EvoLudoLab: Spatial 2x2 Game - Dominance B

Color code:	Cooperators	Defectors
	New cooperator	New defector

Payoffs:	Low High

Note: The gradient of the payoff scale is augmented by pale shades of the strategy colours to mark payoffs that are achieved in homogeneous populations of the corresponding type.

Drop saved state to restore

 

time: -

SettingsInitStartStep

--run --delay 200 --view 0 --reportfreq 1.0 --popsize 100x --popupdate r --playerupdate i --updateprob 1.0 --switchpref 0.0 --geometry m --intertype a1 --numinter 1 --reprotype a8 --initfreqs 2:8 --mutation 0.0 --basefit 1.0 --selection 1.0 --reward 1.0 --punishment 0.0 --temptation 1.16 --sucker -0.16

ApplyDefaultHelp

Error: Mandatory option --module not found!

 

GWT Version: 2.11.0
GUI features: WebGL XML keyboard mouse
ERROR: Mandatory option --module not found!

List of available modules:
--module <m>    select module from:
         Moran: Moran process
        eMoran: Ecological Moran process
      Motility: Selection & Motility
            CG: Conservation Game
           2x2: 2x2 Games
          e2x2: Ecological 2x2 games
          a2x2: Asymmetric 2x2 Games
      Demes2x2: 2x2 Games in Demes
           RSP: Rock-Scissors-Paper Games
           CDL: Volunteering in (non-linear) public goods games
          CDLP: Punishment in voluntary public goods games
         CDLPQ: Peer & pool punishment in voluntary public goods
        Mutual: Mutualisms
          eMut: Ecological Mutualisms
          ePGG: Ecological public goods games
           cSD: Continuous Snowdrift
       cLabour: Continuous Division of Labour
       Dialect: Emergence of Dialects
           Net: Network Games
          Test: Test suite

Type B dominates

In well-mixed populations type $B$ players dominate and take over the population irrespective of the initial configuration. However, in spatially structured populations type $A$ players can survive by forming clusters and thereby reducing exploiting interactions with type $B$ players.

This corresponds to the spatial Prisoner's Dilemma. Spatial structure enable cooperators to survive - albeit only for a small parameter range. This demonstrates that cooperative behavior may persist simply by including spatial extensions and without requiring sophisticated strategic behavior. In the absence of spatial structured and localized interactions cooperators would invariably go extinct.

The parameters above are set to $R=1,P=0,T=1.1$ and $S=-0.5$ with players imitating better strategies proportional to the payoff difference. Reducing the stochasticity (e.g. by choosing the best-takes-over update rule) leads to higher fractions of cooperators while increasing stochasticity is more likely to result in the extinction of cooperators.

Data views

Strategies - Structure	Snapshot of the spatial arrangement of strategies.
Strategies - Mean	Time evolution of the strategy frequencies.
Fitness - Structure	Snapshot of the spatial distribution of payoffs.
Fitness - Mean	Time evolution of average population payoff bounded by the minimum and maximum individual payoff.
Fitness - Histogram	Snapshot of payoff distribution in population.
Structure - Degree	Degree distribution in structured populations.
Statistics - Fixation probability	Statistics of fixation probabilities.
Statistics - Fixation time	Statistics of fixation and absorption times.
Stationary distribution	Statistics of the stationary distribution of the numbers of each strategic type. Note, only available for non-zero mutation rates.
Console log	Message log from engine.

Module parameters

The list below describes only the few parameters related to the Prisoner's Dilemma, Snowdrift and Hawk-Dove games. Follow the link for a complete list and detailed descriptions of the user interface and further parameters such as spatial arrangements or update rules on the player and population level.

--paymatrix <a00,a01;a10,a11>

2x2 payoff matrix. Type $A$ has index 0 and type $B$ index 1.

--inittype <type>

type of initial configuration:

frequency <f0>,<f1>...

random distribution with given trait frequencies, f0, f1,.... Note, only available for frequency based modules and models.

density <d0>,<d1>...

initial trait densities <d1,...,dn>. Note, only available for density based modules and models.

uniform

uniform random distribution, equal frequencies of all traits.

monomorphic <t>[,<v>]

monomorphic initialization with trait t. Note, for modules with variable population densities, the optional parameter v indicates the initial frequency of vacant sites. If omitted the monomorphic trait is initialized at its (estimated) carrying capacity.

mutant <m>,<r>[,<v>]

single mutant with trait m in homogeneous resident population of type r. The mutant is placed in a location selected uniformly at random (mutants arising through cosmic rays). Note, for modules with variable population densities, the optional parameter v indicates the initial frequency of vacant sites. If omitted the resident trait is initialized at its (estimated) carrying capacity.

temperature <m>,<r>[,<v>]

single mutant with trait m in homogeneous resident population of type r. The mutant is placed in a location selected proportional to the in-degree of nodes (temperature initialization, mutants arising through errors in reproduction). Note, for modules with variable population densities, the optional parameter v indicates the initial frequency of vacant sites. If omitted the resident trait is initialized at its (estimated) carrying capacity.

stripes

stripes of traits. Note, only available for 2D lattices.

kaleidoscopes

configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Note, only available for some modules.

Note, for modules that admit multiple species, the initialization types for each species can be specified as an array separated by ;. With more species than initialization types, they are assigned in a cyclical manner.