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Algorithmic Game Theory Algorithmic Game Theory Alexander Skopalik Today • Course Mechanics & Overview • Introduction into game theory and some examples Alexander Skopalik • [email protected] • Office hours: – By appointment (or just drop by if door is open) – Room F 1 221 • Phone: 05251 - 60 6457 Talk to me instead of writing emails! Course Mechanics • 3h lecture + 2h tutorial (6 credit points) – Thursdays 11:15 - 13:30, room 2.211 – Fridays 9:15 – 10:45, room 0.530 – Do you agree? Other suggestions? Lunchbreak anyone? • Exercises integrated into the lecture – Starting today! Solve until tomorrow! – More on exercises in two slides • Exercise seminar-style – A small topic for each of you. Maybe also for teams. – Assignment before Christmas break – Week after Christmas break to prepare (no lectures in this week) – You prepare a small presentation/lecture of approximately 30 minutes No lectures • Week after Christmas break: – Thursday, Jan 11th – Friday, Jan 12th – Use time to prepare your presentation • Friday, November 17th Lecture Style • Mostly using the board • Tell me immediately if you can‘t decipher my handwriting (at least once every lecture) • Take notes yourself. • There are lecture notes of a previous lecture online. • However: This year 3+2 hours instead of 2+1 • Ask questions at any time. Textbook & Website • Book: Algorithmic Game Theory, Edited by Nisan, Roughgarden, Tardos, and Vazirani. • Available online: http://www.cambridge.org/journals/nisan/downloa ds/Nisan_Non-printable.pdf • Website (exercises, links to papers and further material): https://www.hni.uni- paderborn.de/en/alg/teaching/ws1718/algorithmic- game-theory/ Exercises and Exams • Weekly exercise sheets – Solutions will be discussed in class (by you). – You do not have to hand in solutions. • However: – You have to solve 40% of the exercises and present at least one solution during the semester. – There will be a list of attendants and you mark which problem you solved. This should be 40% at the end of the semester. – You will be asked (randomly) to present a solution that you have (marked as) solved. Unless someone volunteers (hint!) • Exercise seminar-style – More details in December What Does Game Theory Study? Interactions of rational decision-makers (agents, players) • Decision-makers: humans, robots, computer programs, firms in the market, political parties • Interactions: 2 or more agents act simultaneously or consequently • Rational: each agent has preferences over outcomes and chooses an action that is most likely to lead to the best feasible outcome Why Study Game Theory? • To understand the behavior of others in strategic situations • To know how to alter our own behavior in such situations to gain advantage • To predict the outcome of strategic situations • To be able to design systems such that the desired outcome is ensured Why Study Game Theory? • Only chance to get a Nobel prize (in economics) • Prizes for game theorists include: – Jean Tirole 2014 – Alvin E. Roth 2012 – Lloyd S. Shapley 2012 – Roger B. Myerson 2007 – Leonid Hurwicz 2007 – Eric S. Maskin 2007 – Robert J. Aumann 2005 – Thomas C. Schelling 2005 – William Vickrey 1996 – Robert E. Lucas Jr. 1995 – John C. Harsanyi 1994 – John F. Nash Jr. 1994 – Reinhard Selten 1994 – Kenneth J. Arrow 1972 – Paul A. Samuelson 1970 Some examples Soviet union Waste money on Spend money on Weapons e.g. healthcare, US education Waste money on No benefit Weapons Spend money on Increase in social e.g. healthcare, welfare for both education societies Some examples • Why do buyers have to pay just a little more than the second highest bidder? • Wouldn‘t it be better for the seller if he has to pay his bid? Some examples • Every driver is choosing the fastest route (given the choices of all others) • Might be inefficient for everybody. • Building new roads can be bad! Some examples • Same in public transport (soon?) • TfL (Transport for London) tracked commuters using WiFi • This may allow real-time information on how crowded trains are Why Algorithmic Game Theory • Many “games” are now being played in the internet. – Auctions (e.g. google) • Behavior can now be measured by computers – even in the “offline” world. – Car traffic • One may want to predict or influence the outcome of a game. Therefore we need to be able to compute the outcome. • One may want to design and implement mechanism that deal with strategic behavior. Game Theory vs. Optimization • Think of traffic routing for example. • Optimization – Global view – “optimizer” controls all variables – Global objective function – Result: globally optimal solution • Games – Each agent controls/influences a part of the environment – Agents each have their own objective functions – Individual success in making choices depends on the choices of others – Result: ? What do we study in this lecture? • Basics of game theory. • Part I: Games and Equilibria – Existence and efficiency of equilibria. – Complexity and computation of equilibria – Zero sum games, potential games, congestion games, stable matching, repeated games (?) – Connection to current research • Part II: Social choice and mechanism design – Impossibility theorems – The famous VCG-mechanism Required Background • Basic math • Complexity and algorithms – NP-hardness – Reductions – O-notation • Some vague ideas of – Linear programming – Convex optimization – Flow problems • Warning: This is a theoretical computer science lecture Introduction into game theory and some examples John F. Nash • Non-Cooperative Games, PhD Thesis, Princeton University, 1950. 28 pages. • Theorem: Nash equilibrium (in mixed strategies) always exists in finite strategic games. • 1994 Nobel Memorial Prize in Economic Sciences .
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