1. *June 13, 1928
† May 23, 2015

2. Controversies in Game Theory III: GAME Theory and John F. NASH
Heinrich H. Nax
COSS, ETH Zurich
May 30, 2016

3. This course is the third one in this series after last years’ courses on
Social Preferences (2014)
Mechanism Design (2015)
Information about the course, and materials/slides of speakers, will be made available at
Also, please contact me (Heinrich) under if you have any questions about the course!

4. 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

5. Structure of the course

6. We have roughly minutes talk plus minutes discussion for each unit and would like you to actively ask and interrupt (unless the speaker says otherwise) with questions or comments at any moment in time!

7. “EXAM”
Please prepare a self-explanatory presentation in slides (which you will not be asked to hold)
Topics: may include one or a combination of issues raised during the week, may prove a good understanding of topics covered during the week, combine several ideas, or propose fresh thoughts,…
Deadline: June 15th!
Send to:

8. AND Before we begin with the first talk…
Let us clarify some basic ingredients of
Game Theory…

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

10. UNDERLYING preference theory
Perhaps we should have defined game theory as
“interactive 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.

11. Game theory No contracts can be written Players are individuals
Noncooperative game theory
Cooperative game theory
No contracts can be written
Players are individuals
Main solution concepts:
Nash equ
Strong equ
Binding contract can be written
Players are individuals and coalitions of individuals
Main solution concepts:
Core
Shapley value

12. cooperative game theory
of 39

13. A cooperative game

14. The core

15. Shapley value
of 39

16. Noncooperative game theory

17. 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

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

19. 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:

20. Strong equilibrium

21. application

22. Public goods game

23. K-strong equilibrium

24. THANKS EVERYBODY!