We assume that producers cannot track individual consumers across
transactions, and that the producer is either unable to observe the
number of articles read by a consumer, or to gain any advantage by
using such information. We choose these somewhat idiosyncratic
assumptions so that an informed producer can do no better than offer
all consumers the same price function, rather than delving into the
complexities of price discrimination. In addition, in this paper we
wanted to limit producers to ``model-free'' learning; that is, trying
to learn profitable strategies without an explicit model of consumer
preferences. There are several motivations for this. A producer
will generally not know the true model generating consumer
preferences, and might find it too expensive or error-prone to try to
estimate the model. Also, the environment might be changing
sufficiently quickly (through consumer exit and entry or preference
changes) that the producer is never able to learn enough about the
form of preferences to be useful. Our assumptions limit producers to
trying to learn the shape, or even just the peak, of the profit
landscape that derives from consumer preferences, without discovering
the underlying preferences.
For now we assume that producers know the distribution of consumers'
's. There is nothing to
learn, and both preferences and production costs are independent over
time, so the problem simplifies to a once and for all determination
of the profit maximizing price schedule. The same schedule will be
offered in all subsequent periods.
Since consumers are anonymous and they believe the value of each
article is drawn from an identical distribution, the producer's
optimal behavior is to base prices solely on the number of articles
purchased, q, for a price schedule T(q). The most general form
of this schedule would be to set an independent payment T for every
possible quantity, 
. However, N may be large, and
for reasons described above, producers may find it unprofitable to set such a
large number of price schedule parameters. Therefore, we explore
producer pricing behavior when it limits itself to functions
expressible with small numbers of parameters. For each price schedule
we derive the optimal parameter choices for the producer, and evaluate
the resulting profits, consumers' surplus, and social welfare (sum of
the prior two measures).