Here, we augment our previous work (see [9]) on simulations
of 2 pricebots of matching types by assuming the uniformly distributed
buyer valuations introduced in Section 3. If we
consider 2 GT pricebots, simulations verify that the cumulative
distribution of prices closely resembles the derived F(p), to within
statistical error. The time-averaged profits for each seller were
0.0319, nearly the theoretical value of 0.03125. When 2 pricebots
use the myoptimal pricing strategy, cyclical price wars result
(see [9]). The myoptimal sellers' expected profits averaged
over one price-war cycle are given by
,
which is equal to 0.0893. Simulation results closely match this
theoretical value with an average profit per time step for MYs of
0.0892, nearly thrice the average profit obtained via the
game-theoretic pricing strategy.
In related work (see [9]), assuming all buyer valuations
to be equal, the behavior of DF pricebots tended towards what is in
effect a collusive state in which all prices approached the
monopolistic price. In this study, 2 DF pricebots once again track
one another closely; in doing so they accumulate greater profits than
either 2 myoptimal or 2 game-theoretic pricebots. The effect of
uniformly distributed buyer valuations is nonetheless apparent in
substantial fluctuations in price, ranging from approximately 0.15 to
0.55 -- the upper bound of which is above the monopolistic price
-- rather than remain in the neighborhood of the monopolistic
price. Specifically, DF pricebots achieved time-averaged profits of
0.1127.