Course notes on finite games and rational choice / / Riccardo Bruni.

• Superior document: Manuali – Umanistica ; 14
• VerfasserIn: Bruni, Riccardo, 1974-
• Place / Publishing House: Firenze : : Firenze University Press,, 2018
• Year of Publication: 2018
• Language: English
• Series: Manuali – Umanistica ; 14.
• Physical Description: 1 online resource (182 pages) :; illustrations; digital, PDF file(s).

This book collects notes that were prepared for a university course taught in the Spring of 2018, and delivered to an audience of students enrolled in the Master course in Logic, philosophy and history of science of the University of Florence. The goal of the course was to introduce students to some basic concepts from the area of research generally known as decision theory. This is done by focussing on the concept of ‘rational choice’, which is analyzed, methodologically speaking, by the means of the theory of games. To minimize prerequisites it was decided to restrict the attention to the theory of finite games in particular. The topics treated are vary, and belongs to both the theory of games ‘in normal form’ as well as that of games ‘in extensive form’, as they are usually referred to. The classical issues in both fields, such as the theory of ‘equilibria’ and the study of properties such as determinacy, are carefully discussed to make them clear to beginners and are addressed from a novel perspective which makes use of formal methods that are typical of researches connected with the study of logic.

Table of Contents

Chapter 1 - Preliminary considerations -- 1.1. Types of choice -- 1.2. A decision and its components 1.3. Aligning things on a scale -- 1.4. Take consequences at face value -- 1.5. Decisions in a game-theoretic setting 1.6. How to design a game -- Chapter 2 - How games are dealt with 2.1. Games in tree or matrix form 2.2. Dynamic choice: games as trees 2.3. Static choice: games as matrices 2.4. Reasoning on trees -- 2.5. Reasoning on matrices -- 2.6. The rationale of rational choice -- Chapter 3 - On games in normal form -- 3.1. Solving the (matrix) riddle -- 3.2. Equilibria -- 3.3. Getting rid of the loop on rationality of actions 3.4. Hypotheses and their revision -- 3.5. Equilibria as fixpoints of the revision operator 3.6. Unique equilibria? -- 3.7. The limits of strict games and strict equilibria -- 3.8. When strictness fails -- 3.9. What if the opponent trembles? -- 3.10. Proper equilibria -- 3.11. Generalizing the analysis to all finite games 3.12. Bibliographical note -- Chapter 4 - Sequential play: games in extensive form -- 4.1. One player after the other -- 4.2. Solving trees, backwards -- 4.3. An abstract, mathematical approach -- 4.4. Preliminary notions and basic notation -- 4.5. Two-person, zero-sum, perfect information games -- 4.6. The model of finite games -- 4.7. Alternative models of finite games -- 4.8. Determinacy of finite games -- 4.9. GRH at work -- 4.10. Bibliographical note -- Bibliography.