EvoLudoLab: Space inhibits cooperation in Snowdrift and Hawk-Dove games

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 Snowdrift or Hawk-Dove game: pure strategies

The system quickly approaches the equilibrium configuration where cooperators and defectors (hawks and doves) co-exist. Spatial extension favors small, isolated and filament like clusters of cooperators but the frequency of cooperators is significantly lower than it would be in well-mixed populations. The above scenario results in roughly 12% cooperators as opposed to 40% in corresponding well-mixed populations.

The parameters are set to [math]\displaystyle{ T = 1.6 }[/math] and [math]\displaystyle{ S = 0.4 }[/math] with individuals arranged on a square [math]\displaystyle{ 101\times 101 }[/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.