  We consider a novel formulation of the dynamic pricing and demand learning
problem, where the evolution of demand in response to posted prices is governed
by a stochastic variant of the popular Bass model with parameters $\alpha,
\beta$ that are linked to the so-called "innovation" and "imitation" effects.
Unlike the more commonly used i.i.d. and contextual demand models, in this
model the posted price not only affects the demand and the revenue in the
current round but also the future evolution of demand, and hence the fraction
of potential market size $m$ that can be ultimately captured. In this paper, we
consider the more challenging incomplete information problem where dynamic
pricing is applied in conjunction with learning the unknown parameters, with
the objective of optimizing the cumulative revenues over a given selling
horizon of length $T$. Equivalently, the goal is to minimize the regret which
measures the revenue loss of the algorithm relative to the optimal expected
revenue achievable under the stochastic Bass model with market size $m$ and
time horizon $T$. Our main contribution is the development of an algorithm that
satisfies a high probability regret guarantee of order $\tilde O(m^{2/3})$;
where the market size $m$ is known a priori. Moreover, we show that no
algorithm can incur smaller order of loss by deriving a matching lower bound.
Unlike most regret analysis results, in the present problem the market size $m$
is the fundamental driver of the complexity; our lower bound in fact, indicates
that for any fixed $\alpha, \beta$, most non-trivial instances of the problem
have constant $T$ and large $m$. We believe that this insight sets the problem
of dynamic pricing under the Bass model apart from the typical i.i.d. setting
and multi-armed bandit based models for dynamic pricing, which typically focus
only on the asymptotics with respect to time horizon $T$.
