Generalizing to an arbitrary number of brokers and categories,
and permitting each broker to myoptimally
update both its price and its interest vector,
we observe more complex analogs
of price wars, in which both prices and interest vectors are
drawn into limit cycles. In the spam regime,
the system tends to behave very wildly. When
is finite, the interest vectors can
display some metastability, but price wars
can develop even among brokers with different
interest vectors (if they overlap sufficiently).
Price wars are even a problem when 
.
Consider a system in this regime with
n brokers and n categories.
Such a system can accommodate each broker's
wish to be a monopolist in a single category.
If all categories
are preferred equally by the users, each broker will ultimately
specialize in a single unique category (even when is
somewhat more than 1) [10].
However, if the consumer population slightly favors
one category, a system
of niche monopolists is unstable, because each broker
will cut its price in an effort to own the favored category.
Simulations reveal that slightly less favored categories tend
to be available much less often than the consumer
population would like. Consequently, the total consumer
utility is often reduced during a price war, despite
the low prices [6].
Intuitively, any sort of economy consisting of myoptimal agents is likely to be plagued with price-war limit cycles. Geometrically, this behavior can be traced to the multi-peaked, discontinuous topology of the profit landscape, which in turn arises from the consumers' preference for the cheapest brokers. Of course, this does not imply that agent economies are doomed to failure. The assumption of myoptimality is unrealistic in several respects, and the fact that price wars occur relatively infrequently in human economies offers some hope.
The economics literature describes several possible mitigating effects that may explain why price wars are less than pervasive in human economies [15]. Expressed in terms of our model, these include explicit collusion among brokers, or tacit collusion -- using foresight to avoid triggering price wars. Other factors thought to hinder price wars include frictional effects (consumers may find it too costly or bothersome to shop around, and brokers may find it costly to update prices or change products too often) or spatial or informational differentiation (i.e. different consumers might value the same good differently, depending on their physical location or knowledge).
These mitigating factors are likely to be
weaker in agent-based economies than they are in human economies.
Explicit collusion might require fairly sophisticated
languages and protocols (and might be declared illegal!)
In large decentralized systems, efforts to employ foresight
may be hampered by imperfect knowledge of the system state and
the strategies of the other agents, and even if these are known
perfectly it may be computationally infeasible to predict the
future 
.
Consumer inertia may be greatly reduced
when agents rather than people are doing the shopping, and
price updates may be cheaper to compute and advertise.
Localization effects are likely to be much smaller
for information goods and services than they are for carrots
and carwashes. Given these considerations, it is
very possible that real agent economies will
experience price wars much more frequently than
do human economies.