Can genetic algorithms explain experimental anomalies? An application to common property resources

distribution on the strategy space [0,50] and then aggregated to compute total resource use,
x^~_i ~U[0,50] with x^~_i iid. The outcome from zero intelligence agents is not reported as a viable
alternative model to explain the data but to provide a benchmark for the GA results, with
special reference to individual heterogeneity. With twice as much aggregate variability
(D2ZI=40.25 vs. D2GA=18.10, Figure 2B), zero intelligence agents are characterized by half

as much individual heterogeneity than GA agents (D2ZI=7.93 vs. D2GA=18.97, Figure 2C).

A fairer evaluation of the impact of randomness in a GA comes from a comparison with

Noisy Nash agents. Noisy Nash agents behave in the same fashion as ZI with probability p

and are best responders to other Noisy Nash agents with probability (1-p),
with prob = p

. NN agents - in the same way of the classical model -
with prob = 1 - p
understand the concept of Nash equilibrium and are able to compute it, but they occasionally
exhibit trembling hand behavior.¹⁰ The level of trembling hand p is set at the same level as
the innovation level of GA agents. The comparison between GA and NN is more intriguing.
The simulation results for efficiency and aggregate variability are not far from the GA results,
but individual heterogeneity is rather small (D2NN=4.22), less than one-quarter the GA level
and less than one-sixth the human agent level. This latter result suggests that the innovation
level is not related to individual heterogeneity in a simple, monotonic fashion. What drives
individual heterogeneity in GA agents is not mainly the random element but the individual

,A                 .           1 l ê              » 1     »               . .                    -

¹⁰ For NN, x_i = 72-— (N-1)1 p — + (1 -p)x_i I, X₁ =14.82; with p=0.1492, E[X₁ ]=16.34 and E[X]=130.70.

There are at least two other options to model Noisy Nash. One model involves ZI agents with probability p and
x*_i=16, the symmetric individual Nash, with probability (1-p). Unlike the chosen model, the behavioral
assumption in this model is that when sane, the agent is not aware that with probability p she is subject to
trembling hand and hence E[xi]=(1-p) 16+p 25=17.34 and E[X]=138.74. Another model involves ZI agents
with probability p and x*i=Best response to E[X-i,t-1] with probability (1-p). This latter model is unstable
because of the aggregate overreaction to the temporary off-equilibrium situation.

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