\section{Conclusions and future work}
\label{sec:7}

In this article we presented an algorithm for the stabilization 
of retail and wholesale prices in the energy market, based on the main result provided 
in \cite{Sanjoy2}. In particular, we obtained a superior bound to
the control parameter ($\gamma$) which ensures local convergence. \\
In order to maximize the 
convergence rate, we tried some fitting functions to estimate the unknown
$\dot v(x)$, and we compared them through numerical simulations.
Afterwards, we modified the previous algorithm
in order to steer to zero the ISO total revenue, according to the non--for--profit nature of the operator.\\
Adding some noise to the consumer behaviour, we noticed from simulations
that the stability of the algorithm still holds.\\
Finally, in the last section, we tested the first algorithm varying
the consumers' value functions, in accordance with the different 
moments of the day, and then introduced a weighting factor, to
simulate a periodic demand.\\
Future developments to the presented framework may involve
effects of production uncertainties and more realistic models that 
take into account physical constraints, possibly testing different 
classes of cost and value functions.\\
Other extending directions may include a more
realistic variation of the consumers' value functions, 
and, in this context, the development of an algorithm to steer to zero the ISO revenue.

