Preprint E56/2018
The Role of Self Loops and Link Removal in Evolutionary Games on Networks
Dario Madeo | Chiara Mocenni | Jean Carlo Moraes | Jorge P. Zubelli
Keywords: Evolutionary game theory | games on graphs | games on networks | Equilibrium states | competition | cooperation | self loops on graphs | connectivity of networks.

Recently, a new mathematical formulation of evolutionary game dynamics has been introduced
accounting for a finite number of players organized over a network, where
the players are located at the nodes of a graph and edges represent connections
between them. Internal steady states are particularly interesting in control
and consensus problems, especially in a networked context where they are
related to the coexistence of different strategies. In this paper we consider
this model including self loops. Existence of internal steady states
is studied for different kind of graph topologies. Results on the effect of removing
links from central players are also presented.