View in EDS

An asymptotic analysis of the evolutionary spatial prisoner’s dilemma on a path

Saved in:
Bibliographic Details
Title: An asymptotic analysis of the evolutionary spatial prisoner’s dilemma on a path
Authors: Burger, A.P. apburger@sun.ac.za, van der Merwe, M. 13705091@sun.ac.za, van Vuuren, J.H. vuuren@sun.ac.za
Source: Discrete Applied Mathematics. Oct2012, Vol. 160 Issue 15, p2075-2088. 14p.
Subjects: Dilemma, Mathematical models, Graph theory, Paths & cycles in graph theory, Game theory, Probability theory
Abstract: Abstract: In this paper, we consider the Evolutionary Spatial Prisoner’s Dilemma (ESPD) in which players are modelled by the vertices of an underlying graph representing some spatial organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in play a classical prisoner’s dilemma against each other, and they update their strategies from one round to the next based on the perceived success achieved by the strategies of neighbouring players during the previous round. In this way, players are able to adapt and learn from each other’s strategies as the game progresses without being able to rationalise good strategies. We characterise all steady states of the ESPD for the case where is a path, and we also characterise the structures of those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game’s states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation. More specifically, we show that there exists a range of game parameters for which the likelihood of the emergence of persistent cooperation increases to almost certainty as the length of the path increases. [Copyright &y& Elsevier]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 78278403
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: An asymptotic analysis of the evolutionary spatial prisoner’s dilemma on a path
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Burger%2C+A%2EP%2E%22">Burger, A.P.</searchLink><i> apburger@sun.ac.za</i><br /><searchLink fieldCode="AR" term="%22van+der+Merwe%2C+M%2E%22">van der Merwe, M.</searchLink><i> 13705091@sun.ac.za</i><br /><searchLink fieldCode="AR" term="%22van+Vuuren%2C+J%2EH%2E%22">van Vuuren, J.H.</searchLink><i> vuuren@sun.ac.za</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Oct2012, Vol. 160 Issue 15, p2075-2088. 14p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Dilemma%22">Dilemma</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Paths+%26+cycles+in+graph+theory%22">Paths & cycles in graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Game+theory%22">Game theory</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Abstract: In this paper, we consider the Evolutionary Spatial Prisoner’s Dilemma (ESPD) in which players are modelled by the vertices of an underlying graph representing some spatial organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in play a classical prisoner’s dilemma against each other, and they update their strategies from one round to the next based on the perceived success achieved by the strategies of neighbouring players during the previous round. In this way, players are able to adapt and learn from each other’s strategies as the game progresses without being able to rationalise good strategies. We characterise all steady states of the ESPD for the case where is a path, and we also characterise the structures of those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game’s states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation. More specifically, we show that there exists a range of game parameters for which the likelihood of the emergence of persistent cooperation increases to almost certainty as the length of the path increases. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=78278403
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.dam.2012.04.022
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
        StartPage: 2075
    Subjects:
      – SubjectFull: Dilemma
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Paths & cycles in graph theory
        Type: general
      – SubjectFull: Game theory
        Type: general
      – SubjectFull: Probability theory
        Type: general
    Titles:
      – TitleFull: An asymptotic analysis of the evolutionary spatial prisoner’s dilemma on a path
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Burger, A.P.
      – PersonEntity:
          Name:
            NameFull: van der Merwe, M.
      – PersonEntity:
          Name:
            NameFull: van Vuuren, J.H.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 10
              Text: Oct2012
              Type: published
              Y: 2012
          Identifiers:
            – Type: issn-print
              Value: 0166218X
          Numbering:
            – Type: volume
              Value: 160
            – Type: issue
              Value: 15
          Titles:
            – TitleFull: Discrete Applied Mathematics
              Type: main
ResultId 1