|
B |
x1 |
12 |
22 |
12 |
22 |
17 |
10 |
5.35 |
0 |
0 |
5.77 |
|
x2 |
22 |
12 |
22 |
12 |
17 |
Note: D=difference between maximum and minimum, SD=standard deviation
The two scenarios are identical when considering both aggregate production Xt=Σi xit and
overall indexes of variability of individual actions, such as the mean of the difference, period
by period, between the maximum and minimum individual productions,
1T
D1V ∑ max {xt}- min {xt}
T t =1 i i
, or the standard deviation of individual actions xit (SD1). The
differences in the patterns of individual variability between scenario A and B can be captured
by splitting the overall individual variability into variability across agents (D2 and SD2) and
over time (SD3). In order to calculate agent-specific variability, first we compute the average
.-1
individual production over time xi = — ∑ xit and, using those data, compute the difference
T t =1
D2=max {Xi} - min {Xi} and the standard deviation for xi (SD2) (Table 2). Scenario A rates
ii
highly in terms of variability across agents, and that is referred to here as high individual
heterogeneity, while scenario B rates highly in terms of variability over time but exhibits no
individual heterogeneity.
When the same statistics developed for the example in Table 2 are applied to the simulation
results (Table 1), a remarkable level of individual heterogeneity emerges from the interaction
of ex-ante identical genetic algorithm agents (Result 3).
Result 3 (Individual heterogeneity with resource use)
Identical genetic algorithm agents (GAs) use the resource at significantly different rates.
Depending on the level of eXperience and of the measure adopted, between 45% and 80% of
the human individual heterogeneity is reproduced by GA agents. In particular, ineXperienced
GA agents have an heterogeneity levels in resource use SD2 not statistically different from
human agents.
12