  In this work we propose and analyze a model which addresses the pulsing
behavior of sellers in an online auction (store). This pulsing behavior is
observed when sellers switch between advertising and processing states. We
assert that a seller switches her state in order to maximize her profit, and
further that this switch can be identified through the seller's reputation. We
show that for each seller there is an optimal reputation, i.e., the reputation
at which the seller should switch her state in order to maximize her total
profit. We design a stochastic behavioral model for an online seller, which
incorporates the dynamics of resource allocation and reputation. The design of
the model is optimized by using a stochastic advertising model from (16) and
used effectively in the Stochastic Optimal Control of Advertising (12). This
model of reputation is combined with the effect of online reputation on sales
price empirically verified in (9). We derive the Hamilton-Jacobi-Bellman (HJB)
differential equation, whose solution relates optimal wealth level to a
seller's reputation. We formulate both a full model, as well as a reduced model
with fewer parameters, both of which have the same qualitative description of
the optimal seller behavior. Coincidentally, the reduced model has a closed
form analytical solution that we construct.
