Course Description

MATH 671. Game Theory and Multiagent Systems
(3 hours of lecture per week).

There are many areas of overlap between computer science and game theory. This is not however only restricted to complexity theory which has been an instrumental tool in assessing the difficulties of game theoretical problems, e.g. optimizing the social welfare. In recent years we have witnessed the research on the interplay between game theory and distributed systems. A comprehensive look at this interplay can be found in A Computer Scientist Looks at Game Theory.

The central theme of this course is the investigation of modeling and reasoning about multi-agent systems (distributed systems of agents), who may operate on the basis of incomplete information about their environment, and with bounded computational/informational resources. We will in particular be interested in reasoning about knowledge of agents who reason about the world and each other's knowledge. An agent can be a software program, a robot or a human. This type of systems show up in a surprising number of contexts from philosophy to economics to cryptography to distributed computing.

In this course we plan to study a framework for understanding and analyzing multi-agent systems that is mathematically rigorous, useful in practice and widely applicable. We shall focus on two important and related approaches:

• Logics of Knowledge
• Game Theory
  The course material will be accessible to audience from a variety of disciplines, including computer science, artificial intelligence, philosophy, game theory and economics. The contents of this course are not related and hence do not require knowledge of MATH 670, Fall 2001. However, the main emphasis of the course will be on studying logical methods in the areas discussed above.

  Course Syllabus: (tentative)

  • A model for knowledge
  • Knowledge in multi-agent systems
  • Protocols and programs
  • Common knowledge and agreement
  • Introduction to game theory
  • Nash Equilibrium
  • Mixed, correlated and evolutionary equilibrium
  • Knowledge and equilibrium
  • Bargaining games
  • Repeated games
  • Mechanism Design
  • Auctions, including Combinatorial Auctions

  Textbooks:
  Lecture notes based on several books and articles including

  1. Multiagent systems, A modern approach to distributed artificial intelligence, edited by Gerhard Weiss
  2. Reasoning about knowledge, R. Fagin, J.Y. Halperin, Y. Moses and M.Y. Vardi
  3. A course in game theory, M. Osborne, A. Rubinstein
  4. Game Theory, D. Fudenberg and J. Tirole, 7th printing, MIT Press, 2000.
  5. Microeconomic Theory, A. Mas-Colell, M.D. Whinston, and J.R. Green, Oxford University Press, 1995.

  Time and Place
  TTh: 10:30-12:00, Place to be announced.

  

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