Symmetry restoration by pricing in a duopoly of perishable goods

摘要

Competition is a main tenet of economics, and the reason is that a perfectly competitive equilibrium is Pareto efficient in the absence of externalities and public goods. Whether a product is selected in a market crucially relates to its competitiveness, but the selection in turn affects the landscape of competition. Such a feedback mechanism has been illustrated in a duopoly model by Lambert et al in which a buyer's satisfaction is updated depending on the freshness of a purchased product. The probability for buyer n to select seller i is assumed to be p(n,) (i) proportional to e(Sn, i/T), where S-n,S- i is the buyer's satisfaction and T is an effective temperature to introduce stochasticity. If T decreases below a critical point T-c, the system undergoes a transition from a symmetric phase to an asymmetric one, in which only one of the two sellers is selected. In this work, we extend the model by incorporating a simple price system. By considering a greed factor g to control how the satisfaction depends on the price, we argue the existence of an oscillatory phase in addition to the symmetric and asymmetric ones in the (T, g) plane, and estimate the phase boundaries through mean-field approximations. The analytic results show that the market preserves the inherent symmetry between the sellers for lower T in the presence of the price system, which is confirmed by our numerical simulations.