scholarly journals Geometrical Exploration of Quantum Games

10.5772/53931 ◽  
2013 ◽  
Author(s):  
David Schneider
Keyword(s):  
Quantum Games

scholarly journals Dynamic Quantum Games

2021 ◽  
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Real Time ◽  
Repeated Games ◽  
Dynamic Games ◽  
Quantum Control ◽  
Diffusion Processes ◽  
Natural Class ◽  
Quantum Games ◽  
Technical Problems ◽  
Modern Development ◽  
Starting Point

AbstractQuantum games represent the really twenty-first century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated games. In this paper, we aim at initiating the truly dynamic theory with strategies chosen by players in real time. Since direct continuous observations are known to destroy quantum evolutions (so-called quantum Zeno paradox), the necessary new ingredient for quantum dynamic games must be the theory of non-direct observations and the corresponding quantum filtering. Apart from the technical problems in organizing feedback quantum control in real time, the difficulty in applying this theory for obtaining mathematically amenable control systems is due partially to the fact that it leads usually to rather non-trivial jump-type Markov processes and/or degenerate diffusions on manifolds, for which the corresponding control is very difficult to handle. The starting point for the present research is the remarkable discovery (quite unexpected, at least to the author) that there exists a very natural class of homodyne detections such that the diffusion processes on projective spaces resulting by filtering under such arrangements coincide exactly with the standard Brownian motions (BM) on these spaces. In some cases, one can even reduce the process to the plain BM on Euclidean spaces or tori. The theory of such motions is well studied making it possible to develop a tractable theory of related control and games, which can be at the same time practically implemented on quantum optical devices.

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.

scholarly journals OCTONIONIZATION OF THREE PLAYER, TWO STRATEGY MAXIMALLY ENTANGLED QUANTUM GAMES

2010 ◽  
Vol 08 (03) ◽  
pp. 411-434 ◽  
Author(s):  
ADEN OMAR AHMED ◽  
STEVEN A. BLEILER ◽  
FAISAL SHAH KHAN
Keyword(s):  
Nash Equilibria ◽  
Payoff Function ◽  
Quantum Games ◽  
Computational Capability

We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then exploited to analyze and potentially classify the Nash equilibria in the quantum games.

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 Arbiter as the Third Man in Classical and Quantum Games

2010 ◽  
Vol 49 (12) ◽  
pp. 3243-3249 ◽  
Author(s):  
Jarosław Pykacz ◽  
Piotr Fra̧ckiewicz
Keyword(s):  
Quantum Games ◽  
The Third
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