Appendix: List of Symbols

: the cost of delivering articles to consumer i.

F: subscription fee.

f: normalized subscription fee = F/N.

: Any nonlinear function for .

G(q;w): cumulative distribution function of g(q;w).

g(q;w): the probability density function from which the consumer valuations w are drawn. q is the distribution parameter which may vary from one consumer to another.

h(r;q): the probability distribution for the consumers' q parameter. r is the distribution parameter.

i: index of consumers as in consumer i.

j: index of valuations as in .

K: set of articles.

k: index of articles; .

M: total number of consumers in the system.

m: proportion of subscribing consumers.

N: number of articles generated by the producer in each subscription period.

n: dimension of problem space as in .

: the price schedule = .

P(k): the price charged for a subset of of the N articles.

: the vector of probabilities that any k is the expected surplus maximizing number of articles.

q: the distribution parameter in g(q;w).

r: the distribution parameter in h(r;q).

s: consumer surplus.

t: index of the subscription period.

: consumer valuation of article j.

x: .

: reflection coefficient in the amoeba algorithm.

: expansion coefficient in the amoeba algorithm.

: normalized production cost assuming linear production cost; .

: normalized price-per-item assuming linear price schedule; .

: contraction coefficient in the amoeba algorithm.

: simplex shrink/expand coefficient in the amoeba algorithm.

: hard threshold function. Equals 1 if consumer i subscribes, else it is 0.

: parameter for the exponential distribution of consumer valuations; .

: normalized expected profit; .

: expected profit.

: the mean of the N valuations received during the subscription period t.

: the consumer's ``flightiness'' factor.