The Two-Envelope Problem Revisited

Abbott, Derek; Davis, B.R.; Parrondo, Juan M. R.

doi:10.1142/s0219477510000022

Cited by 11 publications

(18 citation statements)

References 38 publications

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“…Noise has effects a priori unexpected on the organization of complex systems made of interacting elements, as shown by stochastic resonance (SR) [1], coherence resonance [2], noise-induced phase transitions [3], noiseinduced transport [4] and its game theoretical version, the Parrondo's Paradox [5]. SR occurs in a system when a small applied (sub-threshold) periodic signal is amplified by the addition of noise and the maximum of amplification is found for intermediate noise strengths.…”

Section: Introductionmentioning

confidence: 99%

Noise-induced volatility of collective dynamics

2012

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Noise-induced volatility refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical signature of this phenomenon is that-beyond the increase in the level of fluctuations-the response of the system becomes uncorrelated with the external driving force, making it different from stochastic resonance. Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of this phenomenon, which is argued to be a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems, and of strong selective responses of immune systems of complex biological organisms. Extensive numerical simulations are compared with a mean-field theory for different network topologies.

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Section: Introductionmentioning

confidence: 99%

Noise-induced volatility of collective dynamics

2012

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“…So we obtain γ = 1 that gives Ω = 0. Similarly, for the probability set (56) we also obtain Ω = 0. In view of the Inequalities (51,52), in the quantum MP game with players sharing a maximally entangled state to play the game, this results in any strategy set (x ⋆ , y ⋆ ) being a NE.…”

Section: Analysis Of the Quantum Matching Pennies Gamementioning

confidence: 63%

Constructing quantum games from a system of Bell's inequalities

Iqbal¹,

Abbott²

2010

Physics Letters A

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We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses some of their well known criticisms.Comment: 17 pages, no figure, revised in light of referees' comments, accepted for publication in Physics Letters

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“…This is an area which has not been fully explored yet. The Allison mixture has some resemblance to the thermodynamic picture of the Feynman-Smoluchowski ratchet: At equilibrium, there is detailed balance, time reversibility, and no net displacement, whereas out of equilibrium detailed balance is broken, with time irreversibility leading to net displacement [36,37]. It is worth noting that the Allison mixture process mixes two random sequences in a time-irreversible way only when symmetry in the governing transition probabilities is broken.…”

Section: Introductionmentioning

confidence: 99%

“…Readers can refer to Refs. [8] and [37] for more information on the Allison mixture. There have been discussions to link the Allison mixture to applications in encryption and optimization of file compression [33].…”

Section: Introductionmentioning

confidence: 99%

Allison mixture and the two-envelope problem

2017

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In the present study, we have investigated the Allison mixture, a variant of the Parrondo's games where random mixing of two random sequences creates autocorrelation. We have obtained the autocorrelation function and mutual entropy of two elements. Our analysis shows that the mutual information is nonzero even if two distributions have identical average values. We have also considered the two-envelope problem and solved for its exact probability distribution.

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The Two-Envelope Problem Revisited

Cited by 11 publications

References 38 publications

Noise-induced volatility of collective dynamics

Noise-induced volatility of collective dynamics

Constructing quantum games from a system of Bell's inequalities

Allison mixture and the two-envelope problem

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