Publications on Parrondo's Paradox

The links to the following files are password protected. Please email me if you have difficulty obtaining reprints. They are arranged in chronological order. We have tried (at least) to exhaustively list all the early publications on Parrondo's Paradox—with later publications we become more selective due to their large number. Some papers we don't necessarily agree with—however they are included in the spirit of open debate.

J. M. R. Parrondo, "How to cheat a bad mathematician," in EEC HC&M Network on Complexity and Chaos (#ERBCHRX-CT940546) , ISI, Torino, Italy (1996), Unpublished. [This is actually the seminal work].

G.P. Harmer and D. Abbott, "Parrondo's paradox," Statistical Science, Vol. 14, No. 2, pp. 206-213, 1999. [This is the seminal journal article.]

G.P. Harmer and D. Abbott, "Losing strategies can win by Parrondo's paradox," Nature (London), Vol. 402, No. 6764, p. 864, Dec. 1999.

P.C.W. Davies, "Physics and life," The First Steps of Life in the Universe: Proceedings of the Sixth Trieste Conference on Chemical Evolution, (Ed: J. Chela-Flores, T.C. Owen and F. Raulin), Trieste, Italy, 18-22 September 2000.

G.P. Harmer, D. Abbott and P.G. Taylor, "The paradox of Parrondo's games," Proc. Royal Society London A, Vol. 456, pp. 247-259, 2000.

H. Moraal, "Counterintuitive behaviour in games based on spin models," Journal of Physics A: Math, Vol. 33, pp. L203-L206, 2000.

J.M.R. Parrondo, G.P. Harmer and D. Abbott, "New paradoxical games based on Brownian ratchets," Physical Review Letters, Vol. 85, No. 24, pp. 5226-5229, Dec. 2000.

D. Abbott, "Overview: unsolved problems of noise and fluctuations," Chaos, Vol. 11, No. 3, pp. 526-538, 2001.

R.D. Astumian, "Making molecules into motors," Scientific American, pp. 56-64, Jul. 2001.

A. Allison and D. Abbott, "Control systems with stochastic feedback," Chaos, Vol. 11, No. 3, pp. 715-724, 2001.

A. Allison and D. Abbott, "Stochastic resonance in a Brownian ratchet," Fluctuation and Noise Letters (Elsevier), Vol. 1, No. 4, pp. L239-244, Dec. 2001.

M. Boman, S.J. Johansson and D. Lyback, "Parrondo strategies for artificial traders," Intelligent Agent Technology (Eds: N. Zhong, J. Liu, S. Ohsuga and J. Bradshaw), pp. 150-159, 2001.

G.P. Harmer, D. Abbott, P.G. Taylor and J.M.R. Parrondo, "Brownian ratchets and Parrondo's games," Chaos, Vol. 11, No. 3, pp. 705-714, 2001.

R. Toral, "Cooperative Parrondo's games," Fluctuation and Noise Letters, Vol. 1, No. 1, pp. L7-L12, 2001.

D. Abbott, P.C.W. Davies and C.R. Shalizi, "Order from disorder: the role of noise in creative processes. A special issue on game theory and evolutionary processes—overview," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. C1-C12, 2002.

R. Ait-Haddou and W. Herzog, "Force and motion generation of myosin motors: muscle contraction," Journal of Electromyography and Kinesiology, Vol. 12, pp. 435-445, 2002.

A. Allison and D. Abbott, "The physical basis for Parrondo's games," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L327-L341, 2002.

J. Buceta, K. Lindenberg and J.M.R. Parrondo, "Pattern formation induced by nonequilibrium global alternation of dynamics," Physical Review E, Vol. 66, pp. 036216(1)-036216(11), 2002.

J. Buceta and K. Lindenberg, "Switching-induced Turing instability," Physical Review E, Vol. 66, 046202, 2002.

J. Buceta, K. Lindenberg and J.M.R. Parrondo, "Stationary and oscillatory spatial patterns induced by global periodic switching," Physical Review Letters, Vol. 88, No. 2, 024103, 2002.

