EvoLudoLab: Space promotes cooperation in the Prisoner's Dilemma

From EvoLudo
Color code: Cooperators Defectors
New cooperator New defector
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.

Spatial Prisoner's Dilemma: pure strategies

The spatial Prisoner's Dilemma supports cooperation within a certain parameter range. In that range cooperators can keep up with defectors by forming clusters and thus reducing interactions with (exploitation from) defectors. Even though the parameter range is rather limited, it still demonstrates that cooperation may persist simply because of spatial dimensions and without the need for sophisticated strategic behavior. Whereas in absence of spatial structures and limited local interactions cooperators would invariably go extinct. The parameters are set to [math]\displaystyle{ T = 1.07 }[/math] and [math]\displaystyle{ S = -0.07 }[/math] with individuals arranged on a square [math]\displaystyle{ 70\times 70 }[/math] lattice with four neighbors and players imitating better strategies with a probability proportional to the payoff difference. The inital fraction of cooperators is 50%.

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.

Console log

Message log from engine.

Game 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.
--reward <a11>
the reward for mutual cooperation. The payoff of type \(A\) against its own type (see --paymatrix).
--temptation <a10>
the temptation to defect. The payoff of type \(B\) against type \(A\) (see --paymatrix).
--sucker <a01>
the sucker's payoff of an exploited cooperator. The payoff of type \(A\) against type \(B\) (see --paymatrix).
--punishment <a00>
the punishment for mutual defection. The payoff of type \(B\) against its own type (see --paymatrix).
--init <a,b>
initial frequencies of type \(A\) and \(B\), respectively. Frequencies that do not add up to 100% are scaled accordingly.
--inittype <type>
type of initial configuration:
random distribution with given frequency
uniform random distribution
monomorphic initialization
single mutant in homogeneous population of another type. Mutant and resident types are determined by the types with the lowest and highest frequency, respectively (see option --init).
stripes of traits
(optional) configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Not available for all types of games.