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This paper introduces a problem related to decision-making and the shaping of political strategies in the course of one term of office, in which the government and the opposition shape their proposals for action on two issues that are relevant for the citizens. A variable component is considered regarding both the relevance of the issues to be dealt with and the strategies that the parties are presumed to adopt. The aim of this study is to find the optimum strategies for the two majority parties of a country, while allowing them to vary their proposals to a certain degree. In addition, the process is dynamic because the proposals are intended to be modified taking into account the other party's foreseen action. The contribution of this article lies in this approach, as well as in its taking into account variable components. The problem is dealt with from a geometric point of view, and a search algorithm to find optimum strategies is developed.