  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
{\em freshness} of a purchased product. The probability for buyer $n$ to select
seller $i$ is assumed to be $p_{n,i} \propto e^{ S_{n,i}/T}$, where $S_{n,i}$
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.
