Imagine a product with a single attribute that can be mapped into some notion of ``quality''. In other words, in the absence of any price differentials, all buyers would agree on which of two different values of that attribute was the more desirable. Examples of such an attribute might include processor speed, network communication rates, or monitor resolution. Of course, different buyers would have different tradeoffs between price and quality, represented as a utility function.
Suppose that each seller offers the product at a single
level of quality, and that all buyers survey each
seller's price and quality and choose the one that
maximizes their utility.
Then, if buyers are
sufficiently sensitive to prices, cyclical price wars
such as that illustrated in Fig. 6
can be observed when sellers use the myoptimal algorithm
to adjust prices but keep their qualities fixed.
At the beginning of the cycle, there are two independent
price wars: one between those with qualities Q=1.0 and
Q=0.9 and another between those with Q=0.5 and Q=0.35.
Suddenly, near time 125, the high-quality sellers suddenly
drop their prices to join the other price war. The net result
is that Q=1.0, Q=0.9 and Q=0.5 wind up in a
price war, while Q=0.35 drops its price still lower,
initiating a second price war with Q=0.25. This rather
complex cycle begins anew around time 175.
Figure 6: Price vs. time for five myoptimal sellers of qualities
Q equal to 1.0, 0.9, 0.5, 0.35, 0.25.
As in the shopbot model, a society of five derivative followers will maintain higher average prices and profits [24]. However, just as before, myoptimal pricing can take advantage of derivative following, so there will be a strong incentive to adopt myoptimal pricing even if this leads to lower profits when adopted by all sellers. When the myoptimal sellers control both their quality level and their price, several different cyclical phenomena can occur. These include cyclical prices with fixed qualities, cyclical qualities with fixed prices, and simultaneous cycling in both prices and quality.