Computational Economics

AY2021/2022 Semester 1

This course aims to introduce you to the fundamental concepts of game theory and mechanism design. Game theory, besides being of fundamental mathematical interest, is a main tool to model economic and strategic situations and then study the behavior of rational agents in such situations. Mechanism design is the study of how to design games (such as auctions) so that agents have incentive to act in a desirable way, e.g. by telling the truth. This course will improve your ability to model and analyze economics situations in a mathematical way. We will study the way rational agents will play games, based on their assumptions about the rationality of other agents. We will learn about the concept of Nash equilibria, which are solutions to games that no rational agent has an incentive to deviate from, and learn how to compute these. In the second part of the course we turn to the problem of social choice, namely choosing from a set of alternatives, given the preferences of a set of players. We will see that many desirable properties of social choice functions cannot be satisfied, and then turn to ways to deal with this issue. The first way is to introduce payments and money-valued preferences, which leads to auction theory and related topics. Here students will learn how to design auctions and other economic mechanisms so that players have no incentive to lie, and to learn how to compute expected revenues. Secondly, we will consider mechanisms that do not allow payments, and study the ways manipulations by the players can be limited in this case. In the second part of the course students will learn how to design economic mechanisms that have certain properties (if possible), and how to judge economic mechanisms, as well as to apply Bayesian reasoning to compute expected outcomes. The course is aimed at 3rd and 4th year students interested in economics, mathematical modelling, and applied math in general.