Academic Year 2019-2020

GRAPH AND GAME THEORY

Teachers

Franca Rinaldi
Unit Credits
6
Teaching Period
First Period
Course Type
Affine/Integrativa
Prerequisites. Knowledge of the basic concepts of linear algebra and probability. Familiarity with matrix operations.
Teaching Methods. Theoretical lessons and exercises.
Verification of Learning. The oral exam aims to test the knowledge and ability to present the topics of the course and the ability to apply this knowledge to model and/or solve easy instances of theoretical /application problems.
More Information. ~~~
Objectives
At the end of the course the student should:

Knowledge and understanding: know the main concepts, problems and methods of graph theory; know the fundamental properties of the matrices associated with graphs and their application in networks’ analysis; know some applications of graph theory to the analysis of real systems, in particular of real networks (web, internet, social networks, etc); know the main models of game theory and the related resolution methods.

Applying knowledge and understanding: be able to identify the network structure of some real systems and to formulate an appropriate model in terms of graphs; be able to formalize simple combinatoric and applicative problems as problems on graphs; be able to represent and solve simple game situations.

Autonomy of judgment: be able to propose and discuss an appropriate model for the representation of a real network;

be able to propose and discuss an appropriate model for representing a conflict / game situation.

Communication skills: be able to present t with the necessary formal accuracy the subjects covered in the course and possible other research m

Contents
Graph theory: this part of the course presents the main concepts and results of graph theory with particular attention to topics of interest in the analysis of networks of large dimension. In addition to the basic concepts, the course arguments include the numbers associated with a graph and their relationships, isomorphisms and automorphisms, sets of nodes and arcs with particular properties, paths, connection and centrality indexes based on distances, matrices associated with a graph and their properties, Markov’s chains on graphs.

Game Theory: this part of the course presents the assumptions, the forms of representation and the basic concepts of game theory and the main models used in the analysis of non-cooperative and cooperative games.

Texts
– Lecture notes and other teaching material provided by the teacher

– Thomas S. Ferguson: “Game Theory” available at site http://www.math.ucla.edu/stom/Game Theory/Contents.html.