Persistence-dependent dynamic interactive environment enhances cooperation

Mercenary punishment in structured populations

“…This is surprising, because, as we argued earlier, a structured population could offer an extra supporting condition for cooperation [41,42]. It is also a frequent observation that a mechanism is inefficient in a random system while it has positive consequences in a structured population [43,44,45]. To fill this gap, in this study, we extend the original model to a spatial version setup and find a rather unexpected result.…”

Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities

“…Assigning an environmental state to each edge ( i , j ), as has been done for square lattices in previous studies (He et al. 2023 ; Zhu 2023 ) and for a two-community network in the present study, in the case of regular graphs and general networks may be an interesting generalization.…”

“…Other eco-evolutionary game models assume network structure and assign a local environmental variable to each edge between a pair of players (He et al. 2023 ; Zhu 2023 ).…”

“…Next, we assume that the state of the environment depends on the type of edge in the network, similarly to He et al. ( 2023 ) and Zhu ( 2023 ). We crucially assign one environmental variable to each type of edge, i.e., the edges within the first community, those within the second community, and those connecting the two communities.…”

“…Unlike the previous studies similarly assuming edge-dependent environmental states (He et al. 2023 ; Zhu 2023 ), our two-community network model, which is a minimal network model, allows analytical investigations.…”