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Games and the Treatment Convexity of Cancer

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  • Péter Bayer

    (1 Esplanade de l’Université)

  • Jeffrey West

    (Moffitt Cancer Center)

Abstract

Evolutionary game theory has been highly valuable in studying frequency-dependent selection and growth between competing cancer phenotypes. We study the connection between the type of competition as defined by the properties of the game, and the convexity of the treatment response. Convexity is predictive of differences in the tumor’s response to treatments with identical cumulative doses delivered with different variances. We rely on a classification of $$2\times 2$$ 2 × 2 games based on the signs of “gains of switching,” containing information about the kind of selection through the game’s equilibrium structure. With the disease starting in one game class, we map the type of effects treatment may have on the game depending on dosage and the implications of treatment convexity. Treatment response is a linear function of dose if the game is a Prisoner’s Dilemma, Coordination, or Harmony game and does not change game class, but may be convex or concave for Anti-Coordination games. If the game changes class, there is a rich variety in response types including convex–concave and concave–convex responses for transitions involving Anti-Coordination games, response discontinuity in case of a transition out of Coordination games, and hysteresis in case of a transition through Coordination games.

Suggested Citation

  • Péter Bayer & Jeffrey West, 2023. "Games and the Treatment Convexity of Cancer," Dynamic Games and Applications, Springer, vol. 13(4), pages 1088-1105, December.
  • Handle: RePEc:spr:dyngam:v:13:y:2023:i:4:d:10.1007_s13235-023-00520-z
    DOI: 10.1007/s13235-023-00520-z
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    References listed on IDEAS

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    1. Robert A. Gatenby, 2009. "A change of strategy in the war on cancer," Nature, Nature, vol. 459(7246), pages 508-509, May.
    2. Benjamin Wölfl & Hedy te Rietmole & Monica Salvioli & Artem Kaznatcheev & Frank Thuijsman & Joel S. Brown & Boudewijn Burgering & Kateřina Staňková, 2022. "The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer," Dynamic Games and Applications, Springer, vol. 12(2), pages 313-342, June.
    3. Jorge Peña & Georg Nöldeke, 2023. "Cooperative Dilemmas with Binary Actions and Multiple Players," Dynamic Games and Applications, Springer, vol. 13(4), pages 1156-1193, December.
    4. Péter Bayer & Robert A Gatenby & Patricia H McDonald & Derek R Duckett & Kateřina Staňková & Joel S Brown, 2022. "Coordination games in cancer," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-15, January.
    5. Jingsong Zhang & Jessica J. Cunningham & Joel S. Brown & Robert A. Gatenby, 2017. "Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    6. Peter Bayer & Robert A. Gatenby & Patricia Mcdonald & Derek Duckett & Katerina Stankova & Joel Brown, 2022. "Coordination games in cancer," Post-Print hal-04067690, HAL.
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    Cited by:

    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.

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