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.

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.

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.

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 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.

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.

Gaming the quantum

2013 ◽  
Vol 13 (3&4) ◽  
pp. 231-244
Author(s):  
Faisal Shah Khan ◽  
Simon J.D. Phoenix
Keyword(s):  
Game Theory ◽  
Quantum Mechanics ◽  
Quantum Information Processing ◽  
Quantum Mechanical ◽  
Quantum Game ◽  
Equilibrium Behavior ◽  
Physical Systems ◽  
Quantum Objects ◽  
Distance Minimization ◽  
Zero Sum

In the time since the merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of ``quantized games'', and of applying game theory to quantum mechanics, referred to henceforth as ``gaming the quantum'', have become synonymous under the single ill-defined term ``quantum game''. Here, these two perspectives are delineated and a game-theoretically proper description of what makes a multiplayer, non-cooperative game quantum mechanical, is given. Within the context of this description, finding Nash equilibrium in a zero-sum quantum game is exhibited to be equivalent to finding a solution to a simultaneous distance minimization problem in the state space of quantum objects, thus setting up a framework for a game theory inspired study of ``equilibrium'' behavior of quantum physical systems such as those utilized in quantum information processing and computation.

scholarly journals Quantum games with correlated noise

2006 ◽  
Vol 39 (29) ◽  
pp. 9321-9328 ◽  
Author(s):  
Ahmad Nawaz ◽  
A H Toor
Keyword(s):  
Correlated Noise ◽  
Quantum Games

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.

scholarly journals Bitcoin Mining as a Contest

Ledger ◽  
2017 ◽  
Vol 2 ◽  
pp. 31-37 ◽  
Author(s):  
Nicola Dimitri
Keyword(s):  
Return On Investment ◽  
Pure Strategy ◽  
Simple Game ◽  
Complete Information ◽  
Mining Activity ◽  
Rate Of Return ◽  
Computational Power ◽  
Intrinsic Structure ◽  
Optimal Amount ◽  
Game Theoretic

This paper presents a simple game theoretic framework, assuming complete information, to model Bitcoin mining activity. It does so by formalizing the activity as an all-pay contest: a competition where participants contend with each other to win a prize by investing in computational power, and victory is probabilistic. With at least two active miners, the unique pure strategy Nash equilibrium of the game suggests the following interesting insights on the motivation for being a miner: while the optimal amount of energy consumption depends also on the reward for solving the puzzle, as long as the reward is positive the decision to be an active miner depends only on the mining costs. Moreover, the intrinsic structure of the mining activity seems to prevent the formation of a monopoly, because in an equilibrium with two miners, both of them will have positive expected profits for any level of the opponent’s costs. A monopoly could only form if the rate of return on investment were higher outside bitcoin.  

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