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Landscape and flux for quantifying global stability and dynamics of game theory

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  • Li Xu
  • Jin Wang

Abstract

Game theory has been widely applied to many research areas including economics, biology and social sciences. However, it is still challenging to quantify the global stability and global dynamics of the game theory. We developed a landscape and flux framework to quantify the global stability and global dynamics of the game theory. As an example, we investigated a model of three-strategy game: a special replicator mutator game termed as the repeated Prison Dilemma model. In this model, one stable state, two stable states and limit cycle can emerge under different parameters. The repeated Prisoner’s Dilemma system has Hopf bifurcation from one stable state to limit cycle state, and then to another one stable state or two stable states, and vice versa. We quantified the global stability of the repeated Prisoner’s Dilemma system and identified optimal kinetic paths between the basins of attractor. The optimal paths are irreversible due to the non-zero flux. We also quantified the interplay between Peace and War.

Suggested Citation

  • Li Xu & Jin Wang, 2018. "Landscape and flux for quantifying global stability and dynamics of game theory," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-27, August.
    • Handle: RePEc:plo:pone00:0201130
    DOI: 10.1371/journal.pone.0201130
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    1. Binmore, K.G. & Samuelson, L., 1991. "Evolutionary stability in repeated games played by finite automata," Discussion Paper 1991-31, Tilburg University, Center for Economic Research.
    2. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, vol. 74(1), pages 434-441.
    3. Binmore, K.G. & Samuelson, L., 1991. "Evolutionary stability in repeated games played by finite automata," Other publications TiSEM 2a8b7743-1c37-4371-8656-1, Tilburg University, School of Economics and Management.
    4. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, vol. 112(2), pages 232-260, October.
    5. Binmore, K. & Samuelson, L., 1990. "Evolutionary Stability In Repeated Games Played By Finite Automata," Working papers 90-29, Wisconsin Madison - Social Systems.
    6. Jin Wang & Bo Huang & Xuefeng Xia & Zhirong Sun, 2006. "Funneled Landscape Leads to Robustness of Cell Networks: Yeast Cell Cycle," PLOS Computational Biology, Public Library of Science, vol. 2(11), pages 1-10, November.
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