Game theory
-Another approach to
decision-making
By
Zhang Yixiao
Liu Jjin
and
Definition
Game theory is the science of strategy ,
studying strategic decision making.
It attempts to determine mathematically and
logically the actions that "players" should take
to secure the best outcomes for themselves in a
wide array of "games.”
田忌赛马 is a typical example.
Roughly classification
• zero-sum games
A participant's gain of utility is exactly balanced by the losses
of the utility of other participants. If the total gains of the
participants are added up, and the total losses are
subtracted, they will sum to zero.
• positive sum games
mutual gain
• negative sum games
mutual harm
A famous story : prisoners’ dilemma
A particular “game”
between two captured
prisoners that illustrates
why cooperation is
difficult to maintain even
when it is mutually
beneficial.
The story of prisoners’ dilemma
Two criminals are captured by the police.
Let’s call them Bonnie and Clyde.
Enough evidence :
The minor crime of carrying
an unregistered gun.
Each would spend a year in jail.
Suspect:
The major crime of a bank robbery.
Benefit evaluation
Bonnie’s decision
Confess
Bonnie gets 8 years
Remain silent
Bonnie gets 20 years
Confess
Clyde gets 8 years
Clyde’s
Decision
Bonnie goes free
Remain
silent
Clyde gets 20 years
Clyde goes free
Bonnie gets 1 year
Clyde gets 1 year
In this game between two criminals suspected of committing a crime, the sentence
that each receives depends both on his or her decision whether to confess or remain
silent and on the decision made by the other
What is the result
In this case, confessing is a Dominant strategy
for both Bonnie and Clyde.
So in the end, both Bonnie and Clyde confess, and
both spend 8 years in jail.
What can we learn from PD
Cooperation can be difficult to maintain even
when it would make both players in the game
better off.
To win a game or to successfully solve these
questions, not only should you focus on your
own standpoint, but also you should realize
what your opponent think.
Where to apply
• Economics
Alvin Roth Transformed Kidney Donation System
Where to apply
• Political science
Game Theory Expert Analyzes Fiscal Cliff.
Where to apply
• Biological evolution
–
Examples on textbook
Where to apply
• Daily life
–
Marriage and the
Art of Game Theory (VIDEO)
– They both involve people who are trying to further their own gains
but are limited by the presence of another person.
–They both offer the possibility of a “cooperative strategy” , and a
“non-cooperative strategy” , where it’s every man for himself.
–In both, the non-cooperative option is often the most tempting, but
could result in death, whereas the cooperative option is annoying,
but rarely fatal.
Where to apply
• Daily life
The system help students be matched with
the right school and related applications
Thank you !