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

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"|

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.

The parameters are set to \(b_1 = 5, b_2 = 1, c_1 = 1, c_2 = 10\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(2.8 \pm 0.02\) in a population of \(5'000\) individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.02\).}}