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Stackelberg evolutionary game theory: how to manage evolving systems.

Alexander Stein1, Monica Salvioli2, Hasti Garjani3

  • 1Centre for Cancer Genomics and Computational Biology, Barts Cancer Institute, Queen Mary University London, London EC1M 5PZ, UK.

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|March 19, 2023
PubMed
Summary

Stackelberg evolutionary game (SEG) theory models leader-follower dynamics in evolving systems. Anticipating and steering eco-evolutionary dynamics, rather than constant aggression, yields optimal outcomes for leaders in management applications.

Keywords:
Darwinian dynamicscancer evolutionevolutionary game theoryevolutionary rescuefisheries managementoptimization

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Area of Science:

  • Evolutionary Game Theory
  • Ecological Dynamics
  • Mathematical Biology

Background:

  • Classical and evolutionary game theory are combined in Stackelberg evolutionary game (SEG) theory.
  • SEGs model interactions between a rational leader and evolving followers.
  • Leaders may aim to preserve or drive systems to extinction, with constant aggressive strategies often being suboptimal.

Purpose of the Study:

  • To explore the application of SEG theory in managing evolving biological systems.
  • To demonstrate how leaders can achieve better outcomes by anticipating and steering eco-evolutionary dynamics.
  • To highlight the potential of SEGs in fields like fisheries, pest, and cancer management.

Main Methods:

  • Integration of classical game theory with evolutionary game theory principles.
  • Analysis of leader-follower interactions within ecological dynamics.
  • Identification of Nash and Stackelberg equilibria in eco-evolutionary contexts.

Main Results:

  • Suboptimal outcomes arise from constant aggressive strategies for leaders.
  • Incorporating ecological dynamics improves leader outcomes, aligning with Nash equilibria.
  • The Stackelberg equilibrium represents the most profitable strategy for leaders by steering dynamics.

Conclusions:

  • SEG theory offers a framework for optimizing management in evolving systems.
  • Anticipatory strategies, leading to Stackelberg equilibria, are superior to constant aggressive approaches.
  • SEG applications show promise in fisheries, pest control, and cancer treatment management.