely due to the classical part of the correlation. Generalizing these games to the pure strategy 2-player quantum game where the players have finite strategy sets and a projective joint measurement is made on the output state produced by the players, we show that a given quantum game of this form can always be reproduced by a classical model, such as a communication channel. Where entanglement is a feature of the these 2-player quantum games the matrix of expected outcomes for the players can be reproduced by a classical channel with correlated noise.

Land bidding game with conflicting interest and its quantum solution

2017 ◽  
Vol 15 (05) ◽  
pp. 1750034 ◽  
Author(s):  
Haozhen Situ ◽  
Ramón Alonso-Sanz ◽  
Lvzhou Li ◽  
Cai Zhang
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequalities ◽  
Free Rider ◽  
Common Interest ◽  
Quantum Game ◽  
Quantum Games ◽  
Bidding Game ◽  
Free Rider Problem ◽  
The Common ◽  
Quantum Solution

Recently, the first conflicting interest quantum game based on the nonlocality property of quantum mechanics has been introduced in A. Pappa, N. Kumar, T. Lawson, M. Santha, S. Y. Zhang, E. Diamanti and I. Kerenidis, Phys. Rev. Lett. 114 (2015) 020401. Several quantum games of the same genre have also been proposed subsequently. However, these games are constructed from some well-known Bell inequalities, thus are quite abstract and lack of realistic interpretations. In the present paper, we modify the common interest land bidding game introduced in N. Brunner and N. Linden, Nat. Commun. 4 (2013) 2057, which is also based on nonlocality and can be understood as two companies collaborating in developing a project. The modified game has conflicting interest and reflects the free rider problem in economics. Then we show that it has a fair quantum solution that leads to better outcome. Finally, we study how several types of paradigmatic noise affect the outcome of this game.

NON-CLASSICAL QUANTUM CORRELATIONS IN QUANTUM GAMES

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2552-2558 ◽  
Author(s):  
JIANGFENG DU ◽  
GUANGLEI CHENG ◽  
HUI LI
Keyword(s):  
Quantum Correlation ◽  
Quantum Correlations ◽  
Quantum Game ◽  
Quantum Games ◽  
Classical Counterpart ◽  
Prisoners Dilemma ◽  
Classical Quantum

In this paper we propose an interesting scheme for quantum games. It is found that, for the particular case of the famous Prisoners' Dilemma game, the superiority of the quantum game over its classical counterpart is interconnected to the non-classical quantum correlation between the two players.

scholarly journals ANALYSIS OF TREMBLING HAND PERFECT EQUILIBRIA IN QUANTUM GAMES

2008 ◽  
Vol 08 (01) ◽  
pp. L23-L30 ◽  
Author(s):  
IRENEUSZ PAKUŁA
Keyword(s):  
Game Theory ◽  
Probability Distribution ◽  
Distribution Functions ◽  
Quantum Game ◽  
Quantum Games ◽  
Probability Distribution Functions ◽  
Perfect Equilibria ◽  
Quantum Strategies

We analyse Selten' concept of trembling hand perfect equilibria in the context of quantum game theory. We define trembles as mixed quantum strategies by replacing discrete probabilities with probability distribution functions. Explicit examples of analysis are given.

QUANTUM GAME WITH INCOMPLETE INFORMATION

2002 ◽  
Vol 02 (04) ◽  
pp. L263-L271 ◽  
Author(s):  
YONG-JIAN HAN ◽  
YONG-SHENG ZHANG ◽  
GUANG-CAN GUO
Keyword(s):  
Nash Equilibrium ◽  
Incomplete Information ◽  
Pure Strategy ◽  
Quantum Model ◽  
Quantum Game ◽  
Initial State ◽  
Innovative Work ◽  
Classical Game

Quantum game is an interesting field and many scientists have done a lot of innovative work in it. We give a quantum model about incomplete information. In this model we find whether the pure-strategy Bayes-Nash equilibrium exists or not is strongly dependent on the entanglement of the initial state. We also find the player Bob can always find an initial state and a pure-strategy Bayes-Nash equilibrium to get more payoff than classical game with some parameter.

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