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We introduce and mathematically study a conceptual model for the dynamics ofthe buyers population in markets of perishable goods where prices are notposted. Buyers behaviours are driven partly by loyalty to previously visitedmerchants and partly by sensitivity to merchants intrinsic attractiveness.Moreover, attractiveness evolve in time depending on the relative volumes ofbuyers, assuming profit/competitiveness optimisation whenfavourable/unfavourable. While this negative feedback mechanism is a source ofinstability that promotes oscillatory behaviour, our analysis identifies thosecritical features that are responsible for the asymptotic stability ofstationary states, both in their immediate neighbourhood and globally in phasespace. In particular, we show that while full loss of clientele occurs(depending on the initial state) in case of a bounded reactivity rate, itcannot happen when this rate is unbounded and merchants resilience alwaysprevails in this case. Altogether, our analysis provides mathematical insightsinto the consequences of introducing feedback into buyer-seller interactionsand their diversified impacts on the long term levels of clientele in themarkets.

Population dynamics in fresh product markets with no posted prices