EvoLudoLab: Continuous Snowdrift Game - Branching (sqrt): Difference between revisions

options="--game cSD --run --delay 200 --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 12 --benefitparam 1 --costfcn 3 --costparam 1:0.6 --traitmax 5 --initmean 2.8 --initsdev 0.02 --mutation 0.02 --mutationtype g --mutationsdev 0.02"|

doc=For more complicated payoff functions several singular strategies \(x^*\) may be found. In this example we use \(B(x) = b_0 \sqrt{x+y}\) and \(C(x) = c_0 \ln(c_1 x+1)\). For the parameters indicated below this results in a repellor near \(x_1^*\approx 3.9\) together with a branching point near \(x^*_2 \approx 0.7\). Starting with \(x_0 < 3.9\) drives the population towards lower investments until the branching point is reached. At \(x^*_2\) two branches emerge and diverge until the upper branch reaches the boundary of the trait range. Note that for the dimorphic population the repellor near \(x_1^*\approx 3.9\) no longer exists. The trait range in the above simulation is \([0,5]\).

The parameters are set to \(b_0 = 1, c_0 = 1, c_1 = 0.6\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(3.2 \pm 0.02\) in a population of \(2'000\) individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.01\).}}