Mathematical modeling of institutions

Course goals

Zie onder vakinhoud.

Content

This is a mandatory course for TWECO students and is an elective for other mathematics students (including TWIN, TWINFO).

This course is concerned with the mathematics behind the design of institutions. While economics traditionally emphasizes the role of prices in allocating goods, many “goods” are allocated based, at least in part, on other factors. For instance, it’s generally not possible to get a highly prestigious job by simply accepting the lowest salary; and in most countries, trade in human organs is prohibited (while organ donation is encouraged!).  When factors other than price matter, institutions take on a central role in coordinating transactions. For example, several cities, including Amsterdam, organize the allocation of students to high schools. But how to design the institutions that coordinate such transactions? What are the properties we want them to have? And do institutions that satisfy these properties even exist? What do they look like – and do we observe them in practice? This course develops the mathematics needed to address these questions, with an emphasis on discrete mathematics (order theory, combinatorics) and algorithmic methods.

Applications covered may vary from year to year, but include a subset of:

• School choice and diversity quotas
• Refugee resettlement
• Supply chains and trading networks
• Kidney exchange
• Housing markets
• Online matching

IMPORTANT: Because this is a level-3 course in mathematics, it requires an advanced level of mathematical maturity (e.g., experience with writing proofs, understanding abstract formal arguments). In order to complete the course successfully, it is therefore necessary to have taken at least level-1 or level-2 courses from the BSc program “Wiskunde (en toepassingen)” on top of the prerequisites (“Kansrekening” and “Bewijzen in de wiskunde”, see below).  Mathematics courses from non-mathematics programs do not usually give sufficient background in this regard. For example, “Logica voor informatica” is no substitute for “Bewijzen in de wiskunde” as far as this course is concerned.

Leerdoelen: 
The student: 

• Understands the limitations of markets and institutional design
• Has an in-depth knowledge of matching markets and their essential properties
• Is able to apply the theory to real-world applications and reflect critically on the use of mathematical models to develop social and economic policy.
• Has a deep understanding of the different proof methods used (order-theoretic, algorithmic, and combinatorial) and to reflect on their strengths and limitations.
• Is able to provide simple counterexamples to prove negative results.

Onderwijsvormen:
Lectures (2 hours twice a week) and tutorial sessions (2 hours twice a week).

Toetsing:
Hand-in assignments (20% of final grade), mid-term exam (30% of final grade), and final exam (50% of final grade). For students taking the retake, the final grade is determined by the grade for the hand-in assignments (20% of final grade) and the (retake) exam (80% of final grade).

Herkansing en inspanningsverplichting:
Students with a final grade that is less than 4 are eligible to do the retake exam under the following conditions: (1) they have sat the midterm and the final exam; (2) they have submitted all hand-in assignments and have an average of at least 5 for the hand-in assignments.

Taal van het vak:
English