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

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 {{EvoLudoLab:CSD|
-options="--game cSD --run --delay 100 --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparams 5:1 --costfcn 3 --costparams 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.02 --mutation 0.01 --mutationtype g --mutationsdev 0.02"|
+options="--module cSD --run --delay 100 --view Strategies_-_Distribution --timestep 50 --popsize 5000 --popupdate async --playerupdate imitate-better --geometry M --interactions r1 --references r1 --benefits 14 5,1 --costs 3 1,10 --traitrange 0,3 --init gaussian 2.8,0.02 --mutation 0.01 gaussian 0.02"|
 title=Continuous Snowdrift game: Saturating investments|
 doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^*_1\approx 0.7\) accompanied by a repellor near \(x^*_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.