In this section we illustrate desirable and undesirable phenomena that can occur in our news filtering economy. First, we define the state of the system, from which any desired aspect of behavior can be derived. Then, we derive the state and behavior of simple systems with a few well-informed brokers and an infinite number of consumers. Finally, we simulate a system of many brokers and consumers with limited knowledge of the system state, and show that it can self-organize into a configuration that is beneficial to brokers and consumers alike.
We define the state of the system at time t, 
,
as the collection of broker prices 
, broker interest vectors 
,
and the subscription topology matrix S. Our goal is
to understand the evolution of , given
(i) an initial configuration 
;
(ii) the values of the various extrinsic (possibly time-varying)
variables: the category prevalences 
, the costs 
,
, and 
, the consumer value V, and the consumer interest
vectors 
; and
(iii) the algorithms used by each agent to dynamically modify those
variables over which it has control, including
specification of a) the
state information accessible to the agent and b) the times at which the
modifications are made.
Any desired individual or aggregate aspect of behavior
can be extracted from the history of
and the extrinsic variables.
Two particularly important
quantities are the expected utility per article
for consumers and brokers.
It can be shown that the expected utility per article 
for consumer c is
given by:
where 
is the step function: 
for
x>0, and 0 otherwise. The product term in large parentheses is the
probability that an article in category j is not offered by any
broker for a price less than . The term in square brackets
is the expected value of an article in category j: it always costs
the consumer to process it, regardless of its worth, and with
probability consumer c will pay to receive information
worth V.
The appropriate utility function for the broker is its expected profit per article, given by:
