1. COMPLEXITY AND 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/complexity.html http://www.coss.ethz.ch/education/complexity.html In particular, you will find links to three zip files: overview, papers, and special. "overview" contains some review papers, allowing you to get an overview of the main subjects of the course. "papers" contains papers, among which you are requested to choose for your 10 minute presentations. These presentations are a precondition to be admitted for the written final exam and to earn your 3 credit points. 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: Distribution of talks and talk schedule

5. We have roughly 40 minutes for each part!

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 DISTRIBUTION OF TALKS AND TALK SCHEDULE

26. DATES FOR TALK TALKS: 28.9., 9.11., 16.11., and 7.12. The papers will give you an in-depth experience how mathematical modeling of techno-socio-economic systems is done. In your presentation, you should give an overview of the main assumptions/equations of the respective models and what one can learn from these models and how. You should give the audience an understanding of the key elements and messages. The grade for your presentation will be counted 50%, the final exam another 50%. EXAM: 14.12.

27. PeoplePaperDate * How simple rules determine pedestrian behavior and crowd disasters Analytical approach to continuous and intermittent bottleneck flows * Analytical investigation of oscillations in intersecting flows of pedestrian and vehicle traffic * Optimal self-organization Pattern formation in driven colloidal mixtures: tilted driving forces … (stripe formation) Mathematical model of a saline oscillator (self-organized oscillations) * Active walker model for the formation of human and animal trail systems Pedestrian, Crowd and Evacuation Dynamics. And Crowd disasters as systemic failures: Analysis of the Love Parade Disaster. Cellular automata simulating experimental properties of traffic flows * Determination of interaction potentials in freeway traffic from steady-state statistics * A section-based queueing-theoretical traffic model for congestion and travel time analysis in networks * Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model * Theoretical vs. empirical classification and prediction of congested traffic states * Derivation of a fundamental diagram for urban traffic flow * Operation regimes and slower-is-faster effect in the control of traffic intersections * Self-control of traffic lights and vehicle flows in urban road networks and Self-stabilizing decentralized signal control of realistic, saturated network traffic * A stochastic behavioral model and a `microscopic' foundation of evolutionary game theory * Analytical investigation of innovation dynamics considering stochasticity in the evaluation of fitness * Phase transitions to cooperation in the prisoner's dilemma Dominic Woerner * Cooperation, norms and revolutions: A unified game-theoretical approach * Drift- or fluctuation-induced ordering and self-organisation in driven many-particle systems The outbreak of cooperation among success-driven individuals under noisy conditions, recommend to also look at Migration as a mechanism to promote cooperation. *How individuals learn to take turns: Emergence of alternating cooperation in a congestion game and the prisoner's dilemma * How Natural Selection Can Create Both Self- and Other-Regarding Preferences, and Networked Minds * A mathematical model for the behavior of individuals in a social field Dominic Woerner * Globally networked risks and how to respond, recommend to also look at Modelling of cascading effects and efficient response to disaster spreading in complex networks Bankruptcy cascades in interbank markets * Transient dynamics increasing network vulnerability to cascading failures * Network-induced oscillatory behavior in material flow networks and irregular business cycles, recommend to also look at Supply and production networks: From the bullwhip effect to business cycles

28. THANKS EVERYBODY!