A symmetry-breaking phase transition in a dynamical decision model

We consider a simple decision model in which a set of agents randomly choose one of two competing shops selling the same perishable products (typically food). The satisfaction of agents with respect to a given store is related to the freshness of the previously bought products. Agents select with a higher probability the store that they are most satisfied with. Studying the model from a statistical physics perspective, both through numerical simulations and mean-field analytical methods, we find a rich behaviour with continuous and discontinuous phase transitions between a symmetric phase where both stores maintain the same level of activity, and a phase with broken symmetry where one of the two shops attracts more customers than the other