No abstract

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.

Spatial models of two-player competition in spaces with more than one dimensión almost never have pure-strategy Nash equilibria, and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to avoid the uniqueness of the equilibrium position. As a result, a "región of equilibrium" appears, which can be located by geometric methods. In this área, the players can move around in an "almost-equilibrium" situation and do not necessarily have to adopt the same position.

The study presented makes an original, new and exhaustive analysis of the adaptation of a classical board game which has been named Binary Who is Who? This proposal shows a very useful tool for the consolidation of mathematical concepts related to the study of real-valued functions that are treated in the different levels of the teaching of mathematics (first and second year of superior secondary studies and the first years of some university degrees). The use of games as a means for learning is the authors’ proposal. The aim is to offer teachers the chance of using the games as a method of teaching mathematical concepts, as well as a motivating instrument for them. This game has been created to be played face-to-face in the classroom and it has also been programmed to create a video game which allows the students to play virtually.

This paper proposes a new algorithm (DA3DED) for edge detection in 3D images. DA3DED is doubly adaptive because it is based on the adaptive algorithm EDAS-1 for detecting edges in functions of one variable and a second adaptive procedure based on the concept of projective complexity of a 3D image. DA3DED has been tested on 3D images that modelize real problems (composites and fractures). It has been much faster than the 1D edge detection algorithm for 3D images derived from EDAS-1.