EvoLudoLab: Ecological Public Goods Game - No Q, cooperation
Color code: | Cooperators | Defectors |
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Payoff code: | Low High
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No interior fixed point Q - cooperation
For high \(r\), the interior fixed point \(Q\) disappears and the high density saddle node along \(f = 1\) (no defectors) becomes a stable equilibrium. Cooperators and defectors can no longer co-exist but now its only the defectors that disappear, at least for favorable initial conditions. As always, severe exploitation and low population densities result in extinction.
The parameters are \(r = 7.9\), \(N = 8\), \(c = 1\), \(b = 0\), \(d = 1.6\) using numerical integration of the replicator equation. Note that changing \(d\) was for purely cosmetic reasons - qualitatively the same results are obtained for \(d = 0.5\) and \(r = 7.9\) only with a much larger cooperator density at equilibrium
Data views
Snapshot of the spatial arrangement of strategies. | |
3D view of 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. | |
3D view of 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. |
Game parameters
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.
- --interest <r>
- multiplication factor \(r\) of public good.
- --cost <c>
- cost of cooperation \(c\) (investment into common pool).
- --lonecooperator <l>
- payoff for a cooperator if no one else joins the public goods interaction.
- --lonedefector <l>
- payoff for a defector if no one else joins the public goods interaction.
- --basefit <
b> - 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.
- --deathrate <d>
- constant death rate of all individuals.
- --init <d,c,e>
- initial frequencies of defectors d, cooperators c and vacant space e. 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.