One realm in which economically-motivated software agents may play an important role is information filtering. Imagine an information source (perhaps a newsgroup or newsfeed) that produces a continual stream of articles in a wide variety of categories. Consumers, who are typically interested in only a very small subset of the categories, can avoid the high cost of receiving and examining a torrent of mostly irrelevant articles by subscribing to one or more brokers who purchase selected articles from the source and resell them to consumers. In such an environment, different consumers will be interested in different categories. Thus the market will be horizontally differentiated [29].
In our model of an information filtering economy [12, 18, 19],
consumers experience a processing cost 
for each article that
they receive, and pay an additional fee 
when they decide to
consume an article offered by a broker b. Consumers hold a relevant
article to be worth V, and an irrelevant one to be worth
nothing. Broker b experiences a cost 
for delivering an article
to each consumer. Each broker b controls its price and its
selection of categories (which can be thought of as its ``product'').
Consumers choose the set of brokers to which they subscribe, with
brokers retaining the right to refuse subscriptions from consumers who
appear unprofitable. Consumers seek to subscribe only to brokers
whose selection of categories overlaps well with their own interests.
Conversely, brokers wish to serve only consumers who are likely to be
interested in their categories -- otherwise they incur the cost
with little hope of being recompensed. Given the goals and
capabilities of the consumers and brokers, we wish to understand the
evolution of the brokers' prices, category selections, and profits and
the consumers' broker selections and utilities.
For simplicity, assume that the aggregate demand for each category is
exactly the same. Then, when there is just a single broker, all that
matters is the number of categories it offers, not their
identities. Analysis [12] shows that the broker can
maximize its profit by offering 
categories at a price ,
where and depend on the costs and .
Figure 7: Optimal number of categories for monopolist broker to
offer as a function of 
and 
, with 
.
As illustrated in Fig. 7, three broad behavioral
regimes are observed. When 
, is zero. In this
``dead'' regime, an article costs more to send and process than it is
worth, even if the consumer is guaranteed to be interested in it. No
articles will be bought or sold. At the other extreme, when the costs
are sufficiently low ( 
, where 
is the average
fraction of articles that are relevant to a typical consumer), the
broker is motivated to offer all categories, i.e., 
. In real information filtering applications, one
expects to be quite small, since each consumer regards most
information as junk. It is useful to think of
as a (presumably tiny) spam regime, in which it costs so little
to send information, and the financial impact on a consumer of
receiving junk is so minimal, that it makes economic sense to send all
articles to all consumers. In between these two regimes, the optimal
number of categories is finite.
When there is more than one broker, each will attempt to set its price
and its category set (its product) optimally, taking into account both
consumer demand and the current prices and categories offered by its
competitors. In principle, the myoptimal strategy can be applied in
the large space of possible prices and products: knowing
consumer demand and other competitors' price and product parameters, a
broker could choose a myopically optimal price and product. In
practice, an exhaustive search for the optimal point in price/product
space is only feasible for small numbers of brokers and categories, as
the number of possible choices for each broker is 
, where N
is the number of possible prices.
A more practical variant of the myoptimal strategy [19] replaces the exhaustive search with a limited search in which a fixed number of hypothetical price/product values are considered, and the one yielding the highest expected profit is selected. Candidate price/product values are generated in two ways, neither of which uses information about any of the consumers or other brokers: either by incremental changes to current parameter values or (less frequently) by choosing values completely at random.
Using this variant of the myoptimal algorithm, we simulated a system
of 5 brokers, 5 categories, and 1000 consumers. The aggregate consumer
demand for each category was identical. With and chosen
such that 
, i.e., a monopolist broker would prefer to
offer a single category, the system eventually evolves to a
niche-monopoly state in which each broker offers one distinct
category. The system is perfectly specialized, and consumer utilities
and broker profits are both maximized. A
similar state is reached when and are decreased somewhat
to values such that 
. Evidently, competition creates an
additional pressure to specialize. In both experiments, the transient
period was characterized by rampant competition and undercutting, but
the system stabilized once it reached the fully specialized
state. Finally, we lowered and to values in the spam
regime, i.e. a monopolist would prefer to offer all five
categories. In this case, competition never ceases, although it does
cause the average number of categories offered by the brokers to drop
from 5 down to 2.1.
When the aggregate demand is not identical for all categories, the
system is susceptible to cyclical wars in price/product space. Even
when , the niche monopoly state is unstable because the broker
occupying the most profitable niche is vulnerable to undercutting by
other brokers that willingly abandon their own niches.
Figure 8 illustrates such a situation.
There are three myoptimal brokers that may offer any combination
of three categories. Prices are quantized such that there are
501 possible prices ranging from 0 to 1. Thus, every time a
broker re-evaluates its price and product choice, it does an
exhaustive search over 4008 possibilities.
In the depicted simulation run, each broker started from the same initial state (0.480,111), i.e., each charges P=0.480 for an offering that includes categories 1, 2, and 3. After a brief initial transient in which two brokers compete for the (100) configuration (specialization on category 1), the system enters a cycle consisting of two price wars. The cycle begins with a short-lived competition between two brokers for the (010) configuration. When the price drops a bit, the (101) niche occupied by the third broker becomes more attractive, and all three brokers compete for this niche until the price drops a bit below 0.54, at which point a broker discovers that sole possession of (010) is more profitable. But as soon as it does, a second broker makes the same discovery, and the price war begins anew. (There are minor variations from one cycle to the next because the order in which the brokers re-evaluate their parameters is completely random.)
Figure 8: Price and niche war timeseries: 
vs. t for 3 myoptimal
brokers and 3 categories, with 
, V=1.
During the price wars, consumers who prefer less popular categories may suffer because no brokers are satisfying their needs. Thus, despite somewhat lower prices in favored categories, the aggregate consumer utility is often reduced during price and product wars.
The situation is improved when brokers use the myoptimal variant in which the search over the space of possible choices is limited to a small number of candidates clustered mainly in the vicinity of the current choice. In this case, we observe that the niche monopoly can be metastable. In other words, specialization can occur and it can persist for long periods of time. Eventually, the period of calm and prosperity will be disturbed when a broker in a less profitable niche discovers that it can improve its profits (temporarily) by abandoning its niche and undercutting another broker. After a tumultuous round of competition, the brokers again settle into a niche monopoly, and peace and prosperity reign again for a while [19].