In the information economy, buyer agents will also make strategic
choices based on economic considerations. We have explored
economic decision making by buyers within the context of the
shopbot model [17]. Suppose that there is a cost 
for obtaining
s price quotes. This might represent an intrinsic, implicit cost that
reflects the time and effort required to obtain the quotes, or
it may represent a real fee paid to a shopbot.
Then a rational buyer b would not blindly
adhere to a fixed search strategy. Instead, it would select
a search strategy 
to minimize the expected total cost
of the item plus the search cost 
, given current
market conditions.
By making the simplifying assumption that all sellers use the GT
pricing strategy, we have studied how the buyer strategy vector
evolves as a function of the costs . Suppose that
is a sublinear function of s. One plausible justification for
such a cost structure is that the first few quotes represent the
overhead of going to a shopbot in the first place; additional quotes
are relatively inexpensive because it takes little extra time to
obtain them. At any given time step, we assume that a small fraction
of buyers reconsider their strategy. Given the current GT price
distribution 
, which itself depends on the buyer
strategy vector, a buyer can compute the price it would expect to pay
as a function of the number of quotes s. Of course, this is a
monotonically nonincreasing function of s. On the other hand,
can be assumed to be a monotonically nondecreasing function of
s. Thus there is a balance point -- an optimal s that minimizes
the total expected expenditure. The buyers myopically switch from
their current strategy to the one that is currently optimal. The
sellers immediately readjust their distributions to reflect the
updated value of , and a new set of buyers responds in turn
to the updated .
Figure 4: Evolution of indicated components of
buyer strategy vector for 5 sellers, with
nonlinear search costs 
.
At any given iteration, 0.005 of the buyers reconsider
their strategy.
Final equilibrium oscillates with period 15 around a
mixture of strategy types 1, 2, and 3.
Previous research has shown that, if the search costs
are equal to some constant times s, then the system evolves to
an equilibrium in which only strategies 1 and 2 are present
[3]. However, as depicted
in Fig. 4, nonlinear search costs can lead
to non-equilibrium evolutionary dynamics in which strategies other than 1 and
2 can co-exist. In related experiments, we have found that the
buyer search behavior can be strongly influenced by the price
structure . The oscillations tend to grow in magnitude as the
fraction of buyers that switch
strategies at each time step grows, and the period can become
shorter. Furthermore, different initial conditions can lead
to very different final equilibria or limit-cycle attractors.