EvoLudoLab: Space inhibits cooperation in Snowdrift and HawkDove games
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.
Spatial Snowdrift or HawkDove game: pure strategies
The system quickly approaches the equilibrium configuration where cooperators and defectors (hawks and doves) coexist. Spatial extension favors small, isolated and filament like clusters of cooperators but the frequency of cooperators is significantly lower than it would be in wellmixed populations. The above scenario results in roughly 12% cooperators as opposed to 40% in corresponding wellmixed 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
Snapshot of the spatial arrangement of strategies.  
Time evolution of the strategy frequencies.  
Snapshot of the spatial distribution of payoffs.  
Time evolution of average population payoff bounded by the minimum and maximum individual payoff.  
Snapshot of payoff distribution in population.  
Degree distribution in structured populations.  
Statistics of fixation probabilities.  
Statistics of fixation and absorption times.  
Message log from engine. 
Game parameters
The list below describes only the few parameters related to the Prisoner's Dilemma, Snowdrift and HawkDove 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:
 frequency
 random distribution with given frequency
 uniform
 uniform random distribution
 monomorphic
 monomorphic initialization
 mutant
 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
 stripes of traits
 kaleidoscopes
 (optional) configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Not available for all types of games.