EvoLudoLab: Continuous Snowdrift Game - Repellor: Difference between revisions

options="--game cSD --run --delay 200 --view Strategies_-_Distribution --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"|

doc=In this scenario, selection and mutation drives the population away from the singular strategy \(x^* = 0.6\), i.e. \(x^*\) is a repellor. The final state of the population now depends on the initial configuration of the population. If the initial strategy was \(x_0 < x^*\) then the investments decrease over time and defectors reign. However, if \(x_0 > x^*\) holds the population evolves towards a cooperative state with maximal investments. Also note that if \(x_0\) lies close to \(x^*\) then few mutants may diffuse on the other side of \(x^*\) 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 \(b_0 = -0.5, b_1 = 3.4, c_0 = -1.5, c_1 = 4\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(0.5 \pm 0.05\) in a population of 5'000 individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.01\). 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 \(x^* = 0.6\).}}