*June 13, 1928
† May 23, 2015
CONTROVERSIES IN
GAME THEORY III:
GAME THEORY
AND
JOHN F. NASH
HEINRICH H. NAX ([email protected])
COSS, ETH ZURICH
MAY 30, 2016
• 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
http://www.coss.ethz.ch/education/controversies.html
• Also, please contact me (Heinrich) under
[email protected] if you have any questions
about the course!
• 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
STRUCTURE OF THE COURSE
• We have roughly 45-50 minutes talk plus
5-10 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!
“EXAM”
Please prepare a self-explanatory
presentation
in 20-30 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: [email protected]
AND BEFORE WE BEGIN
WITH THE FIRST TALK…
Let us clarify some basic ingredients of
Game Theory…
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
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.
GAME THEORY
NONCOOPERATIVE
GAME THEORY
COOPERATIVE GAME
THEORY
• No contracts can
be written
• Binding contract
can be written
• Players are
individuals and
coalitions of
individuals
• Main solution
concepts:
• Players are
individuals
• Main solution
concepts:
• Nash equ
• Strong equ
•
•
Core
Shapley value
COOPERATIVE GAME
THEORY
of 39
A COOPERATIVE
GAME
THE CORE
SHAPLEY VALUE
of 39
NONCOOPERATIVE
GAME THEORY
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
EQUILIBRIUM
• Equilibrium concept:
An equilibrium solution is a rule that maps the structure of a
game into an equilibrium set of strategies S*.
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:
STRONG
EQUILIBRIUM
APPLICATION
PUBLIC GOODS GAME
K-STRONG
EQUILIBRIUM
THANKS EVERYBODY!