375690 – Auction Theory

Teacher: Rann Smorodinsky / Bloomfield 315 / rann@ie.technion.ac.il / Office hours: Sun 14:30-15:30
TA: Liri Finkelstein / Cooper 315 / liri@tx.technion.ac.il / Office hours: by request ( e-mail)
Course website: Moodle – make sure you are registered
Class hours: Sundays, 15:30 – 17:30 / Recitation hour: Sundays, 17:30 – 18:30

Course Description:
Auctions are a standard means for buying and selling goods. This format of trade has become very popular in recent years with the prevalence of electronic commerce. Auction theory is a research area, on the border of economics, game theory and computer sciences which studies this topic using mathematical models. The study of auctions involves issues such as economic efficiency, bidders’ incentives, the analysis of revenue on the one hand, and computational and communication complexity on the other hand

Course goals:
The course will provide students with basic knowledge of various topics in auction theory. We will go over a variety of results spanning the classical results to recent advancements in the field. The first part of the course will focus on the simple case of a single item good (such as selling a single artifact in an auction held in Sotheby’s) whereas the second part will consider some natural extensions such as the selling of many goods in a single auction.

Prerequisites:
The course requires no knowledge of advances material but assumes students are sufficiently comfortable with mathematical modeling and mathematical and probabilistic tools.

Grades:
 During the course 4 homework assignments will be given. Each constitutes 8% of the final grade.
 A final assignment will be given at the end of the course which will constitute 68% of the final grade.
All assignments are personal and not to be discussed among the students.
Literature: The lectures will use a slide set which will be available to the students via Moodle.

Course topics (rough outline):
 Basic game-theoretic notions: Normal-form games, Dominant strategies, and Nash Equilibrium The basic auction model: Single item auction with IID valuations and risk-neutral bidders. In particular an analysis of 1st and 2nd price auctions and English and Dutch (dynamic) auctions. Revenue-maximization in auctions: The direct-revelation principle. The revenue-equivalence theorem and the design of an optimal auction
 Relaxing the basic assumptions: The case of risk-averse bidders and of asymmetric bidders
 Interdependent values: The winner’s curse / Revenue and efficiency comparison of the classic auction formats / Design of an optimal auction.
 Digital goods (e.g., selling music files or software): an approximately optimal and detail-free auction
 Mechanism design and VCG: What is mechanism design / the notion of budget balanced mechanisms / VCG mechanism
 Multiple identical goods: Unit-demand vs. decreasing marginal valuations vs. complementarities / Uniform-price auctions vs. VCG / Computational considerations.