Fig 4. The logic of backward induction for low quality signallers when it is worth for the receiver to give the resource to low quality signallers in the absence of high quality ones.

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 3 in case of low quality signallers (i.e. where receivers search and they give the resource to low quality signallers in the absence of high quality ones, however low quality signallers still do not give signals of quality). First step: node 3 vs. node 4 from the receiver’s point of view (R2). Second step: node 1 vs. node 3 from the signaller’s point of view (S2). Third step: nodes 1 and 5 vs. nodes 3 and 7 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 3 vs. node 11 from the signaller’s point of view (S1).