Stackelberg Evolutionary Games of Cancer Treatment - What Treatment Strategy to Choose if Cancer Can be Stabilized - abstract

Sep 21, 2026

Uploaded by Ophelia

A game-theoretic model examines a polymorphic cancer cell population in which treatment-induced resistance is a quantitative trait that evolves over time. When tumor burden stabilization is achievable, the analysis extends to a Stackelberg evolutionary game with the physician as leader selecting a treatment dose to maximize a proxy for patient quality of life. Cancer cells respond by evolving resistance to maximize proliferation and survival. Under ecological equilibrium, three strategies are compared: maximum tolerable dose, an ecologically enlightened therapy, and an evolutionarily enlightened therapy, with the latter yielding the best objective values, lowest dose, and lowest resistance.

LanguageEnglish

CategoryResearch & Report

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Pages20

Reading Time50 min

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Abstract

Introduction

Standard of care and selection for resistance

Evolutionary cancer therapies (adaptive therapies)

Therapy goals: stabilization and cure

Adaptive trial examples (NCT studies)

Stackelberg Evolutionary Games of Cancer Treatment: What Treatment Strategy to Choose if Cancer Can be Stabilized? Monica Salvioli1,6 · Hasti Garjani2 · Mohammadreza Satouri1 · Mark Broom3 · Yannick Viossat4 · Joel S. Brown5 · Johan Dubbeldam2 · Kateina Staková1 Accepted: 26 November 2024 / Published online: 14 December 2024 © The Author(s) 2024 Abstract We present a game-theoretic model of a polymorphic cancer cell population where the treatment-induced resistance is a quantitative evolving trait. When stabilization of the tumor burden is possible, we expand the model into a Stackelberg evolutionary game, where the physician is the leader and the cancer cells are followers. The physician chooses a treatment dose to maximize an objective function that is a proxy of the patient’s quality of life. In response, the cancer cells evolve a resistance level that maximizes their proliferation and survival. Assuming that cancer is in its ecological equilibrium, we compare the outcomes of three different treatment strategies: giving the maximum tolerable dose throughout, corresponding to the standard of care for most metastatic cancers, an ecologically enlightened therapy, where the physician anticipates the short-run, ecological response of cancer cells to their treatment, but not the evolution of resistance to treatment, and an evolutionarily enlightened therapy, where the physician anticipates both ecological and evolutionary consequences of the treatment. Of the three therapeutic strategies, the evolutionarily enlightened therapy leads to the highest values of the objective function, the lowest treatment dose, and the lowest treatment-induced resistance. Conversely, in our model, the maximum tolerable dose leads to the worst values of the objective function, the highest treatment dose, and the highest treatment-induced resistance. Keywords Stackelberg evolutionary games · Evolutionary cancer therapy · Evolutionary game theory · Resistance · Heterogeneity · Mathematical oncology 1 Introduction Metastatic cancer, characterized by the spread of malignant cells from its original site to other parts of the body, remains largely incurable, with cancer death rates declining by only 1.5 percent per year between years 2001 and 2017 [37, 42, 60] . This lack of progress in metastatic cancers is, in part, due to the standard of care in metastatic cancers, which typically applies a drug or drug combination at maximum tolerable dose (MTD), either continuously or in predeﬁned treatment cycles [23, 25, 27, 28, 80] . The Monica Salvioli and Hasti Garjani have contributed equally to this work. Extended author information available on the last page of the article same regimen continues until there is unacceptable toxicity, unambiguous evidence of tumor progression, or cure. However, in metastatic cancers, cure is rare [21, 68, 70] . The goal of killing as many cancer cells as fast as possible may be evolutionarily unwise [22, 24, 28, 74, 75, 86] . This is because MTD imposes a very strong selection pressure for the evolution of treatment-induced resistance, which subsequently leads to treatment failure [1, 22, 24, 36, 42, 53, 61, 84, 85, 92] . Evolutionary cancer therapies (also known as adaptive therapies) provide an alternative to the standard of care [28, 31, 48, 56, 74, 75] . Evolutionary therapies aim to manage treatment-induced resistance in cancer cells by anticipating and steering their ecological and evolutionary dynamics. Such therapies integrate mathematical models, known cancer biology, and patient-speciﬁc data to improve care. Different therapy goals lead to different types of evolutionary therapy: • Delaying progression or tumor burden stabilization: In situations where curative therapies are too risky or unavailable, evolutionary therapies strive to prolong the time to progression (clinical trials NCT02415621, NCT03511196, NCT05393791, NCT03543969, and NCT03630120) or, when possible, to stabilize the tumor bu

FAQs

What is the key assumption about resistance in the proposed cancer model?

Treatment-induced resistance is represented as a quantitative trait that evolves as treatment is applied, shaping how the cancer population responds over time.

How does the Stackelberg evolutionary game structure the interaction between the physician and cancer cells?

The physician acts as the leader by choosing a treatment dose to maximize an objective function related to patient quality of life, while cancer cells act as followers by evolving a resistance level that maximizes proliferation and survival.

How do the three treatment strategies compare in the model when stabilization is possible?

The evolutionarily enlightened therapy produces the highest objective function values, the lowest treatment dose, and the lowest treatment-induced resistance, whereas the maximum tolerable dose strategy produces the worst objective outcomes and highest resistance.

Sep 21, 2026

Uploaded by Ophelia