The three economic models studied here are described in detail elsewhere . At each time step, the consumers buy the lowest-priced product subject to constraints of a maximum allowable price and a minimum allowable quality. Such asymmetries can result in unending cyclic price wars when the sellers employ myoptimal pricing strategies. To the extent that the categories overlap, there can be direct price competition, and to the extent that they differ, there are asymmetries that again lead to the potential for cyclic price wars. In this model, the sellers' products are identical, and their profit functions are symmetric.
Myoptimal pricing leads the sellers to undercut each other until the minimum price point is reached.
At that point, a new price war cycle can be launched, due to asymmetric buyer behavior, rather than seller asymmetries. An example seller profit function, taken from the Price-Quality model, is plotted in figure 1 . This shows the instantaneous profit for seller 1, . For small , the peak profit is obtained at , whereas for larger , there is eventually a discontinuous shift to the other peak, which follows the parabolic-shaped ridge along the diagonal. The Information-Filtering and Shopbot models also have similar profit landscapes.