EvoLudoLab: Rock-Paper-Scissors - SDE with Mutations

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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.

 Color code: Rock Scissors Paper New rock New scissors New paper
 Payoff code: Low High

Stochastic dynamics with mutations - Langevin equation

The interior fixed point $$\hat x$$ of the replicator dynamics is an unstable focus. Even without stochasticity all trajectories spiral away from $$\hat x$$ toward the boundary of the simplex $$S_3$$. However, due to mutations, the boundary is repelling, which results in a stochastic analog of a stable limit cycle. For larger mutation rates the interior fixed point becomes stable again even for $$s<1$$.

The parameters are $$s = 0.2$$, $$N=1000$$, $$\mu=0.005$$ using numerical integration of the stochastic differential equation based on Euler's method with $$dt=0.01$$.

Data views

Strategy - Population

Snapshot of the spatial arrangement of strategies.

Strategy 3D - Population

Snapshot of the spatial arrangement of strategies in 3D.

Strategy - Mean

Time evolution of the strategy frequencies.

Strategy - Simplex $$S_3$$

Trajectories of strategy frequencies shown in the simplex $$S_3$$. Double clicks in the interior of $$S_3$$ set the initial frequencies of strategies.

Fitness - Population

Snapshot of the spatial distribution of payoffs.

Fitness 3D - Population

Snapshot of the spatial distribution of payoffs in 3D.

Fitness - Mean

Time evolution of average population payoff bounded by the minimum and maximum individual payoff.

Fitness - Histogram

Payoff distribution of each strategy in population.

Degree - Histogram

Degree distribution in structured populations.

Console Log

Displays messages, warnings and errors reported by the simulation engine plus information on the applet/application.

Game parameters

The list below describes only the parameters related to the rock-scissors-paper 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.

Payoffs
general $$3\times 3$$ payoff matrix for the three strategic types $$R, S, P$$. The rock-paper-scissors game requires cyclic dominance between the three types.
Init Rock, Scissors, Paper
initial frequencies of rock, paper, and scissors types. If they do not add up to 100%, the values will be scaled accordingly.