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

1 Department of Information Engineering and Mathematics, University of Siena, Italy
2 Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, Brazil
3 Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

Special Issues: Mathematical Methods in the Biosciences

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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Keywords evolutionary game theory; games on graphs; games on networks; equilibrium states; competition; cooperation; self-loops on graphs; connectivity of networks

Citation: Dario Madeo, Chiara Mocenni, Jean Carlo Moraes, Jorge P. Zubelli. The role of self-loops and link removal in evolutionary games on networks. Mathematical Biosciences and Engineering, 2019, 16(5): 5287-5306. doi: 10.3934/mbe.2019264

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