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1 Introduction Testosterone serves as the primary driver of male reproductive function. It not only sustains spermatogenesis but also participates in the modulation of multiple systemic processes, with its deficiency closely associated with immune dysfunction, decreased bone density, cardiovascular diseases, and sleep disorders (Handelsman and Wittert 2024; Kaufman and Lapauw 2020; Ketchem et al. 2023; Liu and Reddy 2022; Moreau et al. 2020; Tenuta et al. 2025).
This paper investigates the existence conditions for incentive design in Stackelberg games and their applications to mean-field large-population team-optimal control. We introduce the concept of incentivability, which characterises when a leader can design incentives that induce followers to adopt team-optimal strategies, serving as a structural criterion analogous to controllability and observability.
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