Journal of Mental Health and Psychiatry Research
ISSN: 3143-7974 | DOI: 10.64030/3143-7974
Prasad Kothari
Objective: To develop a mathematically rigorous, four-population evolutionary-game-theoretic (EGT) framework that specifies the structural conditions under which patient-centric behavior in generative-AI (GenAI)-augmented telemental health is a stable, dominant equilibrium of the joint patient–provider–payer–policymaker system, and to embed this contribution within a comprehensive narrative survey of the lineage of evolutionarily-stable-strategy (ESS) theorists, from Fisher's frequencydependent selection (1930) through Maynard Smith and Price's 1973 founding, the Taylor–Jonker replicator dynamic, the Hofbauer–Sigmund synthesis, the Foster–Young and Nowak finite-population programs, the graph- and structured-population theories of Lieberman, Ohtsuki, Hauert, Antal, Tarnita and Allen, and the algorithmic-strategic-interaction work of Hardt, Liu and Obermeyer, through to the 2023–2026 reassessment by Leimar–McNamara and Traulsen–Glynatsi.
Design: Theoretical modeling study with structured narrative survey. We construct a 3 × 3 × 3 × 3 asymmetric evolutionary game in which patients, providers, payers and policymakers each select among three behavioral strategies, with state-dependent payoffs incorporating clinical outcomes, patient-reported experience and outcome measures (PREMs / PROMs), digital-equity protection, generative-AI safety incidents specific to mental-health applications, and operational costs.
Methodology: Strategy is governed by the multi-population replicator–mutator dynamic. We derive evolutionarily stable strategy (ESS) conditions in closed form and prove local asymptotic stability of the patient-centric equilibrium via a KullbackLeibler-divergence Lyapunov function and LaSalle's invariance principle. Four policy levers are formalized: the outcome-linked reimbursement weight β, the equity weight λ, the platform-redesign cost c_p, and the regulatory enforcement intensity τ for GenAI mental-health tools. Parameter ranges were calibrated against published telemental-health, AI-safety and value-basedpayment literature (2014–2025). No human subjects were enrolled and no original empirical data were collected.
Setting: Conceptual modeling and narrative review. No clinical setting; no patients enrolled. Main Outcome Measures: Existence and local stability of the patient-centric ESS E_C; closed-form thresholds (β*, λ*, c*_p, τ*); qualitative regime classification (transactional, fragmented, mixed, patient-centric); and ten policy recommendations derivable from the threshold inequalities.
Results: The four-population framework yields four qualitatively distinct equilibria: a transactional equilibrium E_T, a fragmented equilibrium E_F, a mixed equilibrium E_X, and a patient-centric equilibrium E_C. We prove (Proposition 4) that E_C is a strict ESS if and only if β ≥ β*, λ ≥ λ*, c_p ≤ c*_p, and τ ≥ τ*, each threshold expressible in closed form in terms of the underlying payoff structure. Under our calibration, β* ≈ 0.45, λ* ≈ 0.30, c*_p ≈ 0.20, τ* ≈ 0.35. A Lyapunov-style argument (Theorem 1) shows that trajectories starting in a neighborhood of E_C converge to E_C under the replicator dynamic whenever all four threshold conditions hold strictly.
Conclusions: Patient centricity in GenAI-augmented telemental health is best characterized as a co-evolutionary property of patients, providers, payers and policymakers, not as a unilateral attribute of any one actor. The framework yields ten concrete, threshold-derived policy recommendations and is intended to guide subsequent empirical estimation, payer contract design, and regulatory rule-making.