EvoLudoLab: Rock-Paper-Scissors - ODE with Mutations
Color code: | Rock | Scissors | Paper |
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New rock | New scissors | New paper |
Payoffs: | Low High
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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.
Replicator-mutator dynamics
The interior fixed point [math]\displaystyle{ \hat x }[/math] is an unstable focus. Near [math]\displaystyle{ \hat x }[/math] all trajectories spiral away but the boundary of the simplex [math]\displaystyle{ S_3 }[/math] is repelling because of mutations, which gives rise to a stable limit cycle. For larger mutation rates the interior fixed point becomes stable again even for [math]\displaystyle{ s\lt 1 }[/math].
The parameters are [math]\displaystyle{ s = 0.2 }[/math], [math]\displaystyle{ \mu=0.005 }[/math] using numerical integration of the replicator-mutator equation.
Data views
Snapshot of the spatial arrangement of strategies. | |
Snapshot of the spatial arrangement of strategies in 3D. | |
Time evolution of the strategy frequencies. | |
Trajectories of strategy frequencies shown in the simplex \(S_3\). Double clicks in the interior of \(S_3\) set the initial frequencies of strategies. | |
Snapshot of the spatial distribution of payoffs. | |
Snapshot of the spatial distribution of payoffs in 3D. | |
Time evolution of average population payoff bounded by the minimum and maximum individual payoff. | |
Payoff distribution of each strategy in population. | |
Degree distribution in structured populations. | |
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:
- 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.
Tip: Use the context menu to switch between forward and backward integration in time.