EvoLudoLab: Ecological Public Goods Game - Unstable focus
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.
Unstable node Q - extinction
For larger \(r\), the interior fixed point \(Q\) turns into an unstable focus. The population still faces extinction but may do so in an oscillatory manner - depending on the initial conditions.
The parameters are \(r = 2.7\), \(N = 8\), \(c = 1\), \(b = 0\), \(d = 0.5\) using numerical integration of the replicator equation.
|Snapshot of the spatial arrangement of strategies.|
|Time evolution of the strategy frequencies.|
|Strategy frequencies plotted in the simplex \(S_3\). If no calculation is running, mouse clicks set the initial frequencies of strategies and stops the calculations otherwise (for the ODE solver it switches to backwards integration).|
|Frequencies plotted in the phase plane spanned by the population density (\(u + v = 1 - w\)) and the relative frequency of cooperators (\(f = u / (u + v)\)). Again, mouse clicks set the initial frequencies of strategies, stop the simulations or switch to backward integration|
|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.|
The list below describes only the parameters related to the public goods game and the population dynamics. Follow the link for a complete list and descriptions of all other parameters such as spatial arrangements or update rules on the player and population level.
- multiplication factor \(r\) of public good.
- cost of cooperation \(c\) (investment into common pool).
- Lone cooperator's payoff
- payoff for a cooperator if no one else joins the public goods interaction.
- Lone defector's payoff
- payoff for a defector if no one else joins the public goods interaction.
- Base birthrate
- baseline reproductive rate of all individuals. The effective birthrate is affected by the individual's performance in the public goods game and additionally depends on the availability of empty space.
- constant death rate of all individuals.
- Init Coop, init defect, init empty
- initial densities of cooperators, defectors and empty space. If they do not add up to 100%, the values will be scaled accordingly.