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Evolutionarily Stable Stackelberg Equilibrium

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  • Sam Ganzfried

Abstract

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and follower-optimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.

Suggested Citation

  • Sam Ganzfried, 2026. "Evolutionarily Stable Stackelberg Equilibrium," Papers 2603.18385, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2603.18385
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    References listed on IDEAS

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    2. 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.
    3. Maria Kleshnina & Sabrina Streipert & Joel Brown & Katerina Stankova, 2023. "Game Theory for Managing Evolving Systems: Challenges and Opportunities of Including Vector-Valued Strategies and Life-History Traits," Post-Print hal-04355341, HAL.
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    5. Sam Ganzfried, 2024. "Computing Stackelberg Equilibrium for Cancer Treatment," Games, MDPI, vol. 15(6), pages 1-7, December.
    6. Sam Ganzfried, 2025. "Computing Evolutionarily Stable Strategies in Imperfect-Information Games," Papers 2512.10279, arXiv.org, revised Dec 2025.
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