In order to understand the implications of widespread
adoption of shopbots and pricebots, we have modeled
a simple market in which S sellers compete
to provide B buyers with a commodity,
such as a specific book. 
The objective of each seller s is to set its price 
so as to
obtain the maximum profit, given a production cost r. Each buyer b
behaves in a very simple way: it compares 
prices and purchases
the good from the seller that charges the least, provided that the
price is less than the buyer's valuation 
. Assuming that the
search strategy and the valuation are uncorrelated, the
buyer population can be represented by a strategy vector w (the
component of which represents the
fraction of buyers that compare i prices) and a valuation
distribution 
. The strategy vector w may be fixed
exogeneously -- for example, 25% of the population may shop
manually, just trying a random seller and buying if the price is right
(s=1) while the remaining 75% may use a shopbot to search
all sellers' prices (s=S). Alternatively, if buyers
set their search strategies so as to minimize the expected cost
of the good plus the cost of the searching, endogeneous forces
may cause w to evolve over time.
In the next three subsections, we explore a few points in a broad spectrum of possible utility maximization strategies that sellers, buyers, or shopbot intermediaries might employ in a competitive environment, focusing on collective phenomena that arise from various strategy choices.