# 252-1407-00L Algorithmic Game Theory

Semester | Autumn Semester 2020 |

Lecturers | P. Penna |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | Game theory provides a formal model to study the behavior and interaction of self-interested users and programs in large-scale distributed computer systems without central control. The course discusses algorithmic aspects of game theory. |

Objective | Learning the basic concepts of game theory and mechanism design, acquiring the computational paradigm of self-interested agents, and using these concepts in the computational and algorithmic setting. |

Content | The Internet is a typical example of a large-scale distributed computer system without central control, with users that are typically only interested in their own good. For instance, they are interested in getting high bandwidth for themselves, but don't care about others, and the same is true for computational load or download rates. Game theory provides a mathematical model for the behavior and interaction of such selfish users and programs. Classic game theory dates back to the 1930s and typically does not consider algorithmic aspects at all. Only a few years back, algorithms and game theory have been considered together, in an attempt to reconcile selfish behavior of independent agents with the common good. This course discusses algorithmic aspects of game-theoretic models, with a focus on recent algorithmic and mathematical developments. Rather than giving an overview of such developments, the course aims to study selected important topics in depth. Outline: - Introduction to classic game-theoretic concepts. - Existence of stable solutions (equilibria), algorithms for computing equilibria, computational complexity. - Speed of convergence of natural game playing dynamics such as best-response dynamics or regret minimization. - Techniques for bounding the quality-loss due to selfish behavior versus optimal outcomes under central control (a.k.a. the 'Price of Anarchy'). - Design and analysis of mechanisms that induce truthful behavior or near-optimal outcomes at equilibrium. - Selected current research topics, such as Google's Sponsored Search Auction, the U.S. FCC Spectrum Auction, Kidney Exchange. |

Lecture notes | Lecture notes will be usually posted on the website shortly after each lecture. |

Literature | "Algorithmic Game Theory", edited by N. Nisan, T. Roughgarden, E. Tardos, and V. Vazirani, Cambridge University Press, 2008; "Game Theory and Strategy", Philip D. Straffin, The Mathematical Association of America, 5th printing, 2004 Several copies of both books are available in the Computer Science library. |

Prerequisites / Notice | Audience: Although this is a Computer Science course, we encourage the participation from all students who are interested in this topic. Requirements: You should enjoy precise mathematical reasoning. You need to have passed a course on algorithms and complexity. No knowledge of game theory is required. |