EvoLudoLab: Rock-Paper-Scissors - SDE

From EvoLudo
Color code: Rock Scissors Paper
New rock New scissors New paper
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.

Stochastic dynamics - Langevin equation

The interior fixed point \(\hat x\) is a stable focus of the replicator dynamics. Demographic stochasticity arises from the finite population size of \(N=1000\). In the absence of mutations, the boundaries remain absorbing and even though the interior fixed point is attracting, stochastic fluctuations nevertheless eventually drive the population to the absorbing boundaries.

The parameters are \(s = 1.4\) using numerical integration (\(dt=0.01\)) of the Langevin equation derived from a continuums approximation of the stochastic dynamics in finite populations. The starting point is close to the attractor \(\hat x=(1/2, 1/3, 1/6)\).

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.

--paymatrix <rr,rs,rp;sr,ss,sp;pr,ps,pp>
general \(3\times 3\) payoff matrix for the three strategic types \(R, S, P\).
--init <r,s,p>
initial frequencies of \(R, S, P\), respectively. Frequencies that do not add up to 100% are scaled accordingly.
--inittype <type>
type of initial configuration:
random distribution with given frequency
uniform random distribution
monomorphic initialization
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 of traits
(optional) configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Not available for all types of games.