25988 - Introduction to Game Theory

Learning outcomes

PART ONE: ELEMENTS OF MATHEMATICS FOR ECONOMISTS

Goal : Providing students with the essential mathematical tools needed for intermediate and advanced economic courses.

Knowledge Outcomes : the ability to understand and solve common formal models used in economics to represent consumers, firms, and a planner.


PART TWO: INTRODUCTION TO GAME THEORY

Goal : Providing insights about situations of conflict and cooperation where there is strategic interaction among participants.

Knowledge Outcomes : A precise language to describe strategic interaction; identification of the the incentive structure of social dilemmas, some voting situations, coordination games, and other important scenarios; insights on the best action rational decision-makers should take in given scenarios and their strength in terms of solution concept; compare predictions of mainstream economic models with common choices that people make, and identify the cases where there are systematic differences.

Course contents

The course is articulated into two parts. A detailed program will be supplied at the beginning of the course.

Lectures in part one will be in English. Lectures in part two may be in English or Italian depending on foreign student enrollments in the course. Please contact the instructor for more details.

PART ONE: ELEMENTS OF MATHEMATICS FOR ECONOMISTS

*** ALGEBRA
Matrices and Determinants
Systems of equation
Linear inequalities
Second degree inequalities

*** CALCULUS
Concept of function
Linear functions
The parable, exponential, logarithms
Monotonicity, concavity/convexity, inverse
Concept of derivative
Derivation rules
Optimization for function in one variable
Function with more than one variable
Partial derivatives
Differentials
Optimization for functions in more than one variable
Constrained optimization, Lagrangian

PART TWO: INTRODUCTION TO GAME THEORY
*** BASICS
Social dilemmas: Prisoner's dilemma, voluntary contribution to public goods, and common pool resource, Dominant strategy equilibrium
Coordination games: Nash equilibrium in pure and mixed strategies
Long-term relationships: the folk theorem, Subgame perfect Nash equilibrium

*** APPLICATIONS
Strategic voting ,Information
Agenda manipulation in voting
Other-regarding preferences: Ultimatum and Trust games, Formal models of other-regarding preferences
An introduction to auctions
Iterative dominant strategy equilibrium: Guessing games

Readings/Bibliography

PRIMA PARTE: Martin Anthony and Norman Biggs (1996) Mathematics for economics and finance: methods and modelling, paperback, Cambridge University Press

SECOND PARTE: James D. Morrow (1994) Game Theory for Political Scientists, Princeton University Press

Additional material will be available for download on the course webpage at http://www2.dse.unibo.it/casari/

Teaching methods

Frontal lectures with use of blackboard and slides.
In class experiments.
Some laboratory sessions in Aula Didattica with teaching experiments

Assessment methods

Written examination on part one of the course and oral examination on part two of the course. In every appello the student can take both the written and the oral examination in the same day. There will be a midterm written examination on part one of the course. Those who pass the midterm can take the oral exam on the date of the first appello after the end of all lectures. For later appelli, all students must take both the written and the oral examinations.

Teaching tools

Part one will be frontal lectures while Part two will have a mixture of frontal lectures and teaching experiments.

Links to further information

http://www2.dse.unibo.it/casari/

Office hours

See the website of Marco Casari