1,276 research outputs found
Nash embedding and equilibrium in pure quantum states
With respect to probabilistic mixtures of the strategies in non-cooperative
games, quantum game theory provides guarantee of fixed-point stability, the
so-called Nash equilibrium. This permits players to choose mixed quantum
strategies that prepare mixed quantum states optimally under constraints. In
this letter, we show that fixed-point stability of Nash equilibrium can also be
guaranteed for pure quantum strategies via an application of the Nash embedding
theorem, permitting players to prepare pure quantum states optimally under
constraints.Comment: 7 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1609.0836
Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits
In the context of quantum information theory, "quantization" of various
mathematical and computational constructions is said to occur upon the
replacement, at various points in the construction, of the classical
randomization notion of probability distribution with higher order
randomization notions from quantum mechanics such as quantum superposition with
measurement. For this to be done "properly", a faithful copy of the original
construction is required to exist within the new "quantum" one, just as is
required when a function is extended to a larger domain. Here procedures for
extending history dependent Parrondo games, Markov processes and multiplexing
circuits to their "quantum" versions are analyzed from a game theoretic
viewpoint, and from this viewpoint, proper quantizations developed
Quantum Matching Pennies Game
A quantum version of the Matching Pennies (MP) game is proposed that is
played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct
the quantum game without using the state vectors, while considering only the
quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We
embed the classical game within the quantum game such that the classical MP
game results when the quantum mechanical joint probabilities become
factorizable. We report new Nash equilibria in the quantum MP game that emerge
when the quantum mechanical joint probabilities maximally violate the
Clauser-Horne-Shimony-Holt form of Bell's inequality.Comment: Revised in light of referees' comments, submitted to Journal of the
Physical Society of Japan, 14 pages, 1 figur
A probabilistic approach to quantum Bayesian games of incomplete information
A Bayesian game is a game of incomplete information in which the rules of the
game are not fully known to all players. We consider the Bayesian game of
Battle of Sexes that has several Bayesian Nash equilibria and investigate its
outcome when the underlying probability set is obtained from generalized
Einstein-Podolsky-Rosen experiments. We find that this probability set, which
may become non-factorizable, results in a unique Bayesian Nash equilibrium of
the game.Comment: 18 pages, 2 figures, accepted for publication in Quantum Information
Processin
N-player quantum games in an EPR setting
The -player quantum game is analyzed in the context of an
Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's
strategies are not unitary transformations as in alternate quantum
game-theoretic frameworks, but a classical choice between two directions along
which spin or polarization measurements are made. The players' strategies thus
remain identical to their strategies in the mixed-strategy version of the
classical game. In the EPR setting the quantum game reduces itself to the
corresponding classical game when the shared quantum state reaches zero
entanglement. We find the relations for the probability distribution for
-qubit GHZ and W-type states, subject to general measurement directions,
from which the expressions for the mixed Nash equilibrium and the payoffs are
determined. Players' payoffs are then defined with linear functions so that
common two-player games can be easily extended to the -player case and
permit analytic expressions for the Nash equilibrium. As a specific example, we
solve the Prisoners' Dilemma game for general . We find a new
property for the game that for an even number of players the payoffs at the
Nash equilibrium are equal, whereas for an odd number of players the
cooperating players receive higher payoffs.Comment: 26 pages, 2 figure
Analysis of two-player quantum games in an EPR setting using geometric algebra
The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR)
type setting is investigated using the mathematical formalism of Clifford
geometric algebra (GA). In this setting, the players' strategy sets remain
identical to the ones in the classical mixed-strategy version of the game,
which is then obtained as proper subset of the corresponding quantum game. As
examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt
when played in the EPR type setting.Comment: 20 pages, no figure, revise
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