Pet Insurance and Veterinary Treatment Decisions: A Game-Theoretic Model of the Owner–Veterinarian Relationship in Türkiye

The economic benefits of pet insurance are generally examined through survey-based empirical studies, while a game-theoretic explanation of how insurance changes treatment decisions remains limited. This study models the clinical decision process between a pet owner and a veterinarian as a static, two-player game within expected utility theory, using an exponential (constant absolute risk aversion, CARA) utility function. The veterinarian’s strategy is {Basic, Comprehensive Treatment}, the owner’s is {Accept, Reject}; severity is a two-state random variable (Mild/Severe). Parameters are calibrated using Turkish market data from the author’s previous study. Findings show that in the uninsured regime, a unique Nash equilibrium (Basic Treatment, Reject) endogenously produces economic treatment-refusal behavior; insurance, by altering the payoff structure, makes available a second, Pareto-superior equilibrium (Comprehensive Treatment, Accept). Sensitivity analyses show comprehensive treatment becomes relatively more attractive as risk aversion increases, but once the co-payment rate exceeds a threshold (~46.3%), insurance loses this effect entirely. Premium level does not affect equilibrium selection, being a sunk cost independent of the treatment decision. These findings indicate that the co-payment rate is a more critical policy variable than premium level in insurance design, and offer a game-theoretic explanation for how pet insurance may affect the veterinarian–owner treatment decision.