Generalized Hamiltonian dynamics and chaos in evolutionary games on networks

Christopher Griffin, Justin Semonsen and Andrew Belmonte

Physica A: Statistical Mechanics and its Applications, 2022, vol. 597, issue C

Abstract: We study the network replicator equation and characterize its fixed points on arbitrary graph structures for 2 × 2 symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of an independent vertex set in the graph and also show that complex behavior cannot emerge in 2 × 2 games. This links a property of the dynamical system with a combinatorial graph property. We contrast this by showing that ordinary rock–paper–scissors (RPS) exhibits chaos on the 3-cycle and that on general graphs with ≥3 vertices the network replicator with RPS is a generalized Hamiltonian system. This stands in stark contrast to the established fact that RPS does not exhibit chaos in the standard replicator dynamics or the bimatrix replicator dynamics, which is equivalent to the network replicator on a graph with one edge and two vertices (K2).

Keywords: Network replicator; Evolutionary games; Generalized Hamiltonian dynamics; Chaos (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437122002394
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:597:y:2022:i:c:s0378437122002394

DOI: 10.1016/j.physa.2022.127281

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().