The role of self-loops and link removal in evolutionary games on networks.

The role of self-loops and link removal in evolutionary games on networks.

Madeo, Dario;Mocenni, Chiara;Moraes, Jean Carlo;Zubelli, Jorge P;
mathematical biosciences and engineering : mbe 2019 Vol. 16 pp. 5287-5306
303
madeo2019themathematical

Abstract

Recently, a new mathematical formulation of evolutionary game dynamics [1] 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 graph topologies in two-strategy games. Results on the effect of removing links from central players are also presented.

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