Suchergebnisse

En este artículo se plantea un juego de competición política entre dos partidos, definido en un espacio de políticas unidimensional, como es la circunferencia unidad. Se estudian las posiciones de equilibrio de Nash en el juego planteado, para lo que se dan unas condiciones necesarias o suficientes de existencia de dichas posiciones de equilibrio. Primeramente, se trabaja con unos equilibrios restringidos analizándose cuáles de ellos dan lugar a equilibrios de Nash. El hecho de que puedan existir posiciones de equilibrio de Nash desventajosas para uno de los partidos, suscita la definición de un nuevo tipo de equilibrio, llamado equilibrio mínimo, caracterizándose las posiciones de equilibrio mínimo en el juego planteado. --- ABSTRACT --- This paper develops a political competition game between two parties. The aim of the game is for each party to attract the greatest possible weight of a weighted set of voters located on the unit circumference. The Nash equilibrium is studied in the proposed game. Firstly, restricted equilibria are employed, and an analysis of which of them will give rise to Nash equilibria carried out. The study of Nash equilibrium raises the definition of a new type of equilibrium: minimum equilibrium. To conclude, necessary and sufficient conditions for the existence of minimum equilibrium positions are given.

This paper considers an application of directional data to political science. A model is presented in which the political preferences of the type of voters of a population are represented as points of the circumference unit with the political parties searching for optimal positions on this in order to gain the most support of that finite set of voter types. Strategies have been developed to search for optimal positions in the case of one party and Nash equilibrium positions are found in the game with two parties. The results reveal how the different parties redirect their stances to adapt to changing situations generated by economic or social circumstances affecting citizen preferences.

This paper considers a problem of political economy in which a Nash equilibrium study is performed in a proposed game with restrictions where the two major parties in a country vary their position within a politically flexible framework to increase their number of voters. The model as presented fits the reality of many countries. Moreover, it avoids the uniqueness of equilibrium positions. The problem is stated and solved from a geometric point of view.

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.