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Complexity
Volume 2017, Article ID 7259032, 14 pages
https://doi.org/10.1155/2017/7259032
Research Article

Evolutionary Network Games: Equilibria from Imitation and Best Response Dynamics

1IMT School for Advanced Studies, 55100 Lucca, Italy
2Istituto dei Sistemi Complessi (ISC-CNR), 00185 Rome, Italy
3Universidad Carlos III, Leganés, 28911 Madrid, Spain

Correspondence should be addressed to Giulio Cimini; ti.accultmi@inimic.oiluig

Received 6 April 2017; Accepted 17 July 2017; Published 24 August 2017

Academic Editor: Tommaso Gili

Copyright © 2017 Giulio Cimini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider games of strategic substitutes and complements on networks and introduce two evolutionary dynamics in order to refine their multiplicity of equilibria. Within mean field, we find that for the best-shot game, taken as a representative example of strategic substitutes, replicator-like dynamics does not lead to Nash equilibria, whereas it leads to a unique equilibrium for complements, represented by a coordination game. On the other hand, when the dynamics becomes more cognitively demanding, predictions are always Nash equilibria: for the best-shot game we find a reduced set of equilibria with a definite value of the fraction of contributors, whereas, for the coordination game, symmetric equilibria arise only for low or high initial fractions of cooperators. We further extend our study by considering complex topologies through heterogeneous mean field and show that the nature of the selected equilibria does not change for the best-shot game. However, for coordination games, we reveal an important difference: on infinitely large scale-free networks, cooperative equilibria arise for any value of the incentive to cooperate. Our analytical results are confirmed by numerical simulations and open the question of whether there can be dynamics that consistently leads to stringent equilibria refinements for both classes of games.