vice versa. This mutation procedure is quite standard in the GA literature. For a mutation rate
pm, the corresponding experimentation level is p=1-(1-pm)L, where L is the number of digits
of the binary string. In the simulations we adopt a mutation rate pm=0.02 with L=8 that
corresponds to an expected fraction of new strategies due to experimentation p=0.1492 of the
total in the memory set. The range of values used in the GA literature is quite wide, and our
experimentation level does not appear particularly elevated. Consider for example the
following four studies: Arifovic (1996) uses two sets of parameters, L=30 with pm=0.0033,
or pm=0.033, which translates into p=0.0944 or p=0.6346, respectively; Andreoni and Miller
(1995), L=10, pm=0.08 with exponential decay and half-life of 250 generations, which
translates into p=0.5656 for the first period of the simulation and p=0.0489 for period 1000;
Bullard and Duffy (1998), L=21 with pm=0.048: p=0.6441; and Nowak and Sigmund (1998)
a direct experimentation rate of p=0.001.
As noted, the parameter L influences the experimentation rate. Its level was set at L=8
before running the simulations in order to establish a reasonably thin grid of the strategy
space, and then was maintained constant throughout. The strategy space [0,50] is divided into
a grid of 255 points (28-1), which corresponds to steps of about 0.2 units. In the experiment
with human agents any real number could be chosen. However, in practice, 87% of the
actions inputted were integer numbers. The grid chosen can accommodate the level of
accuracy in decision making of the laboratory data.
After mutation rate and string length, the third parameter that will be discussed in this
Section is the crossover rate. The crossover operator works in two steps: first, it randomly
selects two strategies out of a population; second, selects at random an integer number w
from [1, L-1]. Two new strategies are formed by swapping the portion of the binary string to
the right of the position w. In general, not all strategies in the population are recombined
using the crossover operator; instead crossover is carried out with some probability, pc,