Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

By Carlos P. Roca, José A. Cuesta, Ángel Sánchez. Physics of Life Reviews, 2009

719 citations recorded by the source corpus.

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.

Subfields: Genetics, Management Science and Operations Research, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/3da0810c47d0bdfa9b2b7317f784ecff658050be

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Citations in the corpus

Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game (2012, background): “Since the pioneering work of Nowak and May [9] spatial games have received ample attention, and they have become inspirational for generations of researchers trying to reveal new ways by means of which cooperation can prevail over defection [10–12].”
Games on graphs (2014, methodology): “We focus primarily on exact results for graphs with symmetry, complementing earlier reviews [95], [82], [87] that take a wider view of the field.”
Statistical physics of human cooperation (2017, background): “Moreover, as is well known, the structure of a network can significantly affect evolutionary outcomes [14,15,36].”
Coupled disease–behavior dynamics on complex networks: A review (2015, background): “Game theory has been extended into evolutionary biology, which has generated great insight into the evolution of strategies [15] [16] [17] [18] [19] under both biological and cultural evolution.”
Evolutionary dynamics of group interactions on structured populations: a review (2013, background): “Although many seminal works concerning evolutionary games on networks have focused on pairwise interactions [23,24], games governed by group interactions are rapidly gaining in popularity.”
Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game (2010, background): “[4,6,23,58]), there always exists a critical cost-to-benefit ratio r~rc at which cooperators in the prisoner’s dilemma die out.”
Cyclic dominance in evolutionary games: a review (2014, background): “The question how the topology of the interaction network affects the outcome of cyclical interaction, and game theoretical models in general [25, 26, 28, 30], is one of great interest.”
Human strategy updating in evolutionary games (2010, background): “The idea is that in a spatial setting, clusters of cooperators can form, leading to a significant degree of cooperation [11, 12, 23, 24].”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “[519] Carlos P Roca, José A Cuesta, and Angel Sánchez.”
Evolution of Cooperation in Multiplex Networks (2012, background): “[17] Roca, C.”