Origin of Cooperators and Defectors: Difference between revisions

More complicated cost and benefit functions lead to very interesting dynamics but generally they make a complete analysis impossible. Here we set <math>B(x) = b \sqrt{(x+y)}+a</math> and <math>C(x) = \ln(c x+1)</math>. This may lead to the simultaneous occurrence of a branching point and a repellor. The results are summarized in the figure to the left. Starting to the left of the repellor (dash-dotted vertical line) investments decrease until they reach the branching point (dashed vertical line) and then two strategies co-exist and diverge until the upper branch reaches the maximum investment, i.e. hits the boundary of the trait range. Note that the dimorphic population after the branching point does no longer 'see' the repellor near <math>x = 4</math>. The small inset show another simulation run starting to the right of the repellor. The trait simply increases until it hits the boundary.