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Accumulation of individual fitness or wealth as a population game

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  • Sylvain Gibaud
  • Jorgen W. Weibull

Abstract

The accumulation of individual fitness or wealth is modelled as a population game in which pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a constant background resource, and their fitness or wealth depreciates over time. For brevity we focus on the well-known Hawk-Dove game. In the base-line model, the probability of winning a fight (that is, when both play Hawk) is the same for both parties. In an extended version, the individual with higher current fitness or wealth has a higher probability of winning. Analytical results are given for the fitness/wealth distribution at any given time, for the evolution of average fitness/wealth over time, and for the asymptotics with respect to time and population size. Long-run average fitness/wealth is non-monotonic in the value of the resource, thus providing a potential explanation of the curse of the riches.

Suggested Citation

  • Sylvain Gibaud & Jorgen W. Weibull, 2017. "Accumulation of individual fitness or wealth as a population game," Papers 1707.00996, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:1707.00996
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    1. Nuno Torres & Óscar Afonso & Isabel Soares, 2013. "A survey of literature on the resource curse: critical analysis of the main explanations, empirical tests and resource proxies," CEF.UP Working Papers 1302, Universidade do Porto, Faculdade de Economia do Porto.
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