Theoretical Model for Analyzing the Links Between Nutritional and Organoleptic Standards, Food Adulteration Strategies, and Food Safety[Modèle théorique d’analyse des liens entre les normes nutritionnelles et organoleptiques, les stratégies de falsification des aliments et la sécurité sanitaire des aliments]

This study analyzes the impact of food adulteration fraud strategies adopted by a company operating in a market subject to nutritional and organoleptic standards. The study is based on a mathematical model inspired by the 2009 milk crisis in China. This model examines the company's strategic decisions and highlights the relationships between food standards, fraud intensity, and health risk.We consider an agri-food company producing a good subject to a nutritional standard imposed by the public authority and an organoleptic standard dictated by consumer demand. The authority implements a control system based on tests designed to verify the product's compliance with the nutritional standard. However, these tests are imperfect and fail to detect certain substances that can mask fraud. The company may exploit this loophole by substituting a cheaper ingredient for the nutrient. The model is structured as a sequential game between two actors: the regulatory authority and the agri-food company. In the first period, the authority sets the nutritional standard based on public health objectives (non-linear bi-objective problems under constraint). In the second period, the company adjusts the fraud intensity while considering several factors: the prevailing nutritional standard, consumer sensitivity to variations in product composition, the cost of acquiring the substitute substance, and its impact on production capacity. The company seeks to maximize its expected profit (maximizing a nonlinear function under a linear constraint) while anticipating the risk of sanctions if fraud is detected through a health crisis. Solving the game using the backward induction technique reveals several results. Strengthening the nutritional standard may encourage the company to intensify fraud, thereby increasing health risks. However, this adverse effect can be mitigated by increasing financial sanctions. Additionally, better consumer awareness reduces the intensity of food fraud.