33 research outputs found
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
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
A Novel Clustering Algorithm Based on Quantum Games
Enormous successes have been made by quantum algorithms during the last
decade. In this paper, we combine the quantum game with the problem of data
clustering, and then develop a quantum-game-based clustering algorithm, in
which data points in a dataset are considered as players who can make decisions
and implement quantum strategies in quantum games. After each round of a
quantum game, each player's expected payoff is calculated. Later, he uses a
link-removing-and-rewiring (LRR) function to change his neighbors and adjust
the strength of links connecting to them in order to maximize his payoff.
Further, algorithms are discussed and analyzed in two cases of strategies, two
payoff matrixes and two LRR functions. Consequently, the simulation results
have demonstrated that data points in datasets are clustered reasonably and
efficiently, and the clustering algorithms have fast rates of convergence.
Moreover, the comparison with other algorithms also provides an indication of
the effectiveness of the proposed approach.Comment: 19 pages, 5 figures, 5 table
Quantum decision making by social agents
The influence of additional information on the decision making of agents, who
are interacting members of a society, is analyzed within the mathematical
framework based on the use of quantum probabilities. The introduction of social
interactions, which influence the decisions of individual agents, leads to a
generalization of the quantum decision theory developed earlier by the authors
for separate individuals. The generalized approach is free of the standard
paradoxes of classical decision theory. This approach also explains the
error-attenuation effects observed for the paradoxes occurring when decision
makers, who are members of a society, consult with each other, increasing in
this way the available mutual information. A precise correspondence between
quantum decision theory and classical utility theory is formulated via the
introduction of an intermediate probabilistic version of utility theory of a
novel form, which obeys the requirement that zero-utility prospects should have
zero probability weights.Comment: This paper has been withdrawn by the authors because a much extended
and improved version has been submitted as arXiv:1510.02686 under the new
title "Role of information in decision making of social agents