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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 politicalalliance with the other parties. The time evolution of what we call \emph{thedecision functions} is deduced by introducing a suitable hamiltonian, whichdescribes the main effects of the interactions of the parties amongstthemselves and with their \emph{environments}, {which are }generated by theirelectors 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, whichtakes into account the role of a party in the decision process of the other twoparties. Moreover, we show how the same hamiltonian can also be used toconstruct a formal structure which can describe the dynamics of buying andselling financial assets (without however implying a specific price settingmechanism).

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