Teaching Nash Equilibrium and Strategy Dominance: A Classroom Experiment on the Beauty Contest

The aim of this investigation is to display how the use of classroom experiments may be a good pedagogical tool to teach the Nash equilibrium (NE) concept. The basic game for our purposes is a repeated version of the Beauty Contest Game (BCG), a simple guessing game whose repetition lets students react to other players’ choices and to converge iteratively to the equilibrium solution. We performed this experiment with undergraduate students without any previous knowledge about game theory. After four rounds, we observed in all groups a clear decreasing tendency in the average chosen number. So, our findings prove that, by playing a repeated BCG, students quickly learn how to reach the NE solution.Classroom Experiments, Beauty Contest Game, Teaching, Nash Equilibrium.

Minimum penalized φ-divergence estimation under model misspecification

This paper focuses on the consequences of assuming a wrong model for multinomial data when using minimum penalized φ-divergence, also known as minimum penalized disparity estimators, to estimate the model parameters. These estimators are shown to converge to a well-defined limit. An application of the results obtained shows that a parametric bootstrap consistently estimates the null distribution of a certain class of test statistics for model misspecification detection. An illustrative application to the accuracy assessment of the thematic quality in a global land cover map is included.Ministerio de Economía y Competitivida

Communication, coordination and competition in the beauty contest game: eleven classroom experiments

Este trabajo ha sido publicado en Central European Journal of Operations Research 12(4): 369-287 (2004).This paper introduces some new features in the standard experimental design of the beauty contest in order to allow communication among participants. With that aim, we use the mode instead of the mean and non-rival payoffs. This design encourages students to communicate their guessed number, with a higher probability if subjects know the 0 Nash equilibrium. The lack of communication can only be explained by subjects endowed with competitive other-regarding preferences. Experiments are run in 11 classrooms ranging from 11 to 60 students in size. Participants are given at least one week to submit their guesses and a questionnaire explaining their choice. Results indicate that: i) communication induces coordination in the responses, ii) communication does not guarantee any improvement in the average reasoning level, iii) there exist significative differences according to classroom size and duration of degree.We gratefully acknowledge the financial support from the University of Jaén R+D program (# 20210/148)

Una herramienta electrónica para la enseñanza de las técnicas de muestreo

Dentro de la enseñanza del muestreo en poblaciones finitas se detecta como una necesidad el uso de datos reales para ilustrar y discutir la particularidad de llevar a la práctica un esquema de muestreo a un problema concreto. El desarrollo de aplicaciones informáticas que permitan implementar los desarrollos teóricos para su aplicación a datos reales, permiten al alumno resolver casos prácticos más adecuados a la posterior vida laboral, a la vez que reduce su recelo e incertidumbre sobre el manejo de este tipo de datos.En este trabajo se presentan los principales resultados en el desarrollo de una aplicación informática en Visual Basic y la elaboración de un cuaderno de prácticas de muestreo, diseñados como complemento del material teórico-práctico utilizado en la enseñanza de muestreo en poblaciones finitas

Adquisición de Competencias Transversales: Comparación entre los Grados en Estadística y Empresa, Administración y Dirección de Empresas y Finanzas y Contabilidad de la Universidad de Jaén

El objetivo de este trabajo es cuantificar la percepción del alumnado de tercer curso de Grado sobre el nivel de adquisición de competencias genéricas alcanzadas hasta el momento. En concreto, son seis las competencias analizadas: capacidad de resolver problemas, capacidad de análisis y síntesis, capacidad de redactar informes, trabajo autónomo, comunicación oral y escrita y trabajo en equipo. Para ello, se han encuestado a 120 estudiantes de los Grados en Estadística y Empresa (EE) (14.17%), Administración y Dirección de Empresas (ADE) (64.17%) y Finanzas y Contabilidad (FC) (21.67%). De los resultados obtenidos se desprende que existen diferencias significativas entre los tres Grados en relación a algunas de las competencias, como son: capacidad para resolver problemas (el 47% de los estudiantes de EE consideran que alcanzan un nivel alto en la aplicación del método apropiado para la resolución de un problema, frente al 23% en FC); capacidad de análisis y síntesis (el 76.47% de los encuestados de EE dicen tener un nivel alto para transmitir sintéticamente las ideas más relevantes, mientras que en ADE es el 29.87%) y comunicación oral y escrita (el 70.6% de los estudiantes de EE se valoran con un nivel alto, siendo en FC un 42.3%)

A Homogeneity Test for Comparing Gridded-Spatial-Point Patterns of Human Caused Fires

The statistical evaluation of the spatial similarity of human caused fire patterns is an important issue for wildland fire analysis. This paper proposes a method based on observed data and on a statistical tool (homogeneity test) that is based on non-explicit spatial distribution hypothesis for the human caused fire events. If a tessellation coming from a space filling curve is superimposed on the spatial point patterns, and a linearization mechanism applied, the statistical problem of testing the similarity between the spatial point patterns is equivalent to the one of testing the homogeneity between the two multinomial distributions obtained by modeling the proportions of cases on each cell of the tessellation. This way of comparing spatial point patterns is free of any hypothesis on any spatial point process. Because data are spatially over-dispersed, the existence of many cells of the grid without any count is a problem for classical statistical homogeneity tests. Our work overcomes this problem by applying specific test statistics based on the square Hellinger distance. Simulations and actual data are used in order to tune the process and to demonstrate the capabilities of the proposal. Results indicate that a new and robust method for comparing spatial point patterns of human caused fires is available

Attracting the Right Crowd under Asymmetric Information: A Game Theory Application to Rewards-Based Crowdfunding

In this paper, we investigate rewards-based crowdfunding as an innovative financing form for startups and firms. Based on game-theory models under asymmetric information, we test research hypotheses about the positive effects of two main campaign features: funding target and number of rewards. Furthermore, we examine how and when these characteristics are effective in attracting crowdfunders, by signaling high-quality projects (target) and by pricing according to backers’ preferences (rewards). Conditional process analysis is applied to a dataset of 1613 projects launched on the Spanish platform Verkami from 2015 to 2018. As expected, our study shows that market size is positively influenced by the target and the number of rewards, separately. Further analysis gives some interesting findings. Firstly, we find significant and positive mediating roles of social networks (in the relationship between target and market size) and of backers’ preferences (between rewards and market size). Secondly, the main orientation of a campaign, commercial or social, is relevant to explain previous relationships. While high funding targets are more effective in commercial projects, a high number of rewards is more effective in the social projects. This research provides new insights into the design of optimal crowdfunding, with theoretical and empirical implications

A New Approach to the Quality Control of Slope and Aspect Classes Derived from Digital Elevation Models

The usefulness of the parameters (e.g., slope, aspect) derived from a Digital Elevation Model (DEM) is limited by its accuracy. In this paper, a thematic-like quality control (class-based) of aspect and slope classes is proposed. A product can be compared against a reference dataset, which provides the quality requirements to be achieved, by comparing the product proportions of each class with those of the reference set. If a distance between the product proportions and the reference proportions is smaller than a small enough positive tolerance, which is fixed by the user, it will be considered that the degree of similarity between the product and the reference set is acceptable, and hence that its quality meets the requirements. A formal statistical procedure, based on a hypothesis test, is developed and its performance is analyzed using simulated data. It uses the Hellinger distance between the proportions. The application to the slope and aspect is illustrated using data derived from a 2×2 m DEM (reference) and 5×5 m DEM in Allo (province of Navarra, Spain)

Control estricto de matrices de confusión por medio de distribuciones multinomiales

Las matrices de confusión son la forma más usual y estándar de informar sobre la exactitud temática de productos derivados de la clasificación de datos procedentes de imágenes. En este marco, son ampliamente utilizados dos índices: el porcentaje de acuerdo y el índice Kappa. Ambos son índices globales y no permiten un control categoría por categoría y, aún menos, establecer dentro de una categoría condiciones específicas. En este trabajo se propone un método novedoso basado en la distribución multinomial y en un test estadístico exacto. De esta forma, se pueden establecer las preferencias de exactitud para cada categoría y también establecer cierto grado de mala clasificación entre distintas categorías

Minimum Penalized ϕ-Divergence Estimation under Model Misspecification

This paper focuses on the consequences of assuming a wrong model for multinomial data when using minimum penalized ϕ -divergence, also known as minimum penalized disparity estimators, to estimate the model parameters. These estimators are shown to converge to a well-defined limit. An application of the results obtained shows that a parametric bootstrap consistently estimates the null distribution of a certain class of test statistics for model misspecification detection. An illustrative application to the accuracy assessment of the thematic quality in a global land cover map is included