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The Spread of Cooperative Strategies on Grids with Random Asynchronous Updating

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Algorithms and Models for the Web Graph (WAW 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10088))

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Abstract

The Prisoner’s Dilemma Process on a graph is an iterative process where each vertex, with a fixed strategy (cooperate or defect), plays the game with each of its neighbours. At the end of a round each vertex may change its strategy to that of its neighbour with the highest pay-off. Here we study the spread of cooperative and selfish behaviours on a toroidal grid, where each vertex is initially a cooperator with probability p. When vertices are permitted to change their strategies via a randomized asynchronous update scheme, we find that for some values of p the limiting ratio of cooperators may be modelled as a polynomial in p. Theoretical bounds for this ratio are confirmed via simulation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada

    Christopher Duffy & Jeannette Janssen

Authors
  1. Christopher Duffy
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  2. Jeannette Janssen
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Corresponding author

Correspondence to Christopher Duffy .

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Editors and Affiliations

  1. Ryerson University, Toronto, Canada

    Anthony Bonato

  2. University of California San Diego, La Jolla, California, USA

    Fan Chung Graham

  3. Ryerson University, Toronto, Canada

    Paweł Prałat

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© 2016 Springer International Publishing AG

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Duffy, C., Janssen, J. (2016). The Spread of Cooperative Strategies on Grids with Random Asynchronous Updating. In: Bonato, A., Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2016. Lecture Notes in Computer Science(), vol 10088. Springer, Cham. https://doi.org/10.1007/978-3-319-49787-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-49787-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49786-0

  • Online ISBN: 978-3-319-49787-7

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