Matematisk mikroøkonomi / Mathematical Microeconomics

Studienævn for Markeds- og ledelsesantropologi, Økonomi, Matematik-Økonomi og Miljø og Ressource Man, Odense
Undervisningsaktivitetsnr.: 8106101.
Undervisningssprog: Engelsk, dansk.ECTS / belastning: 10 ECTS / 0.167 årsværk.
Eksamenssprog: 0.
Eksamensaktivitetsnr.: 8106102.Godkendt: 07-11-17.
Periode: Forårssemestret 2018.
Censur: Internt bedømt.
Bedømmelse: 7-trinsskala.
Udbydes i: Odense.

Fagansvarlig:
Peter Sudhölter, Virksomhedsledelse og økonomi.

Forudsætninger:
The prerequisites for this course are the understanding of basic principles of consumer and producer theory and of equilibrium analysis. The students should have knowledge about optimization problems as they occur when firms maximize profit and consumers maximize utility and about basic methods to solve such problems. Hence, the necessary skills may be obtained in the bachelors' courses Mikroøkonomi (9115501) and Operationsanalyse (9150301).



Formål og sigte:
Microeconomics is regarded as one central field of economics, and it is the aim of this course is to discuss and analyze essential topics of Microeconomic Theory, in particular of Game Theory. Indeed, Game Theory is the major method in mathematical economics for modeling and analyzing interactive multi-personal decision problems, and it can be applied to a wide spectrum of economic phenomena, including auctions, bargaining problems, fair division, oligopolistic competition, social network formation, voting systems, and cost-sharing problems.
The course is therefore designed to provide deep knowledge of the main models and results of the theory of non-cooperative games as well as the theory of cooperative games that are used in economics and in the social sciences in general. Game theoretic problems described in the literature will be discussed and suitable models will be formulated and solved.
Furthermore, it is the aim of the course to give the students the competence to decide which game theoretic model is appropriate for a multi-personal decision problem and to provide them with skills that are necessary to apply the theoretical models to economic phenomena by themselves.
In order to control the necessary methods and results better, students will be encouraged to solve explicit exercises that may be discussed in a subsequent lesson.




Indhold:
Classes of Games:
• Strategic games (with perfect information)
• Bayesian games (strategic games with imperfect information)
• Extensive games with perfect information
• Extensive games with imperfect information
• Cooperative transferable utility games
• Cooperative non-transferable utility games
• Bargaining games

Solutions:
• Games with perfect information: Nash equilibrium (pure or mixed), iterated elimination of dominated actions, correlated equilibrium, existence theorems
• Bayesian games: Bayesian equilibrium
• Extensive games: Subgame perfect equilibrium, sequential equilibrium, perfect Bayesian equilibrium
• Cooperative games: Core, Shapley (NTU) value
• Bargaining games: Nash solution


Målbeskrivelse:
For at opnå fagets formål er det læringsmålet for faget, at de studerende/To fulfill the purposes of the course the student must be able to:

Demonstrerer viden om/Demonstrate knowledge about the course’s focus areas enabling the student to:

• Describe fundamental concepts of the theory of non-cooperative game theory like strategies and Nash equilibrium
• Reflect on von Neumann’s minimax theorem and the properties of Nash equilibria in the constant-sum case
• Explain and describe Bayesian games and Bayesian equilibria
• Describe and compare various refinements of Nash equilibrium like subgame perfect equilibrium, perfect Bayesian equilibrium, and sequential equilibrium, for various kinds of games in extensive form
• Describe, explain, and identify games in cooperative form
• Explain and model cost sharing problems by means of suitable transferable utility (TU) games
• Explain and describe various solution concepts for TU games
• Explain the axiomatic approach on the Shapley value

Demonstrerer færdigheder/Demonstrate skills, such that the student is able to:

• Analyze and compare finite non-cooperative games of various types
• Apply various non-cooperative game theoretical models to simple microeconomic problems
• Compute distinct types of Nash equilibria of explicitly given non-cooperative games
• Analyze and relate game theoretical problems
• Solve specific microeconomic problems by applying theoretical, in particular game theoretical models
• Compare and relate various solutions for TU games
• Criticize and compare underlying assumptions regarding all topics

Demonstrerer kompetencer/Demonstrate competences, such that the student is able to:

• Independently apply models and theories related to non-cooperative game theory
• Formulate and solve game theoretical models by suitable mathematical methods in a range of appropriate and important economic problems
• Identify a need for further development of the models and theories related to both, the non-cooperative as well as cooperative Game Theory
• Use the above knowledge and skills to participate in team work to obtain and expand the competence in collaboration and communication
• Discuss and understand theoretical articles in the mentioned areas and their importance with respect to economics


Litteratur:
Eksempel/Examples
• Osborne, M. J, and A. Rubinstein (1994): A Course in Game Theory, MIT Press, Cambridge, Massachusetts.
• Varian, H. R. (1992): Microeconomic Analysis, Norton & Company.
• Additional material may be disseminated during the course.




Undervisningstidspunkt:
Forår/Spring.


Skemalagt undervisning:
4 hours of lectures weekly in 15 weeks - in total 60 hours.


Undervisningsform:
Undervisningsaktiviteterne udmønter sig i en anslået vejledende fordeling af arbejdsindsatsen hos en gennemsnitsstuderende på følgende måde:
Form of instruction:
The students' workload is expected to be distributed as follows:
Forelæsningstimer/Lectures - 60 hours
Forberedelse til forelæsninger/Preparation, lectures - 100 hours
Forberedelse til øvelses/Homework assignments - 110 hours
Totalt/Total 270 hours.


Eksamenstidspunkt:
Ordinær prøve i løbet af semesteret. Omprøve i august

Den studerende er automatisk tilmeldt den ordinære prøve, når den studerende er tilmeldt undervisning i faget. Framelding kan ikke finde sted, og der er brugt et prøveforsøg, hvis den studerende ikke deltager i prøven.
Universitetet kan dispensere fra reglerne, hvis der foreligger usædvanlige forhold.

Prøve- og bedømmelsesform kan ændres ved omprøven.


Eksamensbetingelser:
None.


Prøveform til eksamensbevis:
Assignments, individually written.
One grade is given.


Supplerende information til prøveform:
Varighed/Duration: Dates for submission will be published on Blackboard.
Sted/Location: Home assignment.
Internetadgang: Internet er nødvendigt./Internet Access: Necessary.
Udlevering af opgaven/Hand Out: Via the course page in Blackboard.
Indlevering af besvarelse: Gennem SDUassignment i kursets side i Blackboard./Hand In: Via SDUassignment in the course page in Blackboard.  
Omfang/Extent: No limitations.
Hjælpemidler/Exam Aids: All exam aids allowed.

With some regularity students will be asked to hand in or to present their homework on exercises announced one week before. Some of the exercises will be taken from the textbooks.

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Den skriftlige prøve tester opfyldelsen af samtlige mål.

Kommentar:
Joint lecture with Advanced Game Theory (8032001)

Studier:
BSc.scient.oecon. (Matematik-Økonomi)
6. semester, obligatorisk. Udbydes i: Odense