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Generalized Hamiltonian dynamics and chaos in evolutionary games on networks

Author

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  • Griffin, Christopher
  • Semonsen, Justin
  • Belmonte, Andrew

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).

Suggested Citation

  • Griffin, Christopher & Semonsen, Justin & Belmonte, Andrew, 2022. "Generalized Hamiltonian dynamics and chaos in evolutionary games on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    • Handle: RePEc:eee:phsmap:v:597:y:2022:i:c:s0378437122002394
    DOI: 10.1016/j.physa.2022.127281
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    References listed on IDEAS

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    Cited by:

    1. Grau-Climent, Juan & Garcia-Perez, Luis & Alonso-Sanz, Ramon & Losada, Juan C., 2023. "Effect of players’ expectations and memory in a quantum Cournot game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Nicolosi, Gabriel & Friesz, Terry & Griffin, Christopher, 2022. "Approximation of optimal control surfaces for 2 × 2 skew-symmetric evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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