First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

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).