  We discuss a non linear extension of a model of alliances in politics,
recently proposed by one of us. The model is constructed in terms of operators,
describing the \emph{interest} of three parties to form, or not, some political
alliance with the other parties. The time evolution of what we call \emph{the
decision functions} is deduced by introducing a suitable hamiltonian, which
describes the main effects of the interactions of the parties amongst
themselves and with their \emph{environments}, {which are }generated by their
electors and by people who still have no clear {idea }for which party to vote
(or even if to vote). The hamiltonian contains some non-linear effects, which
takes into account the role of a party in the decision process of the other two
parties. Moreover, we show how the same hamiltonian can also be used to
construct a formal structure which can describe the dynamics of buying and
selling financial assets (without however implying a specific price setting
mechanism).
