Dynamics of buyer populations in fresh product markets

Based on empirical evidences and previous studies, we introduce and mathematically study a perception-driven model for the dynamics of buyer populations in markets of perishable goods. Buyer behaviours are driven partly by some loyalty to the sellers that they previously purchased at, and partly by the sensitivity to the intrinsic attractiveness of each seller in the market. On the other hand, the sellers update they attractiveness in time according to the difference between the volume of their clientele and the mean volume of buyers in the market, optimising either their profit when this difference is favourable or their competitiveness otherwise. While this negative feedback mechanism is a source of instability that promotes oscillatory behaviour, our analysis identifies the critical features of the dynamics that are responsible for the asymptotic stability of the stationary states, both in their immediate neighbourhood and globally in phase space. Altogether, this study provides mathematical insights into the consequences of introducing feedback into buyer-seller interactions in such markets, with emphasis on identifying conditions for long term constancy of clientele volumes.