J. Buceta, K. Lindenberg and J.M.R. Parrondo, "Spatial patterns induced by random switching," Fluctuation and Noise Letters, Vol. 2, No. 1, pp. L21-L29, 2002.

M. Bucolo, R. Caponetto, L. Fortuna, M. Frasca and A. Rizzo, "Does chaos work better than noise," Circuits and Systems Magazine, IEEE, Vol. 2, No. 3, pp. 4-19, 2002.

B. Cleuren and C. Van den Broeck, "Random walks with absolute negative mobility," Physical Review E, Vol. 65, 030101, 2002.

L. Dinis and J.M.R. Parrondo, "Parrondo's paradox and the risks of short-range optimization," 2002. http://arxiv.org/pdf/cond-mat/0212358

A.P. Flitney, J. Ng and D. Abbott, "Quantum Parrondo's games," Physica A, Vol. 314, pp. 35-42, 2002.

A.P. Flitney and D. Abbott, "An introduction to quantum game theory," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. R175-R188, 2002.

G.P. Harmer and D. Abbott, "A review of Parrondo's paradox," Fluctuation and Noise Letters, Vol. 2, No. 2, pp. R71-R107, 2002.

D. Heath, D. Kinderlehrer and M. Kowalczyk, "Discrete and continuous ratchets: from coin toss to molecular motor," Discrete and Continuous Dynamical Systems-Series B, Vol. 2, No. 2, pp. 153-167, 2002.

E.S. Key, M.M. Klosek and D. Abbott, "On Parrondo's paradox: how to construct unfair games by composing fair games,"
2002. http://arxiv.org/pdf/math/0206151

L. Kocarev and Z. Tasev, "Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox," Physical Review E , Vol. 65, pp. 046215(1)-046215(4), 2002.

C.F. Lee and N.F. Johnson, "Exploiting randomness in quantum information processing," Physics Letter A, Vol. 301, pp. 343-349, 2002.

C.F. Lee, N.F. Johnson, F. Rodriguez and L. Quiroga, "Quantum coherence, correlated noise and Parrondo games," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L293-L298, 2002.

D. A. Meyer and H. Blumer, "Quantum Parrondo games: biased and unbiased," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L257-L262, 2002.

D. A. Meyer and H. Blumer, "Parrondo games as lattice gas automata," Journal of Statistical Physics, Vol. 107, No. 1,2, pp. 225-239, 2002.

O.E. Percus and J.K. Percus, "Can two wrongs make a right? Coin-tossing games and Parrondo's paradox," Mathematical Intelligencer, Vol. 24, No. 3, pp. 68-72, 2002.

R. Pyke, "On random walks and diffusions related to Parrondo's games," 2002. http://arxiv.org/pdf/math.PR/0206150

L. Rasmusson and M. Boman, "Analytical expressions for Parrondo games," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L343-L348, 2002.

P. Reimann, "Brownian motors: noisy transport far from equilibrium," Physics Reports, Vol. 361, pp. 57-265, 2002.

P. Reimann and P. Hanggi, "Introduction to the physics of Brownian motors," Applied Physics A, Vol. 75, pp. 169-178, 2002.

R. Toral, "Capital redistribution brings wealth by Parrondo's paradox," Fluctuation and Noise Letters, Vol. 2, No. 4, pp. L305-L311, 2002.

A. Allison and D. Abbott, "A MEMS Brownian ratchet," Microelectronics Journal (Elsevier), Vol. 33, No. 3, pp. 235-243, Mar. 2002.

S. Rahmann, "Optimal adaptive strategies for games of the Parrondo type," 2002 (Unpublished).

P. Arena, S. Fazzino, L. Fortuna and P. Maniscalco, "Game theory and non-linear dynamics: the Parrondo's paradox case study," Chaos, Solitons and Fractals, Vol. 17, pp. 545-555, 2003.

C.H. Chang and T.Y. Tsong, "Truncation and reset process on the dynamics of Parrondo's games," Physical Review E, Vol. 67, No. 2, 025101, 2003.

L. Dinis and J.M.R. Parrondo, "Optimal strategies in collective Parrondo games," Europhysics Letters, Vol 63, No. 3, pp. 319-325, 2003.

