Information Technology Reference
In-Depth Information
40
40
Most Connected Modified ZIP
Least Connected Modified ZIP
Most Connected Standard ZIP
Least Connected Standard ZIP
Modified ZIP
Standard ZIP
35
35
30
30
25
25
20
20
15
15
10
10
0
50
100
150
200
250
300
350
400
0
50
100
150
200
250
300
350
400
Time
Time
Fig. 2.
Absolute deviation from optimum price averaged over 40000 runs for (left) the most and
least connected agent in each experimental condition, and (right) for the single monitored agents
in markets designed to control for learning rate
number of traders will suffer (although these agents may in some sense be of above
average “importance”).
Before discussing these results further, a slight bias introduced by the adaptive learn-
ing rate scheme must be dealt with. Although the adaptive learning rate is constrained
to lie within the same bounds that constrain regular ZIP agents, the average learning
rate employed by the adaptive ZIP agents is higher than that of standard ZIP traders.
Recall that there are a greater number of weakly connected agents than strongly con-
nected agents. In the case of the weakly connected agents, nearly all of their neighbours
will be at least as well-connected, if not better-connected. This means that the typical
learning rate employed by an agent will rarely be below the population mean. As a re-
sult, the average learning rate of these agents is increased, so faster convergence is not
necessarily surprising. In order to demonstrate that the modified rule has an effect on
convergence above that which would be expected to result from a simple increase in
average learning rate, a further study was designed.
Two equal-sized groups of standard ZIP agents are initialised, the first group forming
a completely connected clique, while the second forms a minimally connected ring. The
quality of information being exchanged in the first group should, therefore, tend to be
much higher than that being trafficked in the second group. A final modified ZIP trader
with an equal number of connections to random agents within each group is added to the
market. This agent does not make any shouts, nor respond to shouts. It simply adapts its
valuation based on the information it hears. This study was run under two conditions:
using a standard ZIP algorithm for the final agent, or using the adaptive learning rule
instead. In the second condition, the connections from the final agent to the rest of the
market are ignored by the adaptive learning rate rule, as they are never used to convey
information
to
the market.
In the second condition, it is possible to set the number of connections from the final
agent such that its average learning rate is equal to the average learning rate of a standard
ZIP agent (0.3 in the studies reported here). The learning rates of the modified ZIP
traders lie within the range [0
.
1
,
0
.
5]. The following equation for the average adaptive
learning rate,
η
(
n
), for a modified ZIP trader with
n
neighbours may be written given
that all agents within each of the two groups share the same connectivity and the final
agent has an equal number of connections to each group.
