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Game Theory for Managing Evolving Systems: Challenges and Opportunities of Including Vector-Valued Strategies and Life-History Traits

Author

Listed:
  • Maria Kleshnina

    (Institute for Advanced Study in Toulouse)

  • Sabrina Streipert

    (University of Pittsburgh)

  • Joel S. Brown

    (Moffitt Cancer Center)

  • Kateřina Staňková

    (Delft University of Technology)

Abstract

Nature exhibits rapid evolution in response to human activities. When using natural resources for their own profit, humans should account for such responses. Stackelberg evolutionary games (SEG) offer a method for modeling interactions between a rational leader (humans) and evolutionary followers (nature). The followers evolve according to the principles of natural selection, and the leader tries to steer these inevitable responses in a desired direction. While the separate elements of this method, Stackelberg and evolutionary game theory, are well established, their joint realization in SEG theory is underdeveloped. Thus far, simple examples and formalisms of SEGs have considered models where the manager and evolving species have a scalar-valued controller and scalar-valued trait, respectively. Here we provide examples from cancer therapy, fisheries management, and pest control to illustrate extensions of SEG theory, where managers are attempting to control a Darwinian system. The models we develop and present highlight extensions of SEG theory to include vector-valued management strategies and vector-valued traits in the evolving species, and traits influencing different life-history stages of the species under management. Throughout we highlight the mathematical challenges that lie ahead.

Suggested Citation

  • Maria Kleshnina & Sabrina Streipert & Joel S. Brown & Kateřina Staňková, 2023. "Game Theory for Managing Evolving Systems: Challenges and Opportunities of Including Vector-Valued Strategies and Life-History Traits," Dynamic Games and Applications, Springer, vol. 13(4), pages 1130-1155, December.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:4:d:10.1007_s13235-023-00544-5
    DOI: 10.1007/s13235-023-00544-5
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    1. Christian Hilbe & Maria Kleshnina & Kateřina Staňková, 2023. "Evolutionary Games and Applications: Fifty Years of ‘The Logic of Animal Conflict’," Dynamic Games and Applications, Springer, vol. 13(4), pages 1035-1048, December.
    2. Sam Ganzfried, 2024. "Computing Stackelberg Equilibrium for Cancer Treatment," Games, MDPI, vol. 15(6), pages 1-7, December.

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