Mathematical Economics I

2018-2019

Doel vak

- Acquaint participants with classic mathematical models of economic
decision making developed in the second half of the twentieth century,
the fundamental critique of fact-driven behavioral economics (classic
anomalies) and a sketch of economic models of the future.
- The focus is on three topics: individual decision making, collective
decision making (voting in groups or societies) and interdependent
decision making (or game theory).
- Participants understand the purpose and the mathematical properties of
each model. Participants are able to execute several strategies to
calculate simple models by hand, embed such strategies in algorithms
(pseudo-code for software) and being able to use freeware Gambit.
- Participants are confronted with the important difference between
descriptive theory, aimed at explaining and predicting reality, and
normative theory, what intervention should ideally be done.
- Economic modeling of reality, embedding economic models in software
and bringing economic models to the data will also be addressed.
To summarize, participants will learn, understand and reflect on
important economic models, their implementation in algorithms, and
experiments.

Inhoud vak

Society asks for evidence-driven economic theories that can be used in
economic decision making in complex economic situations. This
requires on the one hand descriptive theory that explains and predicts
economic reality, and on the other hand normative theory that guides the
decision maker what economic intervention should ideally be done. The
financial crisis of 2007, and its aftermath, made clear that the classic
models of economic decision making developed in the second half of the
twentieth century are not up to this task. Also, these models ignored
the classic anomalies (some dated early 1950s) and fundamental critique
raised by fact-driven behavioral economics for too long. Since the
financial crisis, (mathematical) economics is in transition, and for
good reasons. This transition is reflected in this course and requires
more academic reflection from participants than they are used in other
EOR courses.

This course deals with individuals, companies, governments, NGOs that
(need/want to) take economic decisions. Each decision maker is embedded
by an
economic context, e.g. you deciding how much effort to put in a team
assignment. The interaction of decision makers and their economic
surrounding is at the heart of this course. We distinguish three major
topics: individual decision making, collective decision making (how do
groups or societies reach decisions) and interdependent decision making
(how to bid in an auction anticipating others’ bids).

Individual decision making (period 1)
In order to evaluate whether a decision is a good decision, economists
developed the notion of preference relations that rank possible
alternatives (possible choices) and utility / objective functions. In
this course we introduce these concepts and investigate what
mathematical structure needs to be imposed to move from preference
relations to utility functions. From a descriptive perspective, this
course addresses whether the mathematical structure is evidence-based.
From a normative perspective, how to obtain preferences and how to
compute what is best
according to these preferences. This is facilitated by constructive
mathematical proofs that can transformed into algorithms (and would lend
itself for programming, which is outside the scope of this course).
Classic economic theories about market demand of consumers, or the
market supply of a product and market demand for inputs by price-taking
firms are derived from objective functions. Noisy decision making, as
introduced by Duncan Luce and popular in A/B testing in Data Analytics,
will be introduced. Preferences for risky decisions are developed and
expected utility theory derived. The famous Allais-paradox experiment
that empirically rejects this theory is discussed, and Prospect theory,
which can explain the paradox, will be discussed.

Collective decision making (period 1)
Individual decision makers often participate in groups or teams, and
live in a society. Is it mathematically possible to derive group
preferences from individual preferences? Impossible. What then? This
part of the course is merely normative in analyzing classic ranking
methods and voting procedures that are observed in reality. These
methods and procedures will be compared with each other. One criterion
employed is Pareto efficiency.

Interdependent decision making (period 2)
In many, if not all, economic situations what eventually happens depends
upon decisions made by more than one individual of individuals. Whether
your team assignment is evaluated with a high grade depends upon your
own effort and that of your other teammates. Or, whether you win the
item in an auction depends upon your own bid and the others’ bids.
Predicting what others will do, how they predict what you will do, etc.
becomes crucial in the mathematical analysis. Although this part can be
used for normative theory (f.e. all driving on the same side of the road
reduces accidents, or to develop good antitrust policy to destabilize
cartels), the focus of this part of the course is mainly descriptive
because of the need for evidence-based theories.

We focus on Nash equilibrium, the empirical need to refine Nash
equilibrium and two of such refinements: k-level reasoning and (agent)
quantal response equilibrium. The latter is a descriptive theory, Nash
equilibrium is in trouble while quantal response equilibrium deals
better with experimental data and is easier to bring to data.

In many economic situations some individual are better informed than
others, which is called private information. For example, in Poker you
know the cards you are holding while the others do not. You will be
introduced to the fascinating world of interdependent decision making
with private information. Because analyzing such games by hand is rather
hard, you will solve such games numerically in Gambit. (Freeware Gambit
is an open-source software tool programmed in Python that computes Nash
equilibrium and quantal response equilibrium.) Interpretation of the
computed solution and its economic implications will be addressed.
Gambit will be part of an assignment that counts as part of the final
grade.

This part will also focus on the economic literature during the 1980s
and 1990s that were so influential that many mathematical economists
became Nobel laureates in Economics. Classic theories about Cournot
competition in quantities (e.g. OPEC cartel), Bertrand competition in
prices, sustainable cooperation in repeated games, antitrust policy to
destabilize cartels are part of the course.

Onderwijsvorm

Classes. One lecture and one practical per week. Active participation is
key.
Participants may be partitioned to groups for the practical.
Participants of the practical PREPARE BEFORE coming to class and are
expected TO PRESENT their answers before the Canvas in class and
discuss where problems in solving questions arose.

Toetsvorm

One team assignment based upon Gambit in period 2 – team assessment
Partial exams in October (covering period 1) and December (covering
period 2) – individual assessment
An exam in March (covering period 1 and 2) – individual assessment
Individual Assignment (presenting before class) – individual assessment

Literatuur

A syllabus that contains exercises and that is supplemented by some
videos from Massive Open Online Courses (MOOCs). All compulsory
literature and links will be provided through Canvas.

Doelgroep

This course is an obligatory second-year course in the bachelor
Econometrics and Operations Research. Exchange students and other
students from other bachelors, such as
Economics, are welcome but should be motivated to follow a course with a
lot of mathematics. Preferably, you have a sufficient mathematical
background and can reason logically. For more information, ot in doubt,
contact the course coordinator.

Aanbevolen voorkennis

Knowledge of elementary mathematics and elementary probability theory.
This includes differentiation, the Lagrange method, expectation, Bayes
Rule.
For EOR students this translates in knowledge from Analysis I and II,
Linear Algebra and Probability Theory, and to a much lesser extent
Finance, Statistics and Programming.

Algemene informatie

Vakcode E_EOR2_ME1
Studiepunten 6 EC
Periode P1+2
Vakniveau 200
Onderwijstaal Nederlands
Faculteit School of Business and Economics
Vakcoördinator dr. H.E.D. Houba
Examinator dr. H.E.D. Houba
Docenten dr. H.E.D. Houba
prof. dr. J.R. van den Brink

Praktische informatie

Voor dit vak moet je zelf intekenen.

Werkvormen Hoorcollege, Werkgroep
Doelgroepen

Dit vak is ook toegankelijk als: