30559 - GAME THEORY AND MECHANISM DESIGN
Course taught in English
Go to class group/s: 27
Synchronous Blended: Lessons in synchronous mode in the classroom (for a maximum of one hour per credit in remote mode)
While the course does not require more than familiarity with basic mathematical concepts such as sets, functions, limits, and probability, students should be familiar with formal reasoning and be able to follow and carry out rigorous mathematical proofs.
The aim of the course is twofold. First, to provide students with a rich toolkit allowing them to identify, model, and reason through strategic interactions (such as business strategies, negotiations, etc.) and to apply this toolkit when designing strategic environments (such as auctions, competitions, teamwork, etc.). Second, and in the interdisciplinary spirit of the program, to illustrate the ability of mathematics in modeling, analyzing, and understanding real-world social as well as business interactions.
- What is Game Theory?
- Static Games of Complete Information
- Rationalizability and iterated dominance
- Pure and mixed strategy Nash equilibrium
- Static Games of Incomplete Information
- Formalizing incomplete information in games
- Bayesian Nash equilibrium
- Multistage Games of Complete Information
- Strategies in multistage games
- Backward induction
- Subgame perfect equilibrium
- Multistage Games of Incomplete Information
- Information sets and strategies
- Perfect Bayesian equilibrium
- Signaling Games
- Repeated Games
- Relevance of repeated interactions
- Folk Theorems
- What is Mechanism Design?
- Introduction to designing strategic interactions
- Introduction to the revelation principle and incentive constraints
- Bayesian and Dominant-Strategy Incentive Compatibility
- Efficient Mechanisms
- Revenue Equivalence
- First-Price Auctions
- Second-Price Auctions
- Sponsored-Search Auction
- Applications of the Theory
- Sponsored-Search Auctions, algorithmic pricing and collusion, cryptography, matching markets, voting …
- distinguish between decision- and game-theoretic problems
- identify strategic interactions
- describe strategic interactions using formal models and approaches learned during the course
- express the importance of incentive compatibility and individual rationality when designing strategic environments.
- apply mathematical modeling to real-world strategic interactions
- use the concepts taught to solve and analyze such mathematical models
- prove results in game theory and mechanism design
- translate the models’ insights into various real-world situations, such as auction design.
- Face-to-face lectures
- Individual assignments
In the face-to-face lectures, we will introduce, motivate and discuss the course topics and models and how they apply to various economic and other real-world settings. Moreover, we will prove important game-theoretic/mechanism design results thereby acquiring the relevant skills to formally set up and analyze models individually and solve problems together in these lectures. In addition, we will apply this knowledge to real-world settings and discuss the insights game theory and mechanism design can deliver in practice. The individual assignments, which will take the form of problem sets, are designed to have the students solve problems and prove results by themselves further enhancing students' understanding of the topic and their ability to study strategic interactions as well as their design. After their submission, we will discuss the problem sets and insights from solving them in the class.
Both attending and non-attending students will be treated identically and the form of the assessment is exclusively written. The students can take either two partial exams or one general exam which account for 80% of the final grade. The remaining 20% will be based on individual assignments in the form of problem sets. The written exams ask open questions to prove theoretical results, solve problems related to those presented in the lectures and individual assignments, and discuss the implications in and the relation of findings to the real world. The individual assignments will be similar to the exam and will consist of proving theoretical results and solving problems as well as discussing the findings. Both assessment methods verify the students’ ability to identify, formalize and solve strategic interactions, prove results in game theory and mechanism design, as well as the ability to apply formal reasoning to real-world problems.
There is no mandatory textbook for the class. The material in the form of lecture notes/slides will be distributed during the semester and a list of additional readings will be provided.