R.J. Kay and N.F. Johnson, "Winning combinations of history-dependent games," Physical Review E, Vol. 67, No. 5, 056128, 2003.

G. Latouche and P.G. Taylor, "Drift conditions for matrix-analytic models," Mathematics of Operations Research, Vol. 28, No. 2, pp. 346-360, 2003.

Y. Lee, A. Allison, D. Abbott and H.E. Stanley, "Minimal Brownian ratchet: an exactly solvable model," Physical Review Letters, Vol. 91, No. 22, pp. 220601, 2003.

Z. Mihailovic and M. Rajkovic, "One dimensional asynchronous cooperative Parrondo's games," Fluctuation and Noise Letters, Vol. 3, No. 4, pp. L389-L398, 2003.

J.M.R. Parrondo and B.J. de Cisneros, "Paradoxical games and Brownian thermal engines," 2003. http://arxiv.org/pdf/cond-mat/0309053

Z. Mihailovic and M. Rajkovic, "Synchronous cooperative Parrondo's games," Fluctuation and Noise Letters, Vol. 3, No. 4, pp. L399-L406, 2003.

R. Toral, P. Amengual and S. Mangioni, "Parrondo's games as a discrete ratchet," Physica A, Vol. 327, pp. 105-110, 2003.

R. Toral, P. Amengual and S. Mangioni, "A Fokker-Planck description for Parrondo's games," Proceedings of SPIE, Vol. 309, No. 5114, 2003.

A.W. Ghosh and S.V. Khare, "Breaking of general rotational symmetries by multidimensional classical ratchets," Physical Review E, Vol. 67, 056110, 2003.

G.C. Berresford and A.M. Rocket, "Parrondo's Paradox," International Journal of Mathematics and Mathematical Sciences, Vol. 62, pp. 3957-3962, 2003.

E. Behrends, "Parrondos Paradoxon Ein stochastisches Perpetuum Mobile?" Mitteilungen der Deutschen Mathematiker-Verinigung, Vol. 1, pp. 5-10, 2003.

N.F. Johnson, P. Jefferies and P.M. Hui, Financial Market Complexity: What Physics Can Tell Us About Market Behaviour," Oxford University Press, 2003.

A.P. Flitney and D. Abbott, "Quantum models of Parrondo's games," Physica A, Vol. 324, pp. 152-156, 2003.

P. Amengual, A. Allison, R. Toral and D. Abbott, "Discrete-time ratchets, the Fokker-Planck equation and Parrondo's paradox," Proc. Roy. Soc. London A., Vol. 460, pp. 2269-2284, 2004.

P. Amengual, and R. Toral, "Parrondo games and the zipping algorithm," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 203-212.

P. Amengual, and R. Toral, "Exact ratchet description of Parrondo's games with self-transitions," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 407-415.

E. Behrends, "The mathematical background of Parrondo's paradox," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 510-519.

F.J. Cao, L. Dinis and J.M.R. Parrondo, "Feedback control in a collective flashing ratchet," Physical Review Letters , Vol 93, No. 4, 040603, 2004.

R. Iyengar and R. Kohli, "Why Parrondo’s paradox is irrelevant for utility theory, stock buying, and the emergence of life," Complexity, Vol. 9, No. 1, pp. 23-27, 2004. [Note: there are a number of very amusing basic errors in this paper. For example the authors have misunderstood what a statistical "birth-death process" is and have literally taken it to mean birth and death of humans!]

B. Cleuren and C. Van den Broeck, "Primary Parrondo paradox," Europhysics Letters., Vol. 67, No. 2, pp.151-157, 2004.

J.M.R. Parrondo and L. Dinis, "Brownian motion and gambling: from ratchets to paradoxical games," Contemporary Physics, Vol 45, pp. 147-157, 2004.

T.W. Tang, A. Allison and D. Abbott, "Parrondo's games with chaotic switching," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 520-530.

