Score-dependent Fertility Model for the Evolution of Cooperation in a Lattice

Nakamaru, Mayuko; Nogami, Hajime; Iwasa, Yoh

doi:10.1006/jtbi.1998.0750

Cited by 92 publications

(84 citation statements)

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“…Our result holds for games on cycles (Nakamaru et al, 1997(Nakamaru et al, , 1998Nakamaru & Iwasa, 2005). Furthermore, our result also applies to a wide range of imitation processes of interest to economists (Ellison, 1993;Binmore & Samuelson, 1997;Maruta, 2002), when the detailed balance condition holds.…”

Section: Introductionmentioning

confidence: 55%

“…In fact, our results can also be applied to the study of evolutionary game dynamics on graphs, of which there is a great deal of current interest (Nakamaru et al, 1997(Nakamaru et al, , 1998Nakamaru & Iwasa, 2005;Lieberman et al, 2005;Ohtsuki et al, 2006). In the case of a cycle graph with N nodes, the game dynamics starting from a single mutant can be described by the Moran process.…”

Section: Discussionmentioning

confidence: 82%

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A symmetry of fixation times in evoultionary dynamics

Taylor

Iwasa

Nowak

2006

Journal of Theoretical Biology

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In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies.

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Section: Introductionmentioning

confidence: 55%

Section: Discussionmentioning

confidence: 82%

A symmetry of fixation times in evoultionary dynamics

Taylor

Iwasa

Nowak

2006

Journal of Theoretical Biology

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“…For detailed reviews of the replicator equation and other approaches to evolutionary game dynamics, see Fudenberg and Tirole (1991), Weibull (1995), Samuelson (1997), Cressman (2003), Sigmund (1998, 2003), Gintis (2000) and Nowak and Sigmund (2004). in finite populations Imhof and Nowak, 2006;Taylor et al, 2004;Fudenberg et al, 2006;Traulsen et al, 2006a,b), in spatially extended systems (Nowak and May, 1992;Nakamaru et al, 1998;Killingback and Doebeli, 1996;van Baalen and Rand, 1998;Irwin and Taylor, 2001;Hauert and Doebeli, 2004;Ifti et al, 2004;Nakamaru and Iwasa, 2005;Jansen and van Baalen, 2006) or on graphs (Lieberman et al, 2005;Santos et al, , 2006a. Taylor and Nowak (2006) analyze a scenario where the interaction rate does depend on the strategies.…”

Section: Introductionmentioning

confidence: 99%

Active linking in evolutionary games

Pacheco

Traulsen

Nowak

2006

Journal of Theoretical Biology

234

170

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In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at which they seek new interactions. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In a limiting case, the linking dynamics introduces a simple transformation of the payoff matrix. We outline conditions for evolutionary stability. As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favor cooperation over defection.

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“…Part of the initial motivation was to find a way out of the limitations of both techniques on a well-studied combinatorial optimization problem the Min Euclidean Traveling Salesman problem (Min ETSP). According to the authors, the original inspiration came from computer game tournaments [96] used to study "the evolution of cooperation" [6] (see also [171] and [164] for more recent theoretical results in this field). That approach had several features which anticipated many current algorithms in practice today.…”

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confidence: 99%

“…A few months later, Moscato and Norman discovered that they shared similar views with other researchers [157] [74] and other authors proposing "island models" for GAs. Spacialization is now being recognized as the "catalyzer" responsible of a variety of phenomena [164] [163]. This is an important research issue, currently only understood in a rather heuristic way.…”

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confidence: 99%