EvoLudoLab: Continuous Snowdrift Game - Repellor: Difference between revisions

{{VirtualLab:CSD|

options="--run --delay 200 --view 3 --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --switchpref 0.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 11 --benefitparam -0.5:3.4 --costfcn 1 --costparam -1.5:4 --initmean 0.5 --initsdev 0.02 --mutation 0.01 --mutationtype g --mutationsdev 0.01"|

title=Continuous Snowdrift game: Repellor|doc=In this scenario, selection and mutation drives the population away from the singular strategy <math>x^* = 0.6</math>, i.e. <math>x^*</math> is a repellor. The final state of the population now depends on the initial configuration of the population. If the initial strategy was <math>x_0 < x^*</math> then the investments decrease over time and defectors reign. However, if <math>x_0 > x^*</math> holds the population evolves towards a cooperative state with maximal investments. Also note that if <math>x_0</math> lies close to <math>x^*</math> then few mutants may diffuse on the other side of <math>x^*</math> and then again two branches would evolve. But in contrast to evolutionary branching, this process is not generic as it requires a particular preparation of the initial configuration.

The parameters are set to <math>b_0 = -0.5, b_1 = 3.4, c_0 = -1.5, c_1 = 4</math> with players imitating better strategies proportional to the payoff difference and an initial traits/investment of <math>0.5 \pm 0.05</math> in a population of 5'000 individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is <math>0.01</math>. Note that in this case it may or may not happen that a high investing branch evolves, depending on whether early mutants managed to have investment levels higher than <math>x^* = 0.6</math>.}}