Figure 1

Proposers avoid pure defectors without the need of acceptors in RC games. Composition of the recurrent sets for RC one-shot games. Composition of the recurrent sets for each studied RC type game when all the strategies are included (left) and when acceptors are removed (right). Each pie-chart is associated with a specific (\(\epsilon \), δ) pair. Each strategy is assigned a different colour. The pieces of the pie-chart separated by thick lines correspond to different nodes of the recurrent set. Their sizes are proportional to their probabilities in the stationary state. If a sector is of a single colour it means that the node corresponds to a pure state; if it is subdivided in smaller sectors with different colours it means that the node corresponds to a mixed state, the different colours representing the coexisting strategies. The sizes of these sub-sectors are proportional to their fraction within the mixed state. On the top-right of this figure, a visual explanation through an illustration in the figure has been included.