Allison mixture and the two-envelope problem

Cheong, Kang Hao; Saakian, David B.; Zadourian, Rubina

doi:10.1103/physreve.96.062303

Cited by 35 publications

(7 citation statements)

References 39 publications

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“…[30] Parrondo's paradox was first conceptualized as an abstraction of flashing Brownian ratchets, [31][32][33] wherein diffusive particles exhibit unexpected drift when exposed to alternating periodic potentials. It has since been applied across a wide range of disciplines in the physical sciences and engineering-related fields, [34,35] such as diffusive and granular flow dynamics, [36,37] information thermodynamics, [38][39][40] chaos theory, [41][42][43][44][45][46][47] switching problems, [48][49][50] and quantum phenomena. [51][52][53][54][55][56][57] The paradox has also found numerous applications in life science, [58][59][60][61][62] ecology and evolutionary biology, [63][64][65] social dynamics, [66][67][68][69][70] and interdisciplinary work.…”

Section: Introductionmentioning

confidence: 99%

Relieving Cost of Epidemic by Parrondo's Paradox: A COVID‐19 Case Study

2020

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COVID‐19, also known as SARS‐CoV‐2, is a coronavirus that is highly pathogenic and virulent. It spreads very quickly through close contact, and so in response to growing numbers of cases, many countries have imposed lockdown measures to slow its spread around the globe. The purpose of a lockdown is to reduce reproduction, that is, the number of people each confirmed case infects. Lockdown measures have worked to varying extents but they come with a massive price. Nearly every individual, community, business, and economy has been affected. In this paper, switching strategies that take into account the total “cost” borne by a community in response to COVID‐19 are proposed. The proposed cost function takes into account the health and well‐being of the population, as well as the economic impact due to the lockdown. The model allows for a comparative study to investigate the effectiveness of various COVID‐19 suppression strategies. It reveals that both the strategy to implement a lockdown and the strategy to maintain an open community are individually losing in terms of the total “cost” per day. However, switching between these two strategies in a certain manner can paradoxically lead to a winning outcome—a phenomenon attributed to Parrondo's paradox.

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Section: Introductionmentioning

confidence: 99%

Relieving Cost of Epidemic by Parrondo's Paradox: A COVID‐19 Case Study

2020

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“…The agitation from Game A can lead to increased likelihood of landing in favourable branches when Game B is subsequently invoked, thus manifesting a ratcheting mechanism and enabling the characteristic paradoxical winning outcomes. There have been many examples of such counter-intuitive dynamics studied to date, for instance, in ecological populations [3][4][5][6][7][8][9][10], population genetics [11][12][13], physical quantum systems [14][15][16][17][18][19], reliability theory [20], system design optimization [21,22], and the Allison mixture in information thermodynamics [23].…”

Section: Introductionmentioning

confidence: 99%

Passive network evolution promotes group welfare in complex networks

Hang

Koh

et al. 2020

Chaos, Solitons & Fractals

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The Parrondo's paradox is a counter-intuitive phenomenon in which individually losing strategies, canonically termed Game A and Game B, are combined to produce winning outcomes. In this paper, a co-evolution of game dynamics and network structure is adopted to study adaptability and survivability in multi-agent dynamics. The model includes Action A, representing a rewiring process on the network, and a two-branch Game B, representing redistributive interactions between agents. Simulation results indicate that stochastically mixing Action A and Game B can produce enhanced, and even winning outcomes, despite Game B being individually losing. In other words, a Parrondo-type paradox can be achieved, but unlike canonical variants, the source of agitation is provided by passive network evolution instead of an active second game. The underlying paradoxical mechanism is analyzed, revealing that the rewiring process drives a topology shift from initial regular lattices towards scale-free characteristics, and enables exploitative behavior that grants enhanced access to the favourable branch of Game B.

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“…Molecular motors and enzyme transport had been analyzed through Brownian ratchet models [8][9][10] ; more recently, the broader class of Parrondo's paradox has been used to describe a large range of phenomena, including stability in mixed chaotic systems, [11,12] unexpected drifts in granular flow [13] and switched diffusion processes, [14] and entropic behaviour in information thermodynamics. [15,16] Quantum paradoxical systems have also been studied, some suggesting implications on quantum information processing, [17] and algorithms exploiting the paradox have been devised for engineering optimization. [18,19] In biophysics, evolutionary processes, [20][21][22][23][24][25] population biology, [26] ecological dynamics, [27][28][29] cellular machinery, [30][31][32] and social behavior [33][34][35] have all been linked to the paradox, and a degree of universality across scales is suspected.…”

Section: Introductionmentioning

confidence: 99%

Generalized Solutions of Parrondo's Games

Koh

Cheong

2020

Advanced Science

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In game theory, Parrondo's paradox describes the possibility of achieving winning outcomes by alternating between losing strategies. The framework had been conceptualized from a physical phenomenon termed flashing Brownian ratchets, but has since been useful in understanding a broad range of phenomena in the physical and life sciences, including the behavior of ecological systems and evolutionary trends. A minimal representation of the paradox is that of a pair of games played in random order; unfortunately, closed‐form solutions general in all parameters remain elusive. Here, we present explicit solutions for capital statistics and outcome conditions for a generalized game pair. The methodology is general and can be applied to the development of analytical methods across ratchet‐type models, and of Parrondo's paradox in general, which have wide‐ranging applications across physical and biological systems.

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Allison mixture and the two-envelope problem

Cited by 35 publications

References 39 publications

Relieving Cost of Epidemic by Parrondo's Paradox: A COVID‐19 Case Study

Relieving Cost of Epidemic by Parrondo's Paradox: A COVID‐19 Case Study

Passive network evolution promotes group welfare in complex networks

Generalized Solutions of Parrondo's Games

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