A study of the dynamics of multi-player games on small networks using territorial interactions.

Article English OPEN
Broom, M. ; Lafaye, C. ; Pattni, K. ; Rychtar, J. (2015)

Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection.
  • References (43)
    43 references, page 1 of 5

    Allen B, Nowak MA (2014) Games on graphs. EMS Surveys in Mathematical Sciences 1(1):113{151

    Allen B, Tarnita CE (2014) Measures of success in a class of evolutionary models with xed population size and structure. Journal of Mathematical Biology 68(1-2):109{143

    Allen B, Sample C, Dementieva YA, Medeiros RC, Paoletti C, Nowak MA (2014) The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure. arXiv:14095459

    Antal T, Scheuring I (2006) Fixation of strategies for an evolutionary game in nite populations. Bulletin of Mathematical Biology 68(8):1923{1944

    Antal T, Redner S, Sood V (2006) Evolutionary dynamics on degreeheterogeneous graphs. Physical Review Letters 96(18):188,104

    Broom M, Rychtar J (2008) An analysis of the xation probability of a mutant on special classes of non-directed graphs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 464(2098):2609{2627

    Broom M, Rychtar J (2012) A general framework for analysing multiplayer games in networks using territorial interactions as a case study. Journal of Theoretical Biology 302:70{80

    Broom M, Rychtar J (2013) Game-theoretical models in biology. CRC Press, Boca Raton, FL

    Broom M, Cannings C, Vickers G (1997) Multi-player matrix games. Bulletin of Mathematical Biology 59(5):931{952

    Broom M, Hadjichrysanthou C, Rychtar J, Stadler B (2010) Two results on evolutionary processes on general non-directed graphs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science p rspa20100067

  • Related Research Results (1)
  • Metrics
    No metrics available
Share - Bookmark