Description

We study how to allocate indivisible items or partners when prices do not play an important role. Instead, agents in these markets have preferences over the different choices. You may think of a job market where workers and firms are not only matched based upon the wage but according to their personal skills and taste. Although the allocation cannot be done with the help of the price mechanism, the solution should be economically reasonable which means that it is either efficient or fulfills a fairness criterion. To reach such a solution, different matching mechanisms are used. We study and develop these mechanisms theoretically but also empirically and experimentally in the real world.

Application

There are a lot of different applications where theoretical results are used to solve problems in the real world by analyzing and designing the market and its allocation mechanism. All over the world students are matched to schools with the help of matching algorithms, organs are exchanged, and doctors are allocated to hospitals. At our faculty we use a matching mechanism to allocate students to chairs when they want to write their theses. And perhaps some of you have already used another matching application by using Tinder or another dating app.

Recommended reading

To get started, we recommend the following book, which provides a good, non-technical introduction to the topic:

Roth, Alvin E. (2015) Who gets what-and why: The new economics of matchmaking and market design. Houghton Mifflin Harcourt.

If you want to dig deeper start with the first and most influential paper on matching:

Gale, D., & Shapley, L. S. (1962). College admissions and the stability of marriage, The American Mathematical Monthly, 69(1), 9-15.

If you want to know more about how to allocate students to schools start with the following paper:

Abdulkadiroğlu, A., & Sönmez, T. (2003). School choice: A mechanism design approach. American economic review, 93(3), 729-747.

And of course you should check out our publications here.

Courses:

W4467 - Auctions, Incentives and Matchings

Description

In general, a non-cooperative game describes a situation, in which a set of the players make decisions and utility (payoff) for each player is the measure of her satisfaction. Within the framework of Cooperative Game Theory, the focus is on the interaction between groups of players, rather than between individual players. The groups of players, called coalitions, are the units of decision-making, so that they can practice cooperative behaviour. The questions that we want to answer when we deal with a cooperative game are these: as a result of the dynamics of cooperation, which coalitions will be formed? How will the coalitions split the resulting utility among their members?

Application

Applications range from profit or cost distributions from economic activities to formation of political coalitions that form to improve their voting power. Agreements on how to split future power is the driver for forming political alliances.

Recommended reading

Shapley LS (1953) A value for n-person games. contributions to the theory of games. In Annals of mathematics studies, vol 2. Princeton University Press, Princeton, pp 307-317

Bejan, C. and Gomez, J.C. (2012). axiomatising core extensions. International Journal of Game Theory 41, 885-898.

von Neumann, J. and Morgenstern, O. (1944).Theory of games and economic behaviour. Princeton university press.

And of course you should have a look at our publications here.

Courses

W2441 - Game Theory

W4469 - Advanced Game Theory