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lead both to learning convergence and to economic meanings. Due to the proportional
update mechanism of the strategy selection probability (see Section 4), this is a real
system convergence and not a fictitious one induced by a cooling parameter. We also
observe that at the aggregate the learning process achieves an equilibrium that corre-
sponds to a local optimum rather than to a global one, as the PUN and LMP dependent
both on profits (i.e. payoffs) and on strategy spaces. Similar fictitious results have been
already discussed for the Roth-Erev algorithm in a simplified agent-based electricity
model (see [14]) as well as for Q-Learning (see [24]). Furthermore, in the case of VRE
learning algorithm the shape of the curve suggests that although the probabilities of
strategy spaces of the agents have been updated during the simulation, prices at the
beginning of the simulation are the same as at the end. This directly points out that
agents have not learnt any preferred strategy (i.e. there is no convergence) and leads to
a ”random noise shape” of the prices, as discussed in [14]. It is worth remarking that
these results further point out effectiveness of the proposed Enhanced Roth and Erev
algorithm (with the respect to the other state-of-the-art version proposed by the liter-
ature) and its direct applicability to economic and financial context characterized by
positive, null and negative rewards. Finally, the complete 24 hours PUNs of Wednesday
16th December 2009 have been simulated. Again, we have performed 100 computa-
tional experiments (each with a length of 5,000 steps) with different random seeds in
order to analyze the ensemble results of the same repeated game. It is worth remark-
ing, that the energy market is characterized by a strong seasonality (i.e., daily, weekly,
and yearly), therefore the strategic behavior of Gencos can be properly studied on a
daily base. Figure 9 compares the GAPEX simulated PUNs to the GME real PUNs.
Figure 9 points out that the simulated results are in good agreement throughout the
whole 24 hours. Indeed, most of the GME real PUNs fall within the 95 percent (i.e.,
2*
σ
) confidence band evaluated over the 100 computational experiment whereas the
outliers are however quite close to the limit of the 95 percent confidence band. This
further states the quality and importance of the proposed methodology which is mostly
able to replicate the aggregate results by means of the strategic interactions of the Gen-
cos rather than of a black-box forecast. Understanding the origin of the market results
is a crucial element from an economic point of view as it allows us to determine the
drivers and model of the power exchange. Every policy measure, antitrust action and
market design requires a clear understanding of these elements in order to be effec-
tive. Furthermore, it is worth noting that in the case of the computational experiments,
the generation universe is kept fixed with cost functions unchanged for the whole 24
hours. This has been assumed in order to evaluate the ability of the learning algorithm
for selecting the most profitable strategy in different condition of demands. However,
such condition is not present in the real GME market sessions as the generation plants
are characterized by outages. The absence of outages in the computational experiments
can explain the small difference between GAPEX simulated PUNs to the GME real
PUNs and it is worth noting that including outages in the GAPEX is easy and direct.
However, such an interesting scenario for computer science results of limited interest
from an economics perspective. Indeed, it is characterized by such a large
ex
ante
information (the exact information of the hourly participation of the Gencos to the
power auction) that it results practically irrelevant and for this reason it has not been
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