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

Dario Madeo; Chiara Mocenni; Jean Carlo Moraes; Jorge P. Zubelli; Dario Madeo; Chiara Mocenni; Jean Carlo Moraes; Jorge P. Zubelli

doi:10.3934/mbe.2019264

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 5287-5306. doi: 10.3934/mbe.2019264

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Research article Special Issues

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

Received: 28 December 2018 Accepted: 09 April 2019 Published: 11 June 2019

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.
- 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[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5287-5306. doi: 10.3934/mbe.2019264

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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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