Evolutionary Game Theory: Temporal and Spatial Effects Beyond Replicator Dynamics Articles uri icon

publication date

  • December 2009

start page

  • 208

end page

  • 249

issue

  • 4

volume

  • 6

international standard serial number (ISSN)

  • 1571-0645

electronic international standard serial number (EISSN)

  • 1873-1457

abstract

  • 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.