Fig 3. The logic of backward induction for low quality signallers.

Arrows show the progression, coloured circles show the compared nodes and the label(s) below the circles show the step at which the given nodes are compared. We are looking for a pair of ESS strategies that lead to node 12 in case of low quality signallers (i.e. where receivers search but they do not give the resource to low quality signallers, and accordingly, low quality signallers do not give signals of quality). First step: node 11 vs. node 12 from the receiver’s point of view (R2). Second step: node 9 vs. node 12 from the signaller’s point of view (S2; note, since receivers have an (U,D) strategy node 10 is not obtainable). Third step: nodes 1 and 5 vs. nodes 12 and 16 weighted by the ratio of high to low quality individuals from the receiver’s point of view (R1; the reason behind comparing several nodes is the informational uncertainty the receiver facing at this point). Fourth step: node 4 vs. node 12 from the signaller’s point of view (S1).