C. Van den Broeck and B. Cleuren, "Parrondo games with strategy," Proc. SPIE Noise in Complex Systems and Stochastic Dynamics II, Vol. 5471, Maspalomas, Gran Canaria, Spain, 26-28 May 2004, pp. 109-118.

B. Cleuren and C. Van den Broeck, "Optimizing strategies in the primary Parrondo paradox," Physical Review E, Vol. 70, 06710, 2004.

T. Platkowski, "Evolution of populations playing mixed multiplayer games," Mathematical and Computer Modelling, Vol. 39, pp. 981-989, 2004.

N. Masuda and N. Konno, "Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics," The European Physical Journal B, Vol. 40, pp. 313-319, 2004.

T.K. Philips, and A.B. Feldman, "Parrondo's Paradox is not paradoxical," 2004, http://ssrn.com/abstract=581521

L. Dinis and J.M.R. Parrondo, "Inefficiency of voting in Parrondo's games," Physica A, Vol. 343, pp. 701-711, 2004.

H. Martin and H.C. von Baeyer, "Simple games to illustrate Parrondo's paradox," American Journal of Physics, Vol. 72, No. 5, pp. 710-714, 2004.

T.W. Tang, A. Allison and D. Abbott, "Investigation of chaotic switching strategies in parrondo's games," Fluctuation and Noise Letters, Vol. 4, No. 4., pp. L585-L596, 2004.

A.P. Flitney, D. Abbott and N.F. Johnson, "Quantum walks with history dependence," J. Phys. A: Math. Gen. (IOP), Vol. 37, pp. 7581–7591, 2004.

P.C.W. Davies, "Does quantum mechanics play a non-trivial role in life?" BioSystems (Elsevier), Vol. 78, pp. 69-79, 2004.

P. Gawron and J.A. Miszczak, "Quantum implementation of Parrondo's paradox," 2005. http://arxiv.org/pdf/quant-ph/0502185

R. Spurgin and M. Tamarkin, "Switching investments can be a bad idea when Parrondo's paradox applies," Journal of Behavioural Finance, Vol. 6, No. 1, pp. 15-18, 2005.

J. Almeida, D. Peralta-Salas and M. Romera, "Can two choatic systems give rise to order?" Physica D, Vol. 200, pp. 124-132, 2005.

P. Amegual and R. Toral, "Transfer of information in Parrondo's games," Fluctuation and Noise Letters, Vol. 5, No. 1, pp. L63-L71, 2005.

T.Y. Tsong and C.-H. Chang, "Enzyme as catalytic wheel powered by a Markovian engine: conformational coupling andbarrier surfing models," Physica A, Vol. 350, pp. 108-121, 2005.

D.M. Wolf, V.V. Vazirani and A.P. Arkin, "Diversity in times of adversity: probabilistic strategies in microbial survival games," Journal of Theoretical Biology, Vol. 234, pp. 227-253, 2005.

A. Allison, C.E.M. Pearce and D. Abbott, "State-space visualization and fractal properties of Parrondo's games," Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control, (Eds: A.S. Nowack and K Szajowski), Birkhauser, Boston, Vol. 7, pp. 613-633, 2005, ISBN 0-8176-4362-1.

G.P. Harmer and D.Abbott, "Parrondo's capital and history-dependent games," Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control, (Eds: A.S. Nowack and K Szajowski), Birkhauser, Boston, Vol. 7, pp. 635-648, 2005, ISBN 0-8176-4362-1.

J. Ng and D. Abbott, "Introduction to quantum games and a quantum Parrondo game," Advances in Dynamic Games: Applications to Economics, Finance, Optimization and Stochastic Control, (Eds: A.S. Nowack and K Szajowski), Birkhauser, Boston, Vol. 7, pp. 649-665, 2005, ISBN 0-8176-4362-1.

A. Boyarsky, P. Gora, Md. S. Islam, "Randomly chosen chaotic maps can give rise to nearly ordered behavior," Physica D, Vol. 210, pp. 284-294, 2005.

A.P. Flitney and D. Abbott, "Quantum games with decoherence," J. Phys. A: Math. Gen. (IOP), Vol. 38, pp. 449–459, 2005.

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