Asynchronous spatial evolutionary games

Over the past 50 years, much attention has been given to the Prisoner's Dilemma as a metaphor for problems surrounding the evolution and maintenance of cooperative and altruistic behavior. The bulk of this work has dealt with the successfulness and robustness of various strategies. Nowak and May (1992) considered an alternative approach to studying evolutionary games. They assumed that players were distributed across a two-dimensional (2D) lattice, interactions between players occurred locally, rather than at long range as in the well mixed situation. The resulting spatial evolutionary games display dynamics not seen in their well-mixed counterparts. An assumption underlying much of the work on spatial evolutionary games is that the state of all players is updated in unison or in synchrony. Using the framework outlined in Nowak and May (1992), we examine the effect of various asynchronous updating schemes on the dynamics of spatial evolutionary games. There are potential implications for the dynamics of a wide variety of spatially extended systems in biology, physics and chemistry.

[1]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[2]  Robert M. May,et al.  Dispersal in stable habitats , 1977, Nature.

[3]  Tim D. Fletcher,et al.  Long-term flowering synchrony of box-ironbark eucalypts , 2004 .

[4]  J. French,et al.  Synchronization of ovarian cycles within and between social groups in golden lion tamarins (Leontopithecus rosalia) , 1987, American journal of primatology.

[5]  G. Oster,et al.  Competition, kin selection, and evolutionary stable strategies. , 1978, Theoretical population biology.

[6]  M. McClintock,et al.  Menstrual Synchrony and Suppression , 1971, Nature.

[7]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[8]  Yasusi Kanada,et al.  The Effects of Randomness in Asynchronous 1D Cellular Automata , 1984 .

[9]  David G. Green,et al.  Ordered asynchronous processes in multi-agent systems , 2005 .

[10]  Marcus Frean,et al.  Rock–scissors–paper and the survival of the weakest , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[11]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[12]  Paulien Hogeweg,et al.  Spiral wave structure in pre-biotic evolution: hypercycles stable against parasites , 1991 .

[13]  I. Noble,et al.  The Use of Vital Attributes to Predict Successional Changes in Plant Communities Subject to Recurrent Disturbances , 1980 .

[14]  G. E. Hutchinson,et al.  Homage to Santa Rosalia or Why Are There So Many Kinds of Animals? , 1959, The American Naturalist.

[15]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[16]  Walter J. Freeman,et al.  TUTORIAL ON NEUROBIOLOGY: FROM SINGLE NEURONS TO BRAIN CHAOS , 1992 .

[17]  J. Wallis,et al.  Synchrony of estrous swelling in captive group-living chimpanzees (Pan troglodytes) , 1985, International Journal of Primatology.

[18]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[19]  B A Huberman,et al.  Evolutionary games and computer simulations. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.

[21]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[22]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[23]  C. Johnson,et al.  Selection for restraint in competitive ability in spatial competition systems , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[24]  David G. Green,et al.  Consensus and cohesion in simulated social networks , 2001, J. Artif. Soc. Soc. Simul..

[25]  Jack G. Robinson,et al.  Sex Ratio: Adaptive Response to Population Fluctuations in Pandalid Shrimp , 1978, Science.

[26]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[27]  William J Ray,et al.  Social dominance determines estrous entrainment among female hamsters , 1980, Hormones and Behavior.

[28]  Marcus Frean.  The prisoner’s dilemma without synchrony , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[29]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[30]  M. Nowak,et al.  The Alternating Prisoner's Dilemma , 1994 .