Who to Listen to: Exploiting Information Quality in a ZIP-Agent Market - Agent-Mediated Electronic Commerce - page 204

margin is the amount by which they wish to undercut their limit price to make a trade,
and in the case of sellers, it is the amount by which they wish to exceed there limit
price. When a ZIP trader shouts, the price is constrained by its limit price and profit
margin. The agent uses the market's response to its activity (and the observable activity
of others) to update its profit margin. For instance, buyers observe the bids made on the
market and whether they are accepted or not and adjust their profit margin accordingly
(for full details of this algorithm, see [4]). The ZIP algorithm employs the Widrow-
Hoff learning rule with momentum [11] to adapt these profit margins throughout each
agent's lifetime—maximising for each agent the possibility of making a profitable trade.
This learning rule allows the agents to rapidly converge on the optimal price, while the
momentum term allows blips in the market to be ignored. Unlike ZI-C, ZIP agents are
capable of finding the market equilibrium under a wide range of supply and demand
schedules.
Here, each ZIP agent was initialised with a random profit margin drawn from a uni-
form distribution [0 . 05 , 0 . 35]. Each agent was also initialised with a random learning
rate drawn from a uniform distribution [0 . 1 , 0 . 5] and random momentum value drawn
from a uniform distribution [0 . 2 , 0 . 8].
3In ialR su s
Experiments were performed using markets populated by 100 ZIP traders. Each agent
was randomly allocated a limit price in the range [100 , 200], and either the ability to
buy one unit or sell one unit of an unnamed indivisible commodity. Each market sim-
ulation lasted for 400 time steps. Markets were constrained by networks, constructed
as described above, with P =1 . 5 and m =10, and all markets operated through the
continuous double auction mechanism.
Figure 1(left) shows the price deviation from the theoretical optimum averaged over
forty thousand repetitions. Each agent's valuation was obtained at each time step of
each repetition, and the average calculated. Notice that timeseries are shown for agents
with connectivity rank ranging from 1 s t (most well-connected) to 100 t h (least well-
connected). Over time, the average price shouted by all agents, regardless of connec-
tivity, approaches the equilibrium price. This is to be expected, as it is a fundamental
property of markets that they tend to converge to equilibrium. The agents do not all
converge at the same rate, however. Those agents who have most connections converge
fastest. Agents who are more connected receive more frequent information and so have
a better impression of the state of the market. They are, therefore, better able to accu-
rately judge the equilibrium price.
Agents converge on a market price that deviates from the equilibrium price. This is
due to the allocation of supply and demand. As the market converges, it will become in-
creasingly difficult for agents who have been allocated limit prices beyond the market's
theoretical equilibrium price to find partners prepared to trade with them. Since agents
cannot alter their limit price, and are not prepared to trade at a value below it, some
will effectively price themselves out of the market. Indeed, some agents will be unable
to trade despite the presence of willing partners in the market as a whole, because they
will not have a neighbour prepared to trade with them.