Chaos in nonlinear paradoxical games

L. Drossos, T. Bountis, J. S. Nicolis

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Paradoxical games are nonconstant sum conflicts, where individual and collective rationalities are at variance and refer to a dyadic antagonism where the contestants blackmail each other. The state space dynamics of a class of such games has been previously studied in the planar case of two variables x 1, x 2 (representing the propensities of the two parties to cooperate), for which phase space portraits have been obtained for a wide range of control parameters. In this paper, we extend the analysis to 3 dimensions, by allowing two of these parameters (the so-called «tempting factors») to oscillate in time. We observe on a Poincaré surface of section that the invariant manifolds of two unstable fixed points U 1 and U 1 intersect, and form heteroclinic and homoclinic orbits. Thus, sufficiently close to U 1 and U 2, one finds «horseshoe» chaos and extremely sensitive dependence to initial conditions. Moreover, since the equations of motion can be written in Hamiltonian form, all the known phenomena of periodic, quasi-periodic and chaotic orbits can be observed around two stable fixed points, where the two parties become «deadlocked» in an inconclusive exchange that never ends.

Original languageEnglish
Pages (from-to)155-176
Number of pages22
JournalIl Nuovo Cimento D
Volume12
Issue number2
DOIs
Publication statusPublished - Feb 1990
Externally publishedYes

Fingerprint

games
chaos
orbits
dyadics
equations of motion

Keywords

  • General, theoretical and mathematical biophysics (including logic of biosystems, quantum biology and relevant aspects of thermodynamics, information theory, cybernetics and bionics)

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Drossos, L., Bountis, T., & Nicolis, J. S. (1990). Chaos in nonlinear paradoxical games. Il Nuovo Cimento D, 12(2), 155-176. https://doi.org/10.1007/BF02450453

Chaos in nonlinear paradoxical games. / Drossos, L.; Bountis, T.; Nicolis, J. S.

In: Il Nuovo Cimento D, Vol. 12, No. 2, 02.1990, p. 155-176.

Research output: Contribution to journalArticle

Drossos, L, Bountis, T & Nicolis, JS 1990, 'Chaos in nonlinear paradoxical games', Il Nuovo Cimento D, vol. 12, no. 2, pp. 155-176. https://doi.org/10.1007/BF02450453
Drossos L, Bountis T, Nicolis JS. Chaos in nonlinear paradoxical games. Il Nuovo Cimento D. 1990 Feb;12(2):155-176. https://doi.org/10.1007/BF02450453
Drossos, L. ; Bountis, T. ; Nicolis, J. S. / Chaos in nonlinear paradoxical games. In: Il Nuovo Cimento D. 1990 ; Vol. 12, No. 2. pp. 155-176.
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