| Sumario: | This thesis presents the fruit of 3 years of research. During this time 3 works were developed,
each one with its own mathematical formulations and results. These works are, of
course, related to each other and will be further developed in the near future.
The first work of this thesis is presented in chapter 1 and addresses the problem
of defining an optimality criterion for a semi-public company in a semi-mixed duopoly
model. Here, we have two agents competing, the semi-public company and a private firm,
both producing a homogeneous good to satisfy the demand in the market. The private
firm, as usual, seeks to maximize its net profit, while the semi-public company has a
commitment to watch over the economy of the population, but at the same time, does
not neglect its own profit. The compromise between these two objectives for the semipublic
company is described by a parameter β ∈ (0, 1], where β → 0 represents that the
semi-public company thinks only for its own net profit, and β = 1 represents that the
semi-public company cares solely for the economy of the population without seeking its
own benefit.
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