283 research outputs found
Constructing quantum games from non-factorizable joint probabilities
A probabilistic framework is developed that gives a unifying perspective on
both the classical and the quantum games. We suggest exploiting peculiar
probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to
construct quantum games. In our framework a game attains classical
interpretation when joint probabilities are factorizable and a quantum game
corresponds when these probabilities cannot be factorized. We analyze how
non-factorizability changes Nash equilibria in two-player games while
considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this
framework we find that for the game of Prisoner's Dilemma even non-factorizable
EPR joint probabilities cannot be helpful to escape from the classical outcome
of the game. For a particular version of the Chicken game, however, we find
that the two non-factorizable sets of joint probabilities, that maximally
violates the Clauser-Holt-Shimony-Horne (CHSH) sum of correlations, indeed
result in new Nash equilibria.Comment: Revised in light of referee's comments, submitted to Physical Review
An Analysis of the Quantum Penny Flip Game using Geometric Algebra
We analyze the quantum penny flip game using geometric algebra and so
determine all possible unitary transformations which enable the player Q to
implement a winning strategy. Geometric algebra provides a clear visual picture
of the quantum game and its strategies, as well as providing a simple and
direct derivation of the winning transformation, which we demonstrate can be
parametrized by two angles. For comparison we derive the same general winning
strategy by conventional means using density matrices.Comment: 8 Pages, 1 Figure, accepted for publication in the Journal of
Physical Society of Japa
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
Genetic control of immunoglobulin allotypes in the fowl
Eight immunoglobulin allotypic specificities have been identified in the fowl by isoimmunization. Aa1 and Aa2 are controlled as codominants at the a locus, Ab1 and Ab2 at the b locus, and Ac1, Ac2, Ac3, and Ac4 at the c locus. Column chromatography and ultracentrifugation indicate that the specificities at the a locus are located on molecules corresponding to IgG with sedimentation coefficients 7 S. Immunoelectrophoresis results also indicate that we are dealing with an immunoglobulin G molecule. Further tests are underway to resolve this beyond doubt.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44156/1/10528_2004_Article_BF00520354.pd
Analyzing three-player quantum games in an EPR type setup
We use the formalism of Clifford Geometric Algebra (GA) to develop an
analysis of quantum versions of three-player non-cooperative games. The quantum
games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting.
In this setting, the players' strategy sets remain identical to the ones in the
mixed-strategy version of the classical game that is obtained as a proper
subset of the corresponding quantum game. Using GA we investigate the outcome
of a realization of the game by players sharing GHZ state, W state, and a
mixture of GHZ and W states. As a specific example, we study the game of
three-player Prisoners' Dilemma.Comment: 21 pages, 3 figure
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
PERFECT RECALL AND PRUNING IN GAMES WITH IMPERFECT INFORMATION 1
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72986/1/j.1467-8640.1996.tb00256.x.pd
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
An integrative framework of preemption strategies
Pre-print; author's draftThis paper performs a review of the various pre-emption strategies prescribed in the economics literature. These are cost superiority, consumers' switching cost, channel exclusivity, environmental barriers of entry and credible commitment to react aggressively. Through our analysis, we develop an integrative framework of the pre-emption strategies that will result in long-term payoffs to the firm.
The framework proposes that there are two key dimensions—strategic advantage and strategic focus—and identify five generic types of pre-emption strategies for market incumbents. These are the switching cost, blockade, credible commitment, tie-up, and cost leadership strategies. The pre-emption strategies and the framework presented can assist managerial decision-making for the successful pre-emption of potential competition to complement their existing efforts
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