1. FROM COMPUTATIONAL SOCIAL SCIENCE TO GLOBAL SYSTEMS SCIENCE LECTURE 2: INTRODUCTION TO GAME THEORY HEINRICH H. NAX (HNAX@ETHZ.CH)HNAX@ETHZ.CH COSS, ETH ZURICH SEPTEMBER 28, 2015

2. Information about the course, and materials/slides of speakers, will be made available at http://www.coss.ethz.ch/education/computational.html Also, please contact Professor Helbing’s office under dhuber@ethz.ch if you have questions about the course!dhuber@ethz.ch

3. The course is organized by the GESS Professorship of Computational Social Science (COSS) which aims at bringing modeling and computer simulation of social processes and phenomena together with related empirical, experimental, and data-driven work combining perspectives of different scientific disciplines (e.g. socio-physics, social, computer and complexity science) bridging between fundamental and applied work

4. STRUCTURE OF TODAY’S LECTURE Part 1: Introduction to Game Theory Part 2: Course admin: Aims and requirements of the course and Talk schedule of the course

5. We have roughly 60 minutes for part 1 and 15 for part 2, leaving time for questions.

6. BUT BEFORE WE BEGIN… Let us clarify some basic ingredients of the course: 1.Game Theory 2.Social Preference Theory 3.Mechanism Design 4.Collective Intelligence

7. 1. GAME THEORY A mathematical language to express models “conflict and cooperation between intelligent rational decision-makers” (Myerson) In other words, “interactive decision theory” (Aumann)decision theory Dates back to von Neumann & Morgenstern (1944) Most important solution concept: the Nash (1950) equilibrium

8. 2. SOCIAL PREFERENCE THEORY Perhaps we should have defined game theory as “interactive decision theory”decision theory involving “rational and SELFISH decision-makers” SELFISH = self-regarding in a narrow sense Social preference allows for other concerns such as altruism fairness considerations reciprocity etc.

9. 3. MECHANISM DESIGN Think of it as “reverse game theory” “in a design problem, the goal function is the main given, while the mechanism is the unknown.” (Hurwicz) The mechanism designer is a game designer. He studies What agents would do in various games And what game leads to the outcomes that are most desirable

10. 4. COLLECTIVE INTELLIGENCE Collective intelligence is intelligence that is shared by a group of interacting individuals Models of collective intelligence have been formulated for animal behavior and for human behavior Collective intelligence may be the emergent outcome of interactive collaboration or competition

11. PART 1 “INTRODUCTION” TO GAME THEORY

12. GAME THEORY NONCOOPERATIVE GAME THEORY No contracts can be written Players are individuals Main solution concepts: Nash equ Strong equ COOPERATIVE GAME THEORY Binding contract can be written Players are individuals and coalitions of individuals Main solution concepts: Core Shapley value

13. COOPERATIVE GAME THEORY of 39

14. A COOPERATIVE GAME

15. THE CORE

16. SHAPLEY VALUE of 39

17. NONCOOPERATIVE GAME THEORY

18. A NONCOOPERATIVE GAME (NORMAL-FORM) players: N={1,2,…,n} (finite) actions / strategies: (each player chooses s_i from his own finite strategy set; S_i for each i ∈ N) set of strategy combination: s= (s_1,…,s_n) >outcome of the game payoff: u_i=u_i(s) >payoff outcome of the game

19. EQUILIBRIUM Equilibrium concept: An equilibrium solution is a rule that maps the structure of a game into an equilibrium set of strategies S*.

20. NASH EQUILIBRIUM Definition: Best-response Player i's best-response (or, reply) to the strategies s_-i is the strategy s*_i ∈ S_i such that Definition: (Pure-strategy) Nash equilibrium All strategies are mutual best responses:

21. STRONG EQUILIBRIUM

22. APPLICATION

23. PUBLIC GOODS GAME

24. K-STRONG EQUILIBRIUM

25. PART 2 COURSE ADMIN

26. of 39 1.SCHEDULE 2.REQUIREMENTS

27. 1.SCHEDULE 2.REQUIREMENTS DatePresenter Uni. Topics Sep-21 Dirk Helbing (ETH) Global Systems Science Sep-30 Heinrich Nax (ETH) Game Theory Oct-05 Mortiz Kraemer (Oxford) Population uncertainty dynamics Oct-12 Serguei Saavedra (MIT) Ecological networks & interaction of species Oct-19 Bary Pradelski (ETH) Evolutionary Game Theory; Limited Rationality Oct-26 Peiran Jiao (Oxford) Behavioral Economics Nov-02 Ulf Blanke (ETH) Wearable Computing & Collective Behavior Nov-09 Anke Schorr (ETH) Macroeconomics and Democracy Nov-16 Izabella Moise (ETH) Big Data Analytics Nov-23 Evangelos Pournaras (ETH) Information and Communication Technologies Nov-30 S.P. Dec-07 S.P. Dec-14 S.P.

28. 1.SCHEDULE 2.REQUIREMENTS 1.Regularly attend and participate in Seminar 2.30 Minute Presentation on subject related to Computational Social Science/Global Systems Science Due Oct. 12 th : Select a topic and have it approved Email us your proposed topics, with supporting research paper(s) … or ask and we can suggest topics/papers Nov. 30 th, Dec. 7 th, & Dec. 14 th : Student Presentations Email Dr. Helbing, cc’ing me (caleb.koch@gess.ethz.ch), with questions regarding student presentations!

29. THANKS EVERYBODY!