EvoLudoLab: RockPaperScissors  IBS with Mutations
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 popup 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 

Individual based simulations (IBS) with mutations
The interior fixed point \(\hat x\) of the replicator dynamics is an unstable focus. Even without stochasticity all trajectories spiral away from \(\hat x\) towards 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. Larger mutation rates increasingly limit the range of values that can be attained by the mean frequencies of the three strategies. In particular, in the limit \(\mu\to1\) the game payoffs no longer affect the dynamics and the mean of all three strategies is simply \(1/3\).
The parameters are \(s = 0.2\), \(\mu=0.005\) and the population size is \(N=1000\).
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 rockscissorspaper 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 rockpaperscissors 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.