Mathematical Decision Making

Stefan Rass, Stefan Schauer, Sandra König, Quanyan Zhu

Research output: Chapter in Book/Report/Conference proceedingChapter


Since both, decision- and game theory vitally employ optimization at their core, this chapter will provide the basic ideas, concepts and modeling aspects of optimization. It is intended to provide the mathematical basics for the further chapters. The presentation is to the point of a simple, compact and self-contained description of: (i) what is decision- and game-theory about, (ii) how do the two areas differ, and (iii) how does the practical work with these models look like when we strive for solutions. Specifically, we discuss preference relations, real and stochastic ordering relations and optimization as the most general covering framework, including single- and multi-goal optimization, with applications in being decision theory and game theory. Numeric examples accompany each section and concept. The opening of the chapter will specifically set the notation for all upcoming (mathematical) descriptions, to be consistent throughout the entire presentation (and book).

Original languageEnglish (US)
Title of host publicationAdvanced Sciences and Technologies for Security Applications
Number of pages36
StatePublished - 2020

Publication series

NameAdvanced Sciences and Technologies for Security Applications
ISSN (Print)1613-5113
ISSN (Electronic)2363-9466

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Safety Research
  • Political Science and International Relations
  • Computer Science Applications
  • Computer Networks and Communications
  • Health, Toxicology and Mutagenesis


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