Package org.evoludo.simulator.modules

Class CDLPQ

Object
Module
Discrete
CDL
CDLP
CDLPQ
All Implemented Interfaces:
Runnable, IBS.HasIBS, IBS.HasIBS.DGroups, IBS.HasIBS.DPairs, MilestoneListener, Model.HasDE, Model.HasDE.DGroups, Model.HasDE.EM, Model.HasDE.ODE, Model.HasDE.PDE, Model.HasDE.PDEADV, Model.HasDE.PDERD, Model.HasDE.RK5, Model.HasDE.SDE, Features, Features.Groups, Features.Pairs, Features.Payoffs, HasHistogram, HasHistogram.Degree, HasHistogram.Fitness, HasHistogram.StatisticsStationary, HasMean, HasMean.Fitness, HasMean.Traits, HasPop2D, HasPop2D.Fitness, HasPop2D.Traits, HasPop3D, HasPop3D.Fitness, HasPop3D.Traits, HasS3, CLOProvider
Direct Known Subclasses:
simCDLPQ
public class CDLPQ extends CDLP
Cooperation in voluntary (non-linear) public goods interactions with peer and pool punishment.
Author:
Christoph Hauert

  • Field Details

    • SANCTIONING

      public static final int SANCTIONING
      The trait (and index) value of pool punishers.
      See Also:

    • costPoolPunish

      double costPoolPunish
      The cost of pool punishment.
      See Also:

    • finePoolPunish

      double finePoolPunish
      The pool punishment fine for non-contributors.
      See Also:

    • cloPoolPunish

      public final CLOption cloPoolPunish
      Command line option to set the fine of pool punishment for non-contributors.

    • cloCostPoolPunish

      public final CLOption cloCostPoolPunish
      Command line option to set the cost of pool punishment.

  • Constructor Details

    • CDLPQ

      public CDLPQ(EvoLudo engine)
      Create a new instance of the module for voluntary public goods games with peer and pool punishment.
      Parameters:
      engine - the manager of modules and pacemaker for running the model

  • Method Details

    • load

      public void load()
      Description copied from class: Module
      Load new module and perform basic initializations.
      Overrides:
      load in class CDLP
      See Also:

    • getAuthors

      public String getAuthors()
      Description copied from class: Module
      Returns a string with information about the authors of the module.
      Overrides:
      getAuthors in class CDLP
      Returns:
      the names of the authors

    • getTitle

      public String getTitle()
      Description copied from interface: Features
      Returns title of active module, e.g. 2x2 games in TBT returns "2x2 Games".
      Specified by:
      getTitle in interface Features
      Overrides:
      getTitle in class CDLP
      Returns:
      the title of active module

    • getMinPayoff

      public double getMinPayoff()
      Description copied from interface: Features.Payoffs
      Calculates and returns the minimum payoff/score of an individual. This value is important for converting payoffs/scores into probabilities, for scaling graphical output and some optimizations.
      Specified by:
      getMinPayoff in interface Features.Payoffs
      Overrides:
      getMinPayoff in class CDLP
      Returns:
      the minimum payoff/score
      See Also:

    • getMonoPayoff

      public double getMonoPayoff(int type)
      Calculate and return the payoff/score of individuals in monomorphic populations with trait type.

      Note: Optional implementation. Returns Double#NaN if not defined or not implemented.

      Note, monomorphic populations of peer punishers have the same payoff as monomorphic populations of cooperators. Note, monomorphic populations of pool punishers have the same payoff as monomorphic populations of cooperators.

      Overrides:
      getMonoPayoff in class CDLP
      Parameters:
      type - the index of the trait
      Returns:
      payoff/score in monomorphic population with trait type

    • pairScores

      public double pairScores(int me, int[] traitCount, double[] traitScore)
      Description copied from class: CDLP
      Calculate and return total (accumulated) payoff/score for pairwise interactions of the focal individual with trait me against opponents with different traits. The respective numbers of each of the nTraits opponent traits are provided in the array tCount. The payoffs/scores for each of the nTraits opponent traits must be stored and returned in the array tScore.

      Important: must be overridden and implemented in subclasses that define game interactions between pairs of individuals (nGroup=2, pairwise=true), otherwise see IBS.HasIBS.DGroups.groupScores(int[], double[]).

      Note: Leniency with cooperators (and punishing cooperators that failed to punish defectors) does not matter in pairwise interactions because this requires at least groups of three or more players. For example a cooperator, a defector and a punisher interact. In such a group composition the cooperator reveals the fact that it does not punish the defector (second-order free riding) and in turn may get punished by the punisher.

      Specified by:
      pairScores in interface IBS.HasIBS.DPairs
      Overrides:
      pairScores in class CDLP
      Parameters:
      me - the trait index of the focal individual
      traitCount - number of opponents with each trait
      traitScore - array for returning the scores of each opponent trait
      Returns:
      score of focal individual me accumulated over all interactions

    • groupScores

      public void groupScores(int[] traitCount, double[] traitScore)
      Description copied from interface: IBS.HasIBS.DGroups
      Calculate the payoff/score for interactions in groups consisting of traits with respective numbers given in the array traitCount. The interaction group size is given by the sum over traitCount[i] for i=0,1,...,nTraits. The payoffs/scores for each of the nTraits traits must be stored and returned in the array traitScore.

      Important: must be overridden and implemented in subclasses that define game interactions among groups of individuals (for groups with sizes nGroup>2, otherwise see IBS.HasIBS.DPairs.pairScores(int, int[], double[])).

      Specified by:
      groupScores in interface IBS.HasIBS.DGroups
      Overrides:
      groupScores in class CDLP
      Parameters:
      traitCount - group composition given by the number of individuals with each trait
      traitScore - array for returning the payoffs/scores of each trait

    • mixedScores

      public void mixedScores(int[] count, int n, double[] traitScores)
      Description copied from class: CDLP
      Calculate the average payoff/score in a finite population with the number of each trait provided in count for interaction groups of size n. The payoffs/scores for each of the nTraits traits must be stored and returned in the array traitScores.

      Notes:

      For payoff calculations:
      • each trait sees one less of its own type in its environment
      • the size of the environment is nPopulation-1
      • the fact that the payoff of each trait does not depend on its own type simplifies things
      If explicit calculations of the well-mixed scores are not available, interactions with everyone in well-mixed populations should be checked for and excluded with a warning in IBS.check() (see IBSMCPopulation for an example).

      Important:

      Must be overridden and implemented in subclasses that define game interactions in well-mixed populations where individuals interact with everyone else. Computationally it is not feasible to cover this scenario with IBS.HasIBS.DPairs.pairScores(int, int[], double[]) or IBS.HasIBS.DGroups.groupScores(int[], double[]), respectively.
      standard non-linear PGG:
      \[ \begin{align} f_L =& c \sigma \\ f_D =& \frac{X}{M-1}\frac{N}{M-N} (B + S) + H_2(X+Y-1, 0, M-X-Y, N-1) \sigma c \\ f_C =& \frac{(r_1-1)N}{M-N} \left(1-H_2(X+Y-1, 0, M-X-Y, N-1)\right) c +\\ & \frac{N}{M-N}\left(\frac{X-2}{M-1} S - \frac{Y}{M-1} B\right) + H_2(X+Y-1, 0, M-X-Y, N-1) \sigma c \end{align} \] with \[ \begin{align} B =& \frac{M-1}{X+Y} \frac{M-N}{M}\left(r_1 - \frac{2 S}{N-1}\right) \times \left(\frac{N}{M-N} - \frac{\big(1-H_2(X+Y-1, 0, M-X-Y, N)\big)M}{N(X+Y-1)}\right) c \\ S =& \frac{(r_\text{all}-r_1)(X-1)}{(X+Y-2)} c \end{align} \] using \[ H_2(X, x, Y, y) = \frac{\binom{X}{x}\binom{Y}{y}}{\binom{X+Y}{x+y}} \]
      other's only non-linear PGG:
      \[ \begin{align} f_L =& c \sigma \\ f_D =& \frac{X}{M-1} \frac{N}{M-N} (B + S) + H_2(X+Y-1, 0, M-X-Y, N-1) \sigma c \\ f_C =& \frac{X-2}{M-1} \frac{N}{M-N} (B + S) +\frac{r_1 (N-1)}{(M-N)(X+Y)}c- \frac{N}{M-N}\left(\frac{r_1 (M-X-Y-N+1)}{N(X+Y)(X+Y-1)}+1\right)\times \\ & \left(1-H_2(X+Y-1, 0, M-X-Y, N-1)\right)c+ H_2(X+Y-1, 0, M-X-Y, N-1) \sigma c \end{align} \] with \[ \begin{align} B =& \frac{M-1}{X+Y} \frac{M-N}{M} \left(r_1 - \frac{2 S}{N-1}\right) \times \left(\frac{N}{M-N} - \frac{\big(1-H_2(X+Y-1, 0, M-X-Y, N)\big)M}{N(X+Y-1)}\right)c \\ S =& \frac{(r_\text{all}-r_1)(X-1)}{X+Y-2}\frac{N-1}{N-2}c. \end{align} \]

      Proper sampling in finite populations - formulas for standard public goods interactions with private punishment: \[ \begin{align} f_C =& \sigma-\frac w{M-1}(N-1)\delta\beta\\ f_D =& B-\frac w{M-1}(N-1)\beta\\ f_C =& B-F(z)c-w(N-1)G(y)\alpha\beta\\ f_P =& B-F(z)c-\frac y{M-1}(N-1)\gamma-x(N-1)G(y)\alpha\gamma-\frac z{M-1}(N-1)\delta\gamma \end{align} \] with \[ \begin{align} B =& \frac{\binom z{N-1}}{\binom{M-1}{N-1}}\sigma+r\frac {x+w}{M-z-1}\times\\ \left(1-\frac 1{N(M-z)}\left( M-(z-N+1)\frac{\binom z{N-1}}{\binom{M-1}{N-1}}\right)\right) c\\ F(z) =& 1-\frac rN\frac{M-N}{M-z-1}+\frac{\binom z{N-1}}{\binom{M-1}{N-1}} \left(\frac rN \frac{z+1}{M-z-1}+r\frac{M-z-2}{M-z-1}-1\right)\\ G(y) =& \frac 1{M-1}-\frac 1{M-y-1}\frac{\binom{M-y-1}{N-1}}{\binom{M-1}{N-1}} \end{align} \]

      Specified by:
      mixedScores in interface IBS.HasIBS.DGroups
      Overrides:
      mixedScores in class CDLP
      Parameters:
      count - number of individuals for each trait
      n - interaction group size
      traitScores - array for returning the payoffs/scores of each trait

    • avgScores

      public void avgScores(double[] density, int n, double[] avgscores)
      Description copied from class: CDL
      Calculate the average payoff for the frequency of traits specified in the array state for interactions in groups of size n. The average payoffs for each of the nTraits traits must be stored and returned in the array scores.
      standard non-linear PGG:
      \[ \begin{align} f_L =& c \sigma \\ f_D =& x (B + S) c + \sigma c z^{N-1} \\ f_C =& (r_1-1)\left(1-z^{N-1}\right)c-y B c + x S c + \sigma c z^{N-1} \end{align} \] with \[ \begin{align} B =& \frac1{1-z} \left(r_1 - \frac{2 S}{N-1}\right) \left(1-\frac{1-z^N}{N (1-z)}\right) \\ S =& x \frac{r_\text{all}-r_1}{1-z} \end{align} \]
      other's only non-linear PGG:
      \[ \begin{align} f_L =& c \sigma \\ f_D =& x (B + S) c + \sigma c z^{N-1} \\ f_C =& x (B + S) c - \left(1-z^{N-1}\right)c + \sigma c z^{N-1} \end{align} \] with \[ \begin{align} B =& \frac1{1-z} \left(r_1 - \frac{2 S}{N-1}\right) \left(1 - \frac{1-z^N}{N (1-z)}\right) \\ S =& x \frac{r_\text{all}-r_1}{1-z}\frac{N-1}{N-2} \end{align} \]
      Specified by:
      avgScores in interface Model.HasDE.DGroups
      Overrides:
      avgScores in class CDLP
      Parameters:
      density - the frequency/density of each trait
      n - the size of interaction groups
      avgscores - the array for storing the average payoffs/scores of each trait

    • setPoolPunishCost

      public void setPoolPunishCost(double aValue)
      Set the cost of pool punishment.
      Parameters:
      aValue - the cost of pool punishment

    • getPoolPunishCost

      public double getPoolPunishCost()
      Get the cost of pool punishment.
      Returns:
      the cost of pool punishment

    • setPoolPunishFine

      public void setPoolPunishFine(double aValue)
      Set the pool punishment fine.
      Parameters:
      aValue - the pool punishment fine.

    • getPoolPunishFine

      public double getPoolPunishFine()
      Get the fine for pool punishment.
      Returns:
      the pool punishment fine.

    • collectCLO

      public void collectCLO(CLOParser parser)
      Description copied from interface: CLOProvider
      All providers of command line options must implement this method to collect their options.

      Each command line option is (uniquely) identified by it's name (see CLOption.getName()), which corresponds to the long version of the option. If an attempt is made to add an option with a name that already exists, the parser issues a warning and ignores the option. Thus, in general, implementing subclasses should first register their options and call super.collectCLO(CLOParser) at the end such that subclasses are able to override command line options specified in a parental class.

      Override this method in subclasses to add further command line options. Subclasses must make sure that they include a call to super.

      Specified by:
      collectCLO in interface CLOProvider
      Overrides:
      collectCLO in class CDLP
      Parameters:
      parser - the reference to parser that manages command line options
      See Also: