TY - JOUR
T1 - Generalized Hamiltonian dynamics and chaos in evolutionary games on networks
AU - Griffin, Christopher
AU - Semonsen, Justin
AU - Belmonte, Andrew
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - 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).
AB - 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).
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U2 - 10.1016/j.physa.2022.127281
DO - 10.1016/j.physa.2022.127281
M3 - Article
AN - SCOPUS:85127753398
SN - 0378-4371
VL - 597
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
M1 - 127281
ER -