Scientia Publishing House – Sapientia Hungarian University of Transylvania

 Döntéselmélet közgazdászoknak [Decision Theory for Economists]

Mathematical models of economy are decision models which help leaders to prepare their decision making in the macro- and microlevels of economics. The leaders’ aim is to choose the most convenient strategies in the course of decision making. The operational research and decision theory deal with the selection of these strategies. Based on many years’ educational experience, the economist students’ greatest difficulty in understanding the discipline of operational research is the transcription of the text-mode formulated economic problem to a solvable mathematical model. In order to develop the mathematical model construction to skill level, one has to solve a large number of problems.

Accordingly, the main objective of this book is to practise the inscription of the mathematical model of the economic problems and to help the understanding of the economic meanings of the parameters. The WinQSB (QSB – Quantitative Systems for business) software package and the Excel table calculation program are used to calculate the mathematical model’s numerical solution. This lecture note can also be seen as a continuation of our book Operational Research Exercise Book for Economists published in 2011. Similarly, even in this book, the basic concepts of decision theory and the methods of analysis are presented through examples by using the WinQSB software package and the Excel table calculation program to provide numerical answers to the formulated questions. The lecture note provides an overview of some of the major chapters in decision theory and follows the structure of Decision Support Systems and Decision Theory courses of economic specializations at Sapientia University.

The first chapter begins with an overview of the basic concepts of decision making in uncertain circumstances and simple decision-making criteria. In the second section, we present the Neumann–Morgenstern utility theory. Using illustrative examples, we show how theory can be applied to the study of individual risk behaviour. Kahneman and Twersky studied the human factors that distort the principles of utility theory. In the third section, we analyse the effects that are most important for normative decision making, and the fourth section presents, as an application, how the Nash equilibrium is developed in two person games with two strategies if the distortion effects are also taken into account. We also examine the effect of the reference value on the outcome of the game. The second chapter deals with the construction, evaluation, and Bayesiananalysis of the decision trees. Using examples, we also show how to use the Decision Tree Analysis toolbar of WinQSB. Chapter 3 presents the model of multi-purpose decision making. We also discuss hierarchical and non-hierarchical models and the practical application of WinQSB’s Linear and Integer Goal Programming toolbar. Chapter four includes various applications of the analytical hierarchy process (AHP) developed by Saaty. The estimation of the priority vector using linear programming model and the least deviation method are also presented.

Chapter five discusses Markov’s decision-making processes. The first section deals with the determination of equilibrium distributions and return times. In the second part, we study Markov chains using WinQSB. The third section presents the analysis of absorbing Markov chains. Section four discusses the decisions the decision maker has to make to maximize his or her expected profits or minimize his or her expected losses if the transition between states also depends on a decision. Each chapter begins with a short summary of the necessary theoretical knowledge followed by tutorial examples which illustrate the method of the resolution. We present the related useful WinQS software package or we give the solution by using Excel table calculation program in every chapter. The exercises can be found at the end of the chapters. First of all, this lecture note is recommended for students in Economic Informatics, Economics, Management and Leadership MA as well as Applied Economics and Finance MA. Several tutorials and solved problems provide basic ideas and methods of analysis for the students to elaborate their thesis.