EvoLudoLab: Space inhibits cooperation in Snowdrift and Hawk-Dove games
Along the bottom of the applet there are several buttons to control the execution and the speed of the simulations - for details see the EvoLudo GUI documentation. Of particular importance are the parameters button and the data views pop-up list along the top. The former opens a panel that allows to set and change various parameters concerning the game as well as the population structure, while the latter displays the simulation data in different ways.
|New cooperator||New defector|
Note: The shades of grey of the payoff scale are augmented by blueish and reddish shades indicating payoffs for mutual cooperation and defection, respectively.
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>T = 1.6</math> and <math>S = 0.4</math> with individuals arranged on a square <math>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%.
|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.|
|Message log from engine.|
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.
- reward for mutual cooperation.
- temptation to defect, i.e. payoff the defector gets when matched with a cooperator. Without loss of generality two out of the four traditional payoff values \(R, S, T\) and \(P\) can be fixed and set conveniently to \(R = 1\) and \(P = 0\). This means mutual cooperation pays \(1\) and mutual defection zero. For example for the prisoner's dilemma \(T > R > P > S\) must hold, i.e. \(T > 1\) and \(S < 0\).
- sucker's payoff which denotes the payoff the cooperator gets when matched with a defector.
- punishment for mutual defection.
- Init Coop, init defect
- initial fractions of cooperators and defectors. If they do not add up to 100%, the values will be scaled accordingly. Setting the fraction of cooperators to 100% and of defectors to zero, then the lattice is initialized with a symmetrical configuration suitable for observing evolutionary kaleidoscopes.