Representing games and Nash Bargaining Solution
ECOS3012 - Strategic Behavior
School of Economics, FASS
University of Sydney
Lecture 2, March 9, 2011
ECOS3012 - Strategic Behavior (USYD)
Representing games and Nash Bargaining Solution
Lecture 2, March 9, 2011
1 / 18
In this lecture
1.
How to represent a game?
1.1
Cooperative vs. Non-cooperative games.
1.2
Static (Normal or Strategic form) games vs. Dynamic games
2.
ECOS3012 - Strategic Behavior (USYD)
Representing games and Nash Bargaining Solution
Lecture 2, March 9, 2011
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Two major modeling approaches to games!
1.
Cooperative Game Theory
The “rules of play” are thought to be ﬂuid or that the players are
able to make binding commitments on their behavior.
The focus is then on what diﬀerent coalitions as groups can
achieve and how to distribute the gains from their
cooperation.
2.
Non-cooperative game Theory
The focus is on the individual’s incentives.
The rules of play must be speciﬁed including who does what, in what
order. There are other assumptions on knowledge.
ECOS3012 - Strategic Behavior (USYD)
Representing games and Nash Bargaining Solution
Lecture 2, March 9, 2011
3 / 18
Example of a cooperative game
±
Suppose there are three towns
A
,
B
and
C
. The cost of supplying water
to various towns is known to be
±
$120 for either
A
or
C
alone and $140 for
B
alone.
±
$170 for
A
,
B
together.
±
$190 for
B
,
C
together.
±
$160 for
A
,
C
together.
±
$255 for all three towns together.
±
Based on such information, the question which is set of towns form a
coalition and how are the costs allocated.
±
For instance, if one determines that all three towns are served and cost
allocated equally, the allocation will not be stable.
±
As each town pays $85, the total cost being $170 for
A
and
C
together.
On the other hand,
A
and
C
can provide for themselves by spending $160.
±
Which allocation of costs, for example, will be “stable” against formation
of any sub-coalitions?
ECOS3012 - Strategic Behavior (USYD)
Representing games and Nash Bargaining Solution
Lecture 2, March 9, 2011
4 